Segmentación del objetivo del proyecto

Just like the third law of motion says that forces are equal and opposite, changes in momentum are equal and opposite. This is because when objects exert forces on each other, their motion is affected.

The law of momentum conservation states that if interacting objects in a system are not acted on by outside forces, the total amount of momentum in the system cannot change.

The formula below can be used to find the new velocities of objects if both keep moving after the collision.

If two objects are initially at rest, the total momentum of the system is zero.

For the final momentum to be zero, the objects must have equal momenta in opposite directions.

Example 1: What is the momentum of a 0.2-kilogram steel ball that is rolling at a velocity of 3.0 m/sec?

Example 2: You and a friend stand facing each other on ice skates. Your mass is 50 kilograms and your friend’s mass is 60 kilograms. As the two of you push off each other, you move with a velocity of 4 m/sec to the right.

What is your friend’s velocity?

Looking for

Your friend’s velocity to the left.

Solution

Your friends velocity to the left is 3.33 m/sec.

Given

Your mass of 50 kg.

Your friend’s mass of 60 kg.

Your velocity of 4 m/sec to the right.

Relationship

the momentum of a system before = the total momentum of a system after m₁v_{1 initial( )}+m₂v2 (initial) = m₁v_{3 (final)}+m₂v_{4 (final)}

the momentum of a system before a collision = 0

0 = the momentum of a system after a collision 0 = m₁v₃+m₂v₄

m₁v₃ = –(m₂v₄)

momentum m×v 0.2 kg 3 m ---sec

× 0.6 kg m

sec

---⋅

= = =

m₁v₃ = –(m₂v₄) 50 kg

( ) 4 m/sec( ) = –(60 kg) v( )₄ 200 kg-m/sec

60 kg

( )

---– = v₄ 3.33 m/sec

– = v₄

m₁v₃ = –(m₂v₄)

3.1

1. If a ball is rolling at a velocity of 1.5 m/sec and has a momentum of 10.0 kg·m/sec, what is the mass of the ball?

2. What is the velocity of an object that has a mass of 2.5 kilogram and a momentum of 1,000 kg·m/sec?

3. Tiger Woods hits 45.0-gram golf ball, giving it a speed of 75.0 m/sec. What momentum has Tiger given to the golf ball?

4. A 400-kilogram cannon fires a 10-kilogram cannonball at 20 m/sec. If the cannon is on wheels, at what velocity does it move backward? (This backward motion is called recoil velocity.)

5. "Big" Al stands on a skateboard at rest and throws a 0.5-kilogram rock at a velocity of 10.0 m/sec. "Big" Al moves back at 0.05 m/sec. What is the combined mass of "Big" Al and the skateboard?

6. As the boat in which he is riding approaches a dock at 3.0 m/sec, Jasper stands up in the boat and jumps toward the dock. Jasper applies an average force of 800 newtons on the boat for 0.30 seconds as he jumps.

a. How much momentum does Jasper's 80-kilogram body have as it lands on the dock?

b. What is Jasper's speed on the dock?

7. Daryl the delivery guy gets out of his pizza delivery truck forgetting to set the parking brake. The

2,000 kilogram truck rolls down hill reaching a speed of 30 m/sec just before hitting a large oak tree. The vehicle stops 0.72 seconds after first making contact with the tree.

a. How much momentum does the truck have just before hitting the tree?

b. What is the average force applied by the tree?

8. Two billion people jump up in the air at the same time with an average velocity of 7.0 m/sec. If the mass of an average person is 60 kilograms and the mass of Earth is 5.98 × 10²⁴ kilograms:

a. What is the total momentum of the two billion people?

b. What is the effect of their action on Earth?

9. Tammy, a lifeguard, spots a swimmer struggling in the surf and jumps from her lifeguard chair to the sand beach. She makes contact with the sand at a speed of 6.00 m/sec leaving an indentation in the sand

0.10 meters deep.

a. If Tammy's mass is 60. kilograms, what is momentum as she first touches the sand?

b. What is the average force applied on Tammy by the sand beach?

10. When a gun is fired, the shooter describes the sensation of the gun kicking. Explain this in terms of momentum conservation.

11. What does it mean to say that momentum is conserved?

Work

In science, “work” is defined with an equation. Work is the amount of force applied to an object (in the same direction as the motion) over a distance. By measuring how much force you have used to move something over a certain distance, you can calculate how much work you have accomplished.

The formula for work is:

A joule of work is actually a newton·meter; both units represent the same thing: work! In fact, one joule of work is defined as a force of one newton that is exerted on an object to it a distance of one meter.

How much work is done on a 10-newton block that is lifted 5 meters off the ground by a pulley?

1. In your own words, define work in scientific terms. Be complete in your definition.

2. How are work, force, and distance related?

3. What are two different units that represent work?

4. For the following situations, determine whether work was done. Write “work done” or “no work done” for each situation.

a. An ice skater glides for two meters across ice.

b. The ice skater’s partner lifts her up a distance of 1 meter.

c. The ice skater’s partner carries her across the ice a distance of 3 meters.

d. After setting her down, the ice skater’s partner pulls her across the ice a distance of 10 meters.

e. After skating practice, the ice skater lifts her 20-newton gym bag up 0.5 meter.

Looking for

The amount of work done by a pulley in unit of newtons and meters.

Solution

The pulley did 50 newton·meters or 50 joules of work.

Given

The lift force applied by the pulley = 10 N The distance the force was lifted = 5 meters.

Relationship

Work = Force × distance 1 newton·meter = 1 joule

W = F×d

Work (joules) = Force (newtons)×distance (meters)

1.0 joule = 1.0 N×1.0 meter = 1.0 newton-meter

Work = 10 N×5 m Work = 50 newton-meters

5. A woman lifts her 100-newton child up one meter and carries her for a distance of 50 meters to the 3.2 child’s bedroom. How much work does the woman do?

6. How much work does a mother do if she lifts each of her twin babies upward 1 meter? Each baby weighs 90 newtons.

7. You pull your sled through the snow a distance of 500 meters with a horizontal force of 200 newtons. How much work did you do?

8. Because the snow suddenly gets too slushy, you decide to carry your 100-newton sled the rest of the way home. How much work do you do when you pick up the sled, lifting it 0.5 meter upward? How much work do you do to carry the sled if your house is 800 meters away?

9. An ant sits on the back of a mouse. The mouse carries the ant across the floor for a distance of 10 meters.

Was there work done by the mouse? Explain.

10. You decide to add up all the work you did yesterday. If you accomplished 10,000 newton·meters of work yesterday, how much work did you do in units of joules?

11. You did 150 joules of work lifting a 120-newton backpack.

a. How high did you lift the backpack?

b. How much did the backpack weigh in pounds? (Hint: There are 4.448 newtons in one pound.)

12. A crane does 62,500 joules of work to lift a boulder a distance of 25.0 meters. How much did the boulder weigh? (Hint: The weight of an object is considered to be a force in units of newtons.)

13. A bulldozer does 30,000 joules of work to push another boulder a distance of 20 meters. How much force is applied to push the boulder?

14. You lift a 45-newton bag of mulch 1.2 meters and carry it a distance of 10 meters to the garden. How much work was done?

15. A 450-newton gymnast jumps upward a distance of 0.50 meters to reach the uneven parallel bars. How much work did she do before she even began her routine?

16. It took a 500.0-newton ballerina a force of 250 joules to lift herself upward through the air. How high did she jump?

17. A people-moving conveyor-belt moves a 600-newton person a distance of 100 meters through the airport.

a. How much work was done?

b. The same 600-newton person lifts his 100-newton carry-on bag upward a distance of 1 meter. They travel another 10 meters by riding on the “people mover.” How much work was done in this situation?

18. Which person did the most work?

a. John walks 1,000 meters to the store. He buys 4.448 newtons of candy and then carries it to his friend’s house which is 500 meters away.

b. Sally lifts her 22-newton cat a distance of 0.5 meter.

c. Henry carries groceries from a car to his house. Each bag of groceries weighs 40 newtons. He has ten bags. He lifts each bag up one meter to carry it and then walks 10 meters from his car to his house.