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(1)

1.2 - Medidas e incertidumbres

1. When a voltage V of 12.2 V is applied to a DC motor, the current I in the motor is 0.20 A. Which one of the following is the output power VI of the motor given to the correct appropriate number of significant digits?

A. 2 W

B. 2.4 W

C. 2.40 W

D. 2.44 W

(1)

2. Which one of the following lists a fundamental unit and a derived unit?

A. ampere second

B. coulomb kilogram

C. coulomb newton

D. metre kilogram

(1)

3. A student measures the current in a resistor as 677 mA for a potential difference of 3.6 V. A calculator shows the resistance of the resistor to be 5.3175775 Ω. Which one of the following gives the resistance to an appropriate number of significant figures?

A. 5.3 Ω B. 5.32 Ω C. 5.318 Ω D. 5.31765775 Ω

(2)

4. This question is about nuclear reactions.

(a) (i) Distinguish between fission and radioactive decay.

... ... ... ... ...

(4)

A nucleus of uranium-235 ( U235

92 ) may absorb a neutron and then undergo fission to produce nuclei of strontium-90 ( Sr90

38 ) and xenon-142 ( Xe14254 ) and some neutrons.

The strontium-90 and the xenon-142 nuclei both undergo radioactive decay with the emission of β– particles.

(ii) Write down the nuclear equation for this fission reaction.

... ...

(2)

(iii) State the effect, if any, on the mass number (nucleon number) and on the atomic number (proton number) of a nucleus when the nucleus undergoes β– decay. Mass number: ... Atomic number: ...

(3)

The uranium-235 nucleus is stationary at the time that the fission reaction occurs. In this fission reaction, 198 MeV of energy is released. Of this total energy, 102 MeV and 65 MeV are the kinetic energies of the strontium-90 and xenon-142 nuclei respectively.

(b) (i) Calculate the magnitude of the momentum of the strontium-90 nucleus. ... ... ... ...

(4)

(ii) Explain why the magnitude of the momentum of the strontium-90 nucleus is not exactly equal in magnitude to that of the xenon-142 nucleus.

... ... ... ...

(2)

On the diagram below, the circle represents the position of a uranium-235 nucleus before fission. The momentum of the strontium-90 nucleus after fission is represented by the arrow.

strontium-90

(iii) On the diagram above, draw an arrow to represent the momentum of the xenon-142 nucleus after the fission.

(4)

(c) In a fission reactor for the generation of electrical energy, 25% of the total energy released in a fission reaction is converted into electrical energy.

(i) Using the data in (b), calculate the electrical energy, in joules, produced as a result of nuclear fission of one nucleus.

... ... ...

(2)

(ii) The specific heat capacity of water is 4.2 × 103 J Kg–1 K–1. Calculate the energy required to raise the temperature of 250 g of water from 20°C to its boiling point (100°C).

... ... ...

(3)

(iii) Using your answer to (c)(i), determine the mass of uranium-235 that must be fissioned in order to supply the amount of energy calculated in (c)(ii). The mass of a uranium-235 atom is 3.9 × 10–25 kg.

... ... ... ... ...

(5)

5. This question is about measuring the permittivity of free space ε0.

The diagram below shows two parallel conducting plates connected to a variable voltage supply. The plates are of equal areas and are a distance d apart.

V d

variable voltage supply +

The charge Q on one of the plates is measured for different values of the potential difference V applied between the plates. The values obtained are shown in the table below. Uncertainties in the data are not included.

V / V Q / nC

10.0 30

20.0 80

30.0 100

40.0 160

(6)

(a) Plot a graph of V (x-axis) against Q (y-axis).

(4)

(b) Draw the line of best fit for the data points.

(1)

(c) Determine the gradient of your best-fit line.

(2)

(7)

The relationship between Q and V for this arrangement is given by the expression

Q = V

d A 0 ε

where A is the area of one of the plates.

In this particular experiment A = 0.20 m2 and d = 0.50 mm.

(e) Use your answer to (c) to determine a value for ε0.

... ... ... ...

(3) (Total 11 marks)

6. The resistive force F acting on a sphere of radius r moving at speed v through a liquid is given by

F = cvr

where c is a constant. Which of the following is a correct unit for c?

A. N

B. N s–1 C. N m2 s–1 D. N m–2 s

(8)

7. Which one of the following contains three fundamental units?

A. Metre Kilogram Coulomb

B. Second Ampere Newton

C. Kilogram Ampere Kelvin

D. Kelvin Coulomb Second

(1)

8. The variation with time t of the speed v of an object is given by the expression v = u + at

where u and a are constants.

A graph of the variation with time t of speed v is plotted. Which one of the following correctly shows how the constants may be determined from this graph?

A. v

0

– u

0 t

gradient = a

B. v

0

– u

0 t

gradient = 1a

C.

(9)

9. This question is about radioactive decay.

A nucleus of the isotope xenon, Xe-131, is produced when a nucleus of the radioactive isotope iodine I-131 decays.

(a) Explain the term isotopes.

... ... ...

(2)

(b) Fill in the boxes below in order to complete the nuclear reaction equation for this decay. 131

131 I Xe + +

54 –

(2)

(c) The activity A of a freshly prepared sample of the iodine isotope is 3.2 × 105 Bq. The variation of the activity A with time t is shown below.

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0

0 5.0 10 15 20 25 30 35 40 45

t / days A /10 Bq5

Draw a best-fit line for the data points.

(10)

(d) Use the graph to estimate the half-life of I-131.

...

(1) (Total 6 marks)

10. The kWh is equal to A. 1.0 × 103 J. B. 3.6 × 103 J. C. 6.0 × 104 J. D. 3.6 × 106 J.

(11)

11. The Geiger-Nuttall theory of α-particle emission relates the half-life of the α-particle emitter to the energy E of the α-particle. One form of this relationship is

L = 2 1 166 E – 53.5.

L is a number calculated from the half-life of the α-particle emitting nuclide and E is measured in MeV.

Values of E and L for different nuclides are given below. (Uncertainties in the values are not shown.)

Nuclide E / MeV L

2 1 MeV / 1 2 1E U

238 4.20 17.15 0.488

U

236 4.49 14.87 0.472

U

234 4.82 12.89 0.455

Th

228 5.42 7.78

………….. Rn

208 6.14 3.16 0.404

Po

212 7.39 –2.75 0.368

(a) Complete the table above by calculating, using the value of E provided, the value of 2 1 1 E for the nuclide 228Th. Give your answer to three significant digits.

(12)

The graph below shows the variation with 2 1 1

E of the quantity L. Error bars have not been added.

20

16

12

8

4

0

–4

0.2 0.3 0.4 0.5

L

/ MeV 12 1

2 –

1 E

(b) (i) Identify the data point for the nuclide 208Rn. Label this point R.

(1)

(ii) On the graph, mark the point for the nuclide 228Th. Label this point T.

(13)

(c) (i) Determine the gradient of the line you have drawn in (b)(iii).

... ... ...

(2)

(ii) Without taking into consideration any uncertainty in the values for the gradient and for the intercept on the x-axis, suggest why the graph does not agree with the stated relationship for the Geiger-Nuttall theory.

... ... ... ...

(2)

(d) On the graph above, draw the line that would be expected if the relationship for the Geiger-Nuttall theory were correct. No further calculation is required.

(2) (Total 10 marks)

12. This question is about collisions and radioactive decay. (a) (i) Define linear momentum and impulse.

Linear momentum: ... ... Impulse: ... ...

(14)

(ii) State the law of conservation of momentum.

... ... ...

(2)

(iii) Using your definitions in (a)(i), deduce that linear momentum is constant for an object in equilibrium.

... ... ... ...

(2)

A stationary radon-220 (220Rn

86 ) nucleus undergoes α-decay to form a nucleus of polonium (Po). The α-particle has kinetic energy of 6.29 MeV.

(b) (i) Complete the nuclear equation for this decay. Rn

220

86  Po +

(2)

(ii) Calculate the kinetic energy, in joules, of the α-particle.

... ...

(15)

The diagram below shows the α-particle and the polonium nucleus immediately after the decay. The direction of the velocity of the α-particle is indicated.

-particle polonium nucleus

(c) (i) On the diagram above, draw an arrow to show the initial direction of motion of the polonium nucleus immediately after the decay.

(1)

(ii) Determine the speed of the polonium nucleus immediately after the decay. ... ... ... ... (3)

(iii) In the decay of another radon nucleus, the nucleus is moving before the decay. Without any further calculation, suggest the effect, if any, of this initial speed on the paths shown in (c)(i).

... ... ...

(2)

The half-life of the decay of radon-220 is 55 s.

(d) (i) Explain why it is not possible to state a time for the life of a radon-220 nucleus. ... ... ...

(16)

(ii) Define half-life.

... ... ...

(2)

A sample of radon-220 has an initial activity A0.

(iii) On the axes below, draw a graph to show the variation with time t of the activity A for time t = 0 to time t = 180 s.

A A0

0

0 40 80 120 160 200

(17)

(iv) Use your graph to determine the activity, in terms of A0, of the sample of radon at time t = 120 s. Also, estimate the activity, in terms of A0, at time t = 330 s. Activity at time t = 120 s : ………... Activity at time t = 330 s : ………...

(2) (Total 25 marks)

13. Which one of the following measurements is stated correctly to two significant digits? A. 0.006 m

B. 0.06 m

C. 600 m

D. 620 m

(1)

14. A particle is moving in a circular path of radius r. The time taken for one complete revolution is T. The acceleration a of the particle is given by the expression

a =

4

22

.

T

r

Which of the following graphs would produce a straight-line? A. a against T

B. a against T2

C. a against T

1

D. a against 12 T

(18)

15. Sub-multiples of units may be expressed using a prefix. Which one of the following lists the prefixes in decreasing order of magnitude?

A. centi- micro- milli- nano-

B. milli- centi- nano- micro-

C. centi- milli- micro- nano-

D. milli- micro- centi- nano-

(1)

16. The speed of sound v in a gas is related to the pressure P of the gas by the expression kP

v

where k is a constant.

Which variables should be plotted in order to produce a straight-line graph with the slope equal to k?

A. v2 against P2 B. v2 against P C. v against P D. v against

P

(19)

17. The variation with speed v of the force F acting on an object is given by the expression F = pv2 + qv,

where p and q are constants.

What quantity should be plotted on the y-axis of a graph and what should be plotted on the x-axis in order to give a straight-line graph?

y-axis x-axis

A. Fv v

B. Fv v2

C. F v

D. F v2

(20)

18. As part of a road-safety campaign, the braking distances of a car were measured.

A driver in a particular car was instructed to travel along a straight road at a constant speed v. A signal was given to the driver to stop and he applied the brakes to bring the car to rest in as short a distance as possible. The total distance D travelled by the car after the signal was given was measured for corresponding values of v. A sketch-graph of the results is shown below.

0 0 v

D

(a) State why the sketch graph suggests that D and v are not related by an expression of the form

D =mv + c, where m and c are constants.

... ...

(21)

(b) It is suggested that D and v may be related by an expression of the form D = av + bv2,

where a and b are constants.

In order to test this suggestion, the data shown below are used. The uncertainties in the measurements of D and v are not shown.

v / m s–1 D / m / ........

v D

10.0 14.0 1.40

13.5 22.7 1.68

18.0 36.9 2.05

22.5 52.9

27.0 74.0 2.74

31.5 97.7 3.10

(i) In the table above, state the unit of .

v D

(1)

(ii) Calculate the magnitude of ,

v

D to an appropriate number of significant digits, for

v = 22.5 m s–1.

... ...

(22)

(c) Data from the table are used to plot a graph of v

D(y-axis) against v (x-axis). Some of the data points are shown plotted below.

3.50

3.00

2.50

2.00

1.50

1.00

0.50

0.00

35.00 30.00

25.00 20.00

15.00 10.00

5.00 0.00

v / m s–1

D (S. v

I.

un

its

)

(23)

(d) Use your graph in (c) to determine

(i) the total stopping distance D for a speed of 35 m s–1.

... ... ...

(2)

(ii) the intercept on the v D axis.

...

(1)

(iii) the gradient of the best-fit line.

... ... ...

(2)

(e) Using your answers to (d)(ii) and (d)(iii), deduce the equation for D in terms of v. D = ...

(1)

(f) (i) Use your answer to (e) to calculate the distance D for a speed v of 35.0 m s–1. ... ...

(1)

(ii) Briefly discuss your answers to (d)(i) and (f)(i).

... ... ...

(24)

19. This question is about data analysis.

Data for the refractive index n of a type of glass and wavelength λ of the light transmitted through the glass are shown below.

Only the uncertainties in the values of n are significant and these uncertainties are shown by error bars.

300 350 400 450 500 550 600 650

1.6020 1.6060

1.6055

1.6050

1.6045

1.6040

1.6035

1.6030

1.6025 1.6065

1.6015

/nm n

(a) State why the data do not support the hypothesis that there is a linear relationship between refractive index and wavelength.

... ...

(25)

(c) The rate of change of refractive index D with wavelength is referred to as the dispersion.

At any particular value of wavelength, D is defined by

D =

 n

Use the graph to determine the value of D at a wavelength of 380 nm.

... ... ... ... ... ...

(26)

(d) Based on the plotted data, it is suggested that the relationship between n and λ is of the form

n = A + 2

B

where A and B are constants.

To test this suggestion, values of n are plotted against values of 12

 . The resulting graph

with the line of best fit is shown below.

1.6020 1.6060

1.6055

1.6050

1.6045

1.6040

1.6035

1.6030

1.6025 1.6065

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2

1.6015 1.6010

1 / 10 m

n

-15 -2

(27)

(i) Use the graph to determine the value of the constant A.

... ... ...

(3)

(ii) State the significance of the constant A.

... ...

(1) (Total 11 marks)

20. Which of the following graphs shows the best-fit line for the plotted points? A. y

0

B. y

0

0 x 0 x

C. y

0

D. y

0

0 x 0 x

(28)

21. The density of a metal cube is given by the expression V M

ρ where M is the mass and V is the volume of the cube. The percentage uncertainties in M and V are as shown below.

M 12

V 4.0

The percentage uncertainty in the calculated value of the density is A. 3.0.

B. 8.0. C. 16. D. 48.

(29)

22. This question is about the electrical power available from a wind turbine.

The maximum electrical power generated by a wind turbine, Pout , was measured over a range of incident wind speeds, vin.

The graph below shows the variation with vin of Pout. Uncertainties for the data are not shown.

(a) It is suggested that Pout is proportional to vin. (i) Draw the line of best-fit for the data points.

(1)

(ii) State one reason why the line you have drawn does not support this hypothesis. ... ... ...

(1)

(iii) The uncertainty in the power at 15 m s–1 is 5. Draw an error bar on the graph to represent this uncertainty.

(30)

(b) The theoretical relationship between the available power in the wind, Pin, and incident wind speed is shown in the graph below.

4000 3500 3000 2500 2000 1500 1000 500 0 25 20 15 10 5 0

Vm / ms–1 Pm / kW

Using both graphs,

(31)

(ii) suggest, without calculation, how the efficiency of the turbine changes with increasing wind speed.

... ... ... ... ...

(3)

(c) Outline one advantage and one disadvantage of using wind turbines to generate electrical energy.

Advantage: ... ... ... ... Disadvantage: ... ... ... ...

(32)

1.3 - Vectores y escalares

1. The diagram below shows a boat that is about to cross a river in a direction perpendicular to the

bank at a speed of 0.8 m s–1. The current flows at 0.6 m s–1 in the direction shown.

0.8 ms

Boat

Bank

Bank –1

–1 0.6 ms

The magnitude of the displacement of the boat 5 seconds after leaving the bank is

A. 3 m.

B. 4 m.

C. 5 m.

D. 7 m.

(1)

2. Which one of the following is a vector quantity?

A. Electric power

B. Electrical resistance

C. Electric field strength

(33)

D. Weight

(1)

4. Two objects X and Y are moving away from the point P. The diagram below shows the velocity

vectors of the two objects.

P Velocity vector for object Y

Velocity vector for object X

Which of the following velocity vectors best represents the velocity of object X relative to object Y?

A. B.

C. D.

(34)

5. This question is about power output of an outboard motor.

A small boat is powered by an outboard motor of variable power P. The graph below shows the variation with speed v of P when the boat is carrying different loads.

5.0 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 350 kg 300 kg 250 kg 200 kg

P / kW

v / ms–1

The masses shown are the total mass of the boat plus passengers,

(a) For the boat having a steady speed of 2.0 m s–1 and with a total mass of 350 kg

(i) use the graph to determine the power of the engine.

...

(35)

Consider the case of the boat moving with a speed of 2.5 m s–1.

(b) (i) Use the axes below to construct a graph to show the variation of power P with the total mass W.

200 250 300 350 400 450

W / kg

(6)

(ii) Use data from the graph that you have drawn to determine the output power of the motor for a total mass of 330 kg.

...

(36)

6. Three equal point charges X, Y and Z are fixed in the positions shown.

Z q3

1.0 m

X

1.0 m 90 Y

q1 q2

The distance between q1 and q2 and the distance between q2 and q3 is 1.0 m. The electric force

between the charges at X and Y is F. The electric force between the charges at X and Z is

A. .

2

F

B.

.

2

F

C. F.

D. 2F.

(37)

7. Which one of the following includes three vector quantities?

A. velocity weight field strength

B. weight mass field strength

C. velocity energy weight

D. mass energy field strength

(38)

8. This question is about vectors.

A student sets up the apparatus shown below to investigate forces.

spring balance B

spring balance B

10 N weight

The weight of 10.0 N is suspended from spring balance A by means of a light string. Spring balance B is also attached to the string. The spring balance B is pulled horizontally as shown.

(39)

(b) Suggest why it is not possible for the whole length of the string joining spring balances A

and B to be horizontal with the weight still suspended.

...

...

(1) (Total 5 marks)

9. A uniform metal bar XY of weight W is hung from a horizontal support at point P by two wires

of negligible mass.

P

T T

X Y

W

Each wire makes an angle  with the vertical.

Which of the following is equal to the tension T in one of the wires?

(40)

10. Which of the following contains three scalar quantities?

A. mass charge speed

B. density weight mass

C. speed weight charge

D. charge weight density

(41)

2.1 – Cinemática

1. A ball, initially at rest, takes time t to fall through a vertical distance h. If air resistance is ignored, the time taken for the ball to fall from rest through a vertical distance 9h is

A. 3t.

B. 5t.

C. 9t.

D. 10t.

(1)

2. A raindrop falling through air reaches a terminal velocity before hitting the ground. At terminal velocity, the frictional force on the raindrop is

A. zero.

B. less than the weight of the raindrop.

C. greater than the weight of the raindrop.

D. equal to the weight of the raindrop.

(1)

3. This question is about waves and wave properties.

(a) By making reference to waves, distinguish between a ray and a wavefront.

...

...

...

...

(42)

The diagram below shows three wavefronts incident on a boundary between medium I and medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is incomplete.

medium I

medium R A

B

C

D

E

F

(b) (i) On the diagram above, draw a line to complete the wavefront EF.

(1)

(ii) Explain in which medium, I or R, the wave has the higher speed.

...

...

...

...

(3)

(43)

The graph below shows the variation with time t of the velocity v of one particle of the medium through which the wave is travelling.

8 6 4 2 0 –2 –4 –6 –8

0 1 2 3 4 5 6

t / ms

v / ms–1

7

(c) (i) Explain how it can be deduced from the graph that the particle is oscillating.

...

...

...

(2)

(ii) Determine the frequency of oscillation of the particle.

...

...

(2)

(iii) Mark on the graph with the letter M one time at which the particle is at maximum displacement.

(1)

(iv) Estimate the area between the curve and the x-axis from the time t = 0 to the time t = 1.5 ms.

...

...

(44)

(v) Suggest what the area in c (iv) represents.

...

(1) (Total 17 marks)

4. This question is about forces on charged particles in electric and magnetic fields.

The diagram shows two parallel plates situated in a vacuum. One plate is at a positive potential with respect to the other.

+

– Path of positively charged particle

A positively charged particle passes into the region between the plates. Initially, the particle is travelling parallel to the plates.

(a) On the diagram,

(i) draw lines to represent the electric field between the plates.

(3)

(45)

(b) An electron is accelerated from rest in a vacuum through a potential difference of 750 V.

(i) Determine the change in electric potential energy of the electron.

...

...

...

(2)

(ii) Deduce that the final speed of the electron is 1.6 × 107 m s–1.

...

...

...

(2)

The diagram below shows a cross-section through a current-carrying solenoid. The current is moving into the plane of the paper at the upper edge of the solenoid and out of the plane of the paper at the lower edge. There is a vacuum in the solenoid.

× × × × × × × × × × × × × × × × × × × × × × × × × × ×Current into plane of paper

Current out plane of paper

(c) (i) Sketch lines to represent the magnetic field inside and at each end of the solenoid.

(4)

(ii) A positively charged particle enters the solenoid along its axis. On the diagram, show the path of the particle in the solenoid.

(46)

An electron is injected into a region of uniform magnetic field of flux density 4.0 mT. The velocity of the electron is 1.6 × 107 m s–1 at an angle of 35° to the magnetic field, as shown below.

1.6 × 10 m s

35°

–1 7

Direction of magnetic field

(d) (i) Determine the component of the velocity of the electron normal to the direction of the magnetic field.

...

...

(2)

(ii) Describe, making calculations where appropriate, the motion of the electron due to this component of the velocity.

...

...

...

... ...

(4)

(47)

(iv) State and explain the magnitude of the force on the electron due to this component of the velocity.

...

...

...

(2)

(e) With reference to your answers in (d), describe the shape of the path of the electron in the magnetic field. You may draw a diagram if you wish.

...

...

(2) (Total 25 marks)

5. An athlete runs round a circular track at constant speed. Which one of the following graphs best represents the variation with time t of the magnitude d of the displacement of the athlete from the starting position during one lap of the track?

(48)

6. A stone is thrown horizontally from the top of a high cliff. Assuming air resistance is negligible, what is the effect of gravitational force on the horizontal and on the vertical components of the velocity of the stone?

Vertical component of velocity Horizontal component of velocity A. increases to a constant value stays constant

B. increases continuously stays constant

C. increases to a constant value decreases to zero

D. increases continuously decreases to zero

(1)

7. This question is about the kinematics of an elevator (lift).

(a) Explain the difference between the gravitational mass and the inertial mass of an object.

...

...

...

...

...

(49)

An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its motion is controlled by an electric motor. A simplified graph of the variation of the elevator’s velocity with time is shown below.

0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0

time / s velocity / m s–1

(b) The mass of the elevator is 250 kg. Use this information to calculate

(i) the acceleration of the elevator during the first 0.50 s.

...

... ...

(2)

(ii) the total distance travelled by the elevator.

...

...

...

(2)

(iii) the minimum work required to raise the elevator to the higher floor.

...

...

...

(50)

(iv) the minimum average power required to raise the elevator to the higher floor.

...

...

...

(2)

(v) the efficiency of the electric motor that lifts the elevator, given that the input power to the motor is 5.0 kW.

...

...

...

(2)

(c) On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain your reasoning. (The simplified version is shown as a dotted line)

0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0

time / s velocity / m s–1

(51)

The elevator is supported by a cable. The diagram below is a free-body force diagram for when the elevator is moving upwards during the first 0.50 s.

tension

weight

(d) In the space below, draw free-body force diagrams for the elevator during the following time intervals.

(i) 0.5 to 11.50 s (ii) 11.50 to 12.00 s

(3)

(52)

(e) On the axes below, sketch a graph to show how the reading on the scales varies during the whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph – you do not need to add any values.)

0.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0

time / s reading on scales

W

(3)

(f) The elevator now returns to the ground floor where it comes to rest. Describe and explain the energy changes that take place during the whole up and down journey.

...

...

...

...

...

...

(53)

8. A ball is dropped from rest at time t = 0 on to a horizontal surface from which it rebounds. The graph shows the variation of time t with speedv of the ball.

0 0 B D

A C

v

t

Which one of the following best represents the point at which the ball just loses contact with the surface after the first bounce?

A. A

B. B

C. C

D. D

(1)

9. Juan is standing on the platform at a railway station. A train passes through the station with speed 20 m s–1 in the direction shown measured relative to the platform. Carmen is walking along one of the carriages of the train with a speed of 2.0 m s–1 measured relative to the carriage in the direction shown. Velocity is measured as positive in the direction shown on the diagram.

Juan Carmen

platform 2.0 ms

20 ms

velocity measured as a positive in this direction

(54)

The velocity of Carmen relative to Juan is

A. –22 m s–1.

B. –18 m s–1.

C. +18 m s–1.

D. +22 m s–1.

(1)

10. The graph below shows the variation with time of the distance moved by a car along a straight road. During which time interval does the car have its greatest acceleration?

A B C D

distance moved

time

(55)

11. This question is about throwing a stone from a cliff.

Antonia stands at the edge of a vertical cliff and throws a stone vertically upwards.

Sea

v = 8.0ms–1

The stone leaves Antonia’s hand with a speed v = 8.0ms–1.

The acceleration of free fall g is 10 m s–2 and all distance measurements are taken from the point where the stone leaves Antonia’s hand.

(a) Ignoring air resistance calculate

(i) the maximum height reached by the stone.

...

...

...

(2)

(ii) the time taken by the stone to reach its maximum height.

...

...

(56)

The time between the stone leaving Antonia’s hand and hitting the sea is 3.0 s.

(b) Determine the height of the cliff.

...

...

...

...

(3) (Total 6 marks)

12. The variation with time t of the speed v of a car moving along a straight road is shown below.

v

t

00

S1 S2 S3

Which area, S1, S2 or S3, or combination of areas, represents the total distance moved by the car during the time that its speed is reducing?

A. S1

B. S3

(57)

13. Four cars W, X,Yand Z are on a straight road. The graph below shows the variation with time t of the distance s of each car from a fixed point.

s

t

X

Y

Z W

0 0

Which car has the greatest speed?

A. W

B. X

C. Y

D. Z

(58)

14. A boat is moving in the direction shown with a speed of 5 m s−1 as measured by Nico who is at rest on the beach. Aziz walks along the deck of the boat in the direction shown with a speed of 2 m s−1 measured relative to the boat.

positive direction Aziz

5 m s–1

Nico

If velocity is measured as positive in the direction shown, the velocity of Nico relative to Aziz is

A. − 7 m s−1.

B. − 3 m s−1.

C. + 3 m s−1.

D. + 7 m s−1.

(59)

15. Two points P and Q are at distances r and 2r respectively from the centre of a compact disc (CD) as shown.

P

r

2r

Q

When the disc is rotating about its centre, the ratio of the

is

Q

at

on

accelerati

P

at

on

accelerati

A. . 2 1

B. 1.

C.

2

.

D. 2.

(60)

16. A ball is thrown vertically upwards from the ground. The graph shows the variation with time t of the vertical displacement d of the ball.

d

D

0

0 T t

Which one of the following gives the final displacement after time T and the average speed between time t = 0 and time t = T?

Displacement Average speed

A. 0 0

B. 0

T D

2

C. 2D

T D

2

D. 2D 0

(61)

17. The graph below shows the variation with time t of the displacement d of a body moving along a straight-line.

d

0

0 t

Which graph best represents the variation with time t of the velocity v of this body?

A. v

0

B. v

0

0 t 0 t

C. v

0

D. v

0

0 t 0 t

(62)

18. A toy cannon is mounted vertically on a cart. The cart is moving along a straight-line with constant speed. A spring inside the cannon shoots a ball vertically upwards.

cannon

cart

No resistance forces act on the cart and on the ball. Which one of the following statements is true about the position where the ball will land?

A. The position depends on the speed of the cart.

B. The ball will land behind the cannon.

C. The ball will land inside the cannon.

D. The ball will land in front of the cannon.

(63)

19. The graph below shows the variation with time t of the displacement s of an object moving along a straight-line.

s / m

20.0

0.0

0.0 2.0 4.0 t / s

The best estimate of the instantaneous speed of the object at t = 2.0 s is

A. 0.0 ms–1.

B. 0.2 ms–1.

C. 5.0 ms–1.

D. 10.0 ms–1.

(1)

20. An object is falling, in air, towards the Earth’s surface.

What changes occur in the acceleration and in the velocity of the object as it approaches terminal velocity?

acceleration velocity

A. decreases to zero increases continuously B. decreases to zero increases to a constant value C. constant increases to a constant value D. constant increases continuously

(64)

21. A car has a speed of + 15 m s–1 relative to the ground. It passes a cyclist travelling in the same straight-line. The speed of the car relative to the cyclist is + 12 m s–1.

The speed of the cyclist relative to the ground is

A. –3.0 m s–1.

B. –1.5 m s–1.

C. +1.5 m s–1.

D. +3.0 m s–1.

(65)

22. A ball is thrown vertically upwards from the ground. The graph shows the variation with time t of the vertical displacement d of the ball.

Which of the following gives the final displacement after time T and the average speed between time t = 0 m aand time t = T?

Displacement Average speed

A. 0 0

B. 0

T D

2

C. 2D

T D

2

D. 2D 0

(66)

2.2 - Fuerzas y dinámica

1. When a body is accelerating, the resultant force acting on it is equal to its

A. change of momentum.

B. rate of change of momentum.

C. acceleration per unit of mass.

D. rate of change of kinetic energy.

(1)

2. A sphere of mass m strikes a vertical wall and bounces off it, as shown below.

momentum p

momentum p B

A

wall

The magnitude of the momentum of the sphere just before impact is pBand just after impact is

pA.The sphere is in contact with the wall for time t. The magnitude of the average force exerted

by the wall on the sphere is

A.

(67)

3. The weight of a mass is measured on Earth using a spring balance and a lever balance, as shown below.

spring balance lever balance

What change, if any, would occur in the measurements if they were repeated on the Moon’s surface?

Spring balance Lever balance

A. same same

B. same decrease

C. decrease same

D. decrease decrease

(1)

4. This question is about the kinematics of an elevator (lift).

(a) Explain the difference between the gravitational mass and the inertial mass of an object.

...

...

...

...

...

(68)

An elevator (lift) starts from rest on the ground floor and comes to rest at a higher floor. Its motion is controlled by an electric motor. A simplified graph of the variation of the elevator’s velocity with time is shown below.

0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 time / s velocity / m s–1

(b) The mass of the elevator is 250 kg. Use this information to calculate

(i) the acceleration of the elevator during the first 0.50 s.

...

... ...

(2)

(ii) the total distance travelled by the elevator.

...

...

(69)

(iv) the minimum average power required to raise the elevator to the higher floor.

...

...

...

(2)

(v) the efficiency of the electric motor that lifts the elevator, given that the input power to the motor is 5.0 kW.

...

...

...

(2)

(c) On the graph axes below, sketch a realistic variation of velocity for the elevator. Explain your reasoning. (The simplified version is shown as a dotted line)

0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 time / s velocity / m s–1

(70)

The elevator is supported by a cable. The diagram below is a free-body force diagram for when the elevator is moving upwards during the first 0.50 s.

tension

weight

(d) In the space below, draw free-body force diagrams for the elevator during the following time intervals.

(i) 0.5 to 11.50 s (ii) 11.50 to 12.00 s

(3)

(71)

(e) On the axes below, sketch a graph to show how the reading on the scales varies during the whole 12.00 s upward journey of the elevator. (Note that this is a sketch graph – you do not need to add any values.)

0.00

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 time / s reading on scales

W

(3)

(f) The elevator now returns to the ground floor where it comes to rest. Describe and explain the energy changes that take place during the whole up and down journey.

...

...

...

...

...

...

(72)

5. A ball of mass m, travelling in a direction at right angles to a vertical wall, strikes the wall with a speed v1. It rebounds at right angles to the wall with a speed v2. The ball is in contact with the

wall for a time Δt. The magnitude of the force that the ball exerts on the wall is

A.

t v v m   2 1 .

B. m(v1 + v2)Δt.

C.

t v v m   2 1 .

D. m(v1 – v2)Δt.

(1)

6. A truck collides head on with a less massive car moving in the opposite direction to the truck. During the collision, the average force exerted by the truck on the car is FT and the average

force exerted by the car on the truck is FC. Which one of the following statements is correct?

A. FT will always be greater in magnitude than FC.

B. FT will always be equal in magnitude to FC.

C. FT will be greater in magnitude than FC only when the speed of the car is less than the

speed of the truck.

D. FT will be equal in magnitude to FC only when the speed of the truck is equal to the speed

of the car.

(1)

(73)

(ii) Light is emitted from a candle flame. Explain why, in this situation, it is correct to refer to the “speed of the emitted light”, rather than its velocity.

...

...

...

(2)

(b) (i) Define, by reference to wave motion, what is meant by displacement.

...

...

(2)

(ii) By reference to displacement, describe the difference between a longitudinal wave and a transverse wave.

... ... ... ... (3)

The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves (S waves). The graph below shows the variation with time t of the distance d moved by the two types of wave.

d / km

t / s

P wave S wave

1200

800

400

0

0 25 50 75 100 125 150 175 200 225

(74)

(c) Use the graph to determine the speed of

(i) the P waves.

...

...

...

(1)

(ii) the S waves.

...

...

...

(75)

The waves from an earthquake close to the Earth’s surface are detected at three laboratories L1,

L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the

others by a distance of 900 km, as shown in the diagram below.

L L

L

1 2

(76)

The records of the variation with time of the vibrations produced by the earthquake as detected at the three laboratories are shown below. All three records were started at the same time.

time start of trace

L

L

L 1

2

(77)
(78)

(d) (i) On the trace produced by laboratory L2, identify, by reference to your answers in

(c), the pulse due to the P wave (label the pulse P).

(79)

(ii) Using evidence from the records of the earthquake, state which laboratory was closest to the site of the earthquake.

...

(80)

(iii) State three separate pieces of evidence for your statement in (d)(ii).

(3) 1. ...

...

2. ...

...

3. ...

(81)

(iv) The S-P intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3 respectively.

Use the graph, or otherwise, to determine the distance of the earthquake from each laboratory. Explain your working.

...

...

... Distance from L1 = ...km

... Distance from L2 = ...km

... Distance from L3 = ...km

...

(82)

(v) Mark on the diagram a possible site of the earthquake.

(83)

There is a tall building near to the site of the earthquake, as illustrated below.

building

ground

direction of vibrations

(84)

(e) (i) On the diagram above, draw the fundamental mode of vibration of the building caused by these vibrations.

(85)

The building is of height 280 m and the mean speed of waves in the structure of the building is 3.4 × 103 ms–1.

(ii) Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to be very destructive.

...

...

...

...

(86)

8. For an object to be in translational equilibrium

A. it must be at rest.

B. it must be moving with a constant acceleration.

C. no external force must be acting on it.

D. the net force acting on it must be zero.

(87)

9. This question is about equilibrium.

Explain whether each of the following is in equilibrium.

(a) A satellite in orbit at constant speed round the Earth.

...

...

...

(88)

(b) A small weight suspended on a string and blown to one side by a wind so that the string makes a constant angle with the vertical, as shown below.

Wind

...

...

(89)

10. This question is about estimating energy changes for an escalator (moving staircase).

The diagram below represents an escalator. People step on to it at point A and step off at point B.

30m

40° A

(90)

(a) The escalator is 30 m long and makes an angle of 40° with the horizontal. At full capacity, 48 people step on at point A and step off at point B every minute.

(i) Calculate the potential energy gained by a person of weight 7.0 × 102 N in moving from A to B.

...

...

...

(91)

(ii) Estimate the energy supplied by the escalator motor to the people every minute when the escalator is working at full capacity.

...

...

(92)

(iii) State one assumption that you have made to obtain your answer to (ii).

...

...

(93)

The escalator is driven by an electric motor that has an efficiency of 70%.

(b) Using your answer to (a) (ii), calculate the minimum input power required by the motor to drive the escalator.

...

...

...

...

(94)

11. Which one of the following objects is in equilibrium?

A. A stone trapped in the tread of a rotating tyre

B An air molecule as a sound wave passes through the air

C. A steel ball falling at constant speed through oil

D. An electron moving through a metal under the action of a potential difference

(95)

12. A mass is suspended from the roof of a lift (elevator) by means of a spring balance, as illustrated below.

lift (elevator)

(96)

The lift (elevator) is moving upwards and the readings of the spring balance are noted as follows.

Accelerating: Ra

Constant speed: Rc

(97)

Which one of the following is a correct relationship between the readings?

A. Ra > Rc

B. Ra = Rs

C. Rc = Rs

D. Rc < Rs

(98)

13. A small boat in still water is given an initial horizontal push to get it moving. The boat gradually slows down. Which of the following statements is true for the forces acting on the boat as it slows down?

A. There is a forward force that diminishes with time.

B. There is a backward force that diminishes with time.

C. There is a forward force and a backward force both of which diminish with time.

D. There is a forward force and a backward force that are always equal and opposite.

(99)

14. This question is about circular motion.

A linear spring of negligible mass requires a force of 18.0 N to cause its length to increase by 1.0 cm.

A sphere of mass 75.0 g is attached to one end of the spring. The distance between the centre of the sphere M and the other endPof the unstretched spring is 25.0 cm, as shown below.

25.0 cm

M P

The sphere is rotated at constant speed in a horizontal circle with centre P. The distance PM increases to 26.5 cm.

(a) Explain why the spring increases in length when the sphere is moving in a circle.

...

...

...

(100)

(b) Determine the speed of the sphere.

...

...

...

...

...

(101)

15. This question is about collisions and radioactive decay.

(a) (i) Define linear momentum and impulse.

Linear momentum: ...

...

Impulse: ...

...

(102)

(ii) State the law of conservation of momentum.

...

...

...

(103)

(iii) Using your definitions in (a)(i), deduce that linear momentum is constant for an object in equilibrium.

...

...

...

...

(104)

A stationary radon-220 (220Rn

86 ) nucleus undergoes α-decay to form a nucleus of polonium (Po).

The α-particle has kinetic energy of 6.29 MeV.

(b) (i) Complete the nuclear equation for this decay.

Rn

220

86  Po +

(105)

(ii) Calculate the kinetic energy, in joules, of the α-particle.

...

...

(106)

(iii) Deduce that the speed of the α-particle is 1.74 × 107 m s–1.

...

...

...

(107)

The diagram below shows the α-particle and the polonium nucleus immediately after the decay. The direction of the velocity of the α-particle is indicated.

(108)

(c) (i) On the diagram above, draw an arrow to show the initial direction of motion of the polonium nucleus immediately after the decay.

(109)

(ii) Determine the speed of the polonium nucleus immediately after the decay.

...

...

...

...

(110)

(iii) In the decay of another radon nucleus, the nucleus is moving before the decay. Without any further calculation, suggest the effect, if any, of this initial speed on the paths shown in (c)(i).

...

...

...

(111)

The half-life of the decay of radon-220 is 55 s.

(d) (i) Explain why it is not possible to state a time for the life of a radon-220 nucleus.

...

...

...

(112)

(ii) Define half-life.

...

...

...

(113)

A sample of radon-220 has an initial activity A0.

(iii) On the axes below, draw a graph to show the variation with time t of the activity A

for time t = 0 to time t = 180 s.

A

A0

0

0 40 80 120 160 200

t s /

(114)

(iv) Use your graph to determine the activity, in terms of A0, of the sample of radon at

time t = 120 s. Also, estimate the activity, in terms of A0, at time t = 330 s.

Activity at time t = 120 s : ………...

Activity at time t = 330 s : ………...

(115)

16. The velocity of a body of mass m changes by an amount v in a time t. The impulse given to the body is equal to

A. mt.

B. . t v

 

C. . t v m

 

D. mv.

(116)

17. A ball is held at rest at point X and is then released. It drops on to a flat horizontal surface and rebounds to a maximum height at point Y.

point X

point Y

before after

Which one of the following graphs best shows the variation with time t of the momentum p of the ball as it moves between point X and point Y?

A. B.

C. D.

p

t 0

0

p

t 0

0

(117)

18. A ball of weight W is dropped on to the pan of a top pan weighing balance and rebounds off the pan.

pan

00.00

At the instant that the ball has zero velocity when in contact with the pan, the scale will read

A. zero.

B. a value less than W but greater than zero.

C. W.

D. a value greater than W.

(118)

19. A small ball P moves with speed v towards another identical ball Q along a line joining the centres of the two balls. Ball Q is at rest. Kinetic energy is conserved in the collision.

P Q at rest

v

Which one of the following situations is a possible outcome of the collision between the balls?

P Q

P Q

P Q

P Q

A. B.

C. D.

v v

v 3v

4 4

v = 0 v

v v

2 2

(1)

20. Kinematics

(a) State the principle of conservation of energy.

...

...

(119)

(c) The mass of the aircraft is 8.0  103 kg.

(i) The average resultant force on the aircraft while travelling along the runway is 70 kN. The speed of the aircraft just as it lifts off is 75 m s–1. Estimate the distance travelled along the runway.

...

...

...

...

(3)

(ii) The aircraft climbs to a height of 1250 m. Calculate the potential energy gained during the climb.

...

...

...

...

(120)

When approaching its destination, the pilot puts the aircraft into a holding pattern. This means the aircraft flies at a constant speed of 90 m s–1 in a horizontal circle of radius 500 m as shown in the diagram below.

500 m

(d) For the aircraft in the holding pattern,

(i) calculate the magnitude of the resultant force on the aircraft;

...

...

(2) (ii) state the direction of the resultant force.

... ...

(1) (Total 11 marks)

21. Linear momentum

(a) Define

(i) linear momentum;

...

...

(121)

(b) Explain whether momentum and impulse are scalar or vector quantities.

...

...

(1)

(c) By reference to Newton’s laws of motion, deduce that when two particles collide, momentum is conserved.

...

...

...

...

...

...

(5)

A rubber ball of mass 50 g is thrown towards a vertical wall. It strikes the wall at a horizontal speed of 20 m s–1 and bounces back with a horizontal speed of 18 m s–1 as shown below.

speed before  20 m s–1

speed after 18 m s–1

The ball is in contact with the wall for 0.080 s.

(d) (i) Calculate the change in momentum of the ball.

...

...

...

...

(122)

(ii) Calculate the average force exerted by the ball on the wall.

...

...

...

...

(2)

(iii) Suggest, in terms of Newton’s laws of motion, why a steel ball of the same mass and the same initial horizontal speed exerts a greater force on the wall.

...

...

...

...

(3) (Total 15 marks)

22. The velocity of a particle is changing. The rate of change of the momentum of the particle is equal to the

A. acceleration of the particle.

B. net force acting on the particle.

C. work done on the particle.

D. change in kinetic energy of the particle.

(123)

23. Two spheres of masses m1 and m2 are moving towards each other along the same straight-line with speeds v1 and v2 as shown.

positive direction

m1 v1 v2 m2

The spheres collide. Which of the following gives the total change in linear momentum of the spheres as a result of the collision?

A. 0

B. m1v1 + m2v2

C. m1v1 − m2v2

D. m2v2 − m1v1

(1)

24. Electric motor

(a) In an experiment to measure the efficiency of a small dc electric motor, the motor is clamped to the edge of a bench. The motor is used to raise a small weight that is attached to a pulley wheel by cotton thread. The pulley wheel is rotated by the motor. The thread wraps around the pulley wheel, so raising the weight.

Side view

motor

axel

pulley wheel

cotton thread

weight

End-on-view

(124)

(i) Draw a labelled free-body force diagram of the forces acting on the accelerating weight.

...

...

...

(3)

(ii) The weight has a mass of 15 g and it takes 2.2 s to raise it from rest through a height of 0.84 m. Calculate the tension in the thread as the weight is being raised. (Acceleration of free fall g = 10 m s−2.)

...

...

...

...

...

...

(4)

(b) In a second experiment, the current is adjusted so that the weight of mass 15 g is raised at constant speed. The motor is connected to a 6.0 V supply and it now takes the motor 3.4 s to raise the weight through 0.84 m.

(i) Suggest how it might be determined that the weight is being raised at constant speed.

...

(125)

(ii) Determine the power delivered to the weight by the motor. (Acceleration of free fall g = 10 m s−2.)

...

...

...

...

(2)

(iii) The current in the motor is 45 mA. Estimate the efficiency of the motor.

...

...

...

...

(2) (Total 13 marks)

25. Which one of the following is the condition necessary for an object to be in translational equilibrium?

A. The lines of action of all the forces acting on the object must pass through a single point.

B. Every force must be balanced by another force that is equal in magnitude but opposite in direction.

C. The resultant of all the forces acting on the object in any direction must be zero.

D. The total upward force on the object must be equal to the total downward force.

(126)

26. A stationary metal plate is hanging freely on a string. A steel ball, travelling horizontally, hits the plate. The speed of the ball after the collision is less than before, but still in a horizontal direction, as shown below.

before collision

after collision

string

metal plate

Which one of the following gives a correct statement, with a valid reason, about the type of collision between the ball and the plate?

Type of collision Reason

A. inelastic The sphere has changed its momentum during the collision.

B. inelastic The sphere has lost kinetic energy during the collision.

C. unknown The change in momentum of the plate during the collision is unknown.

D. unknown The kinetic energy of the plate after the collision is unknown.

(1)

27. This question is about nuclear energy.

(a) Define nuclear binding energy.

(127)

(b) A neutron collides with a nucleus of uranium-235 and the following reaction takes place. n 2 Cs Rb n U 1 0 138 55 96 37 1 0 235

92    

State the name of this type of reaction.

...

(1)

(c) The mass of nuclei can be expressed in terms of unified mass units (u).

(i) Define the term unified mass unit.

...

...

(1) (ii) Using the data below, calculate the energy, in MeV, that is released in the reaction.

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We have also shown that the stability of the di fferent moiré patterns is the result of a subtle energy balance between the energy required to corrugate the gra- phene, that

The tentative spin and parity assignment to the observed levels in 44 S is based on the comparison between the calcu- lated and experimental (i) excitation energies, (ii)

Even though the 1920s offered new employment opportunities in industries previously closed to women, often the women who took these jobs found themselves exploited.. No matter