Análisis de la Demanda

In the second column of the table below, write each of Newton’s three laws of motion. Use your own wording. In the third column of the table, describe an example of each law. To find examples of Newton’s laws, think about all the activities you do in one day.

1. When Jane drives to work, she always places her purse on the passenger’s seat. By the time she gets to work, her purse has fallen on the floor in front of the passenger seat. One day, she asks you to explain why this happens in terms of physics. What do you say?

2. You are waiting in line to use the diving board at your local pool. While watching people dive into the pool from the board, you realize that using a diving board to spring into the air before a dive is a good example of Newton’s third law of motion. Explain how a diving board illustrates Newton’s third law of motion.

3. You know the mass of an object and the force applied to the object to make it move. Which of Newton’s laws of motion will help you calculate the acceleration of the object?

4. How many newtons of force are represented by the following amount: 3 kg·m/sec²? Select the correct answer (a, b, or c) and justify your answer.

5. Your shopping cart has a mass of 65 kilograms. In order to accelerate the shopping cart down an aisle at 0.3 m/sec², what force would you need to use or apply to the cart?

6. A small child has a wagon with a mass of 10 kilograms. The child pulls on the wagon with a force of 2 newtons. What is the acceleration of the wagon?

7. You dribble a basketball while walking on a basketball court. List and describe the pairs of action-reaction forces in this situation.

Newton’s laws of motion

Write the law here in your own words

Example of the law

The first law The second law

The third law

a. 6 newtons b. 3 newtons c. 1 newton

Momentum

Which is more difficult to stop: A tractor-trailer truck barreling down the highway at 35 meters per second, or a small two-seater sports car traveling the same speed?

You probably guessed that it takes more force to stop a large truck than a small car. In physics terms, we say that the truck has greater momentum.

We can find momentum using this equation:

Velocity is a term that refers to both speed and direction. For our purposes we will assume that the vehicles are traveling in a straight line. In that case, velocity and speed are the same.

The equation for momentum is abbreviated like this: .

Momentum, symbolized with a p, is expressed in units of kg·m/sec; m is the mass of the object, in kilograms; and v is the velocity of the object in m/sec.

Use your knowledge about solving equations to work out the following problems:

1. If the truck has a mass of 2,000 kilograms, what is its momentum? Express your answer in kg·m/sec.

2. If the car has a mass of 1,000 kilograms, what is its momentum?

3. An 8-kilogram bowling ball is rolling in a straight line toward you. If its momentum is 16 kg·m/sec, how fast is it traveling?

4. A beach ball is rolling in a straight line toward you at a speed of 0.5 m/sec. Its momentum is 0.25 kg·m/sec.

What is the mass of the beach ball?

5. A 4,000-kilogram truck travels in a straight line at 10.0 m/sec. What is its momentum?

6. A 1,400-kilogram car is also traveling in a straight line. Its momentum is equal to that of the truck in the previous question. What is the velocity of the car?

7. Which would take more force to stop in 10 seconds: an 8.0-kilogram ball rolling in a straight line at a speed of 0.2 m/sec or a 4.0-kilogram ball rolling along the same path at a speed of 1.0 m/sec?

8. The momentum of a car traveling in a straight line at 20 m/sec is 24,500 kg·m/sec. What is the car’s mass?

9. A 0.14-kilogram baseball is thrown in a straight line at a velocity of 30 m/sec. What is the momentum of the baseball?

10. Another pitcher throws the same baseball in a straight line. Its momentum is 2.1 kg·m/sec. What is the velocity of the ball?

11. A 1-kilogram turtle crawls in a straight line at a speed of 0.01 m/sec. What is the turtle’s momentum?

momentum = mass of object×velocity of object

p = m v×

Impulse

A change in momentum for an object is equal to impulse. Momentum changes when velocity changes.

Force is what changes velocity. Therefore, when momentum changes a force must be involved for a period of time. The following equation relates impulse to change in momentum.

Momentum (p) is expressed in units of kg·m/s; m is the mass of the object, in kg; and v is the velocity of the object in m/sec. Impulse is expressed in units of N·sec.

1 N·sec = 1 kg·m/sec because 1 newton = 1 kg·m/sec²:

A net force of 50 newtons is applied to a 20-kilogram cart that is already moving at 1 meter per second. The final speed of the cart was 3 meters per second. For how long was the force applied?

Looking for

The speed of the cart after 3 seconds.

Solution

The force was applied to the cart for 0.8 second.

Given

Force applied = 50 newtons Mass of the car = 20 kilograms Initial speed of the cart = 1 m/sec Final speed of the cart = 3 m/sec Relationships

time = change in momentum ÷ Force

impulse = change in momentum

Force×time = Final momentum–Initial momentum F×t = mv₂–mv₁

1 N-sec 1kg-m sec²

---×sec 1kg-m ---sec

= =

t mv₂–mv₁ ---F

=

t (20 kg) 3 m/sec( )–(20 kg) 1 m/sec( ) ---50 N

=

t (60 kg-m/sec)–(20 kg-m/sec) ---50 N

=

t (40 kg-m/sec)

---50 N 0.8 sec

= =

t mv₂–mv₁ ---F

=

3.1

1. A net force of 100 newtons is applied to a 20-kilogram cart that is already moving at 3 meter per second. The final speed of the cart was 8 meters per second. For how long was the force applied?

2. A 3-kilogram ball is accelerated from rest to a speed of 10 m/sec.

a. What is the ball’s change in momentum?

b. What is the impulse?

c. If a constant force of 40 newtons is applied to change the momentum in this situation, for how long does the force act?

3. A 2,000-kilogram car uses a braking force of 12,000 newtons to stop in 5 seconds.

a. What impulse acts on the car?

b. What is the change in momentum of the car?

c. What is the initial speed of the car?

4. A 60-kilogram high jumper lands on a mat after her jump. The mat brings her to a stop after 1 second. She was traveling at 5.0 m/sec when she landed on the mat. Note: The speed of the jumper at the top of her jump, before she started to fall toward the mat, was 0 m/sec.

a. What is the change in momentum for the jumper?

b. What is the force felt by the jumper upon impact with the mat?

5. A 0.5-kilogram soccer ball is kicked with a force of 50 newtons for 0.2 seconds. The ball was at rest before the kick. What is the speed of the soccer ball after the kick?

6. A baseball player hits a 0.155-kilogram fastball traveling at 44.0 m/sec into center field at a speed of 50.0 m/sec. If the impact lasts for 0.00450 second, with what force does he hit the baseball?

7. Tow Sawyer launches his 180-kilogram raft on the Mississippi River by pushing on it with a force of 75 newtons. How long must Tom push on the raft to accelerate it to a speed of 2.0 m/sec?

8. In terms of impulse, why is the ride much more comfortable when an airplane is flying at constant speed versus when it is taking off or landing?

Thought questions

9. In certain martial arts, people practice breaking a piece of wood with the side of their bare hand. Use your understanding of impulse to explain how this can be done without injury to the hand.

10. If identical bullets are shot from a pistol and a rifle, a bullet shot from the rifle will travel at a higher speed than a bullet from the pistol. Why? (Hints: Assume shooting force is the same in each case. The barrel of the rifle is longer than the barrel of the pistol.)

Looking for Solution

Given

Relationships

11. Boxers attempt to move with an opponent’s punch when it is thrown. In other words, a boxer moves in 3.1 the same direction as their opponent's punch. This movement may prevent a knockout blow being delivered by their opponent. Explain how.

12. Show that the relationship between impulse and the change in momentum is another way of stating Newton's second law of motion.

13. Mats in a gym, airbags, and padding in sports uniforms are used to protect people from being injured.

Explain why these soft objects used instead of rigid objects using your understanding of impulse and change of momentum.