Momentum and CollisionsSection 1 Preview Section 1 Momentum and ImpulseMomentum and Impulse Section...

Momentum and Collisions Section 1

Preview

Section 1 Momentum and Impulse

Section 2 Conservation of Momentum

Section 3 Elastic and Inelastic Collisions

Section 4 Extra Questions


What do you think?

• Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2007 model car. In both cases, the car and passengers are stopped abruptly.• List the features in the newer car that are designed to

protect the passenger and the features designed to minimize damage to the car.

• How are these features similar?


What do you think?

• What are some common uses of the term momentum?• Write a sentence or two using the term momentum.

• Do any of the examples provided reference the velocity of an object?

• Do any of the examples reference the mass of an object?


Momentum

• Momentum (p) is proportional to both mass and velocity.• A vector quantity• SI Units: kg • m/s


Momentum and Newton’s 2nd Law

• Prove that the two equations shown below are equivalent.

F = ma and F = p/t

• Newton actually wrote his 2nd Law as F = p/t.– Force depends on how rapidly the momentum

changes.


Impulse and Momentum

• The quantity Ft is called impulse.– SI units: N•m or kg•m/s

• Impulse equals change in momentum.– Another version of Newton’s 2nd Law– Changes in momentum depend on both the force and the

amount of time over which the force is applied.


Click below to watch the Visual Concept.

Visual Concept

Impulse-Momentum Theorem

Section 1Momentum and Collisions

Changing momentum

• Greater changes in momentum(p) require more force (F) or more time (t) .

• A loaded truck requires more time to stop.– Greater p for truck with

more mass– Same stopping force


Classroom Practice Problems

• A 1350 kg car has a velocity of 22.0 m/s to the north. When braking rapidly, it stops in 4.50 s.– What was the momentum of the car before braking?– What is the magnitude of the force required to stop

the car?

• Answers: – 2.97 x 104 kg • m/s to the north– 6.60 x 103 N


Stopping Time

Ft = p = mv• When stopping, p is the same for rapid or gradual

stops.• Increasing the time (t) decreases the force (F).

– What examples demonstrate this relationship?• Air bags, padded dashboards, trampolines, etc

• Decreasing the time (t) increases the force (F).– What examples demonstrate this relationship?

• Hammers and baseball bats are made of hard material to reduce the time of impact.



• A 65 kg passenger in a car travels at a speed of 8.0 m/s. If the passenger is stopped by an airbag in 0.75 s, how much force is required?– Answer: 6.9 x 102 N

• If the car does not have an air bag and the passenger is instead stopped in 0.026 s when he strikes the dashboard, by what factor does the force increase?– Answer: F = 2.0 x 104 N so it is 29 times greater


Now what do you think?

• Imagine an automobile collision in which an older model car from the 1960s collides with a car at rest while traveling at 15 mph. Now imagine the same collision with a 2007 model car. In both cases, the car and passengers are stopped abruptly.– List the features in the newer car that are designed to

protect the passenger and the features designed to minimize damage to the car.

– How are these features similar?



• How is momentum defined?• How is Newton’s 2nd Law written using

momentum? • What is impulse?• What is the relationship between impulse and

momentum?


What do you think?

• Two skaters have equal mass and are at rest. They are pushing away from each other as shown.• Compare the forces on the two girls.• Compare their velocities after the push.

• How would your answers change if the girl on the right had a greater mass than her friend?

• How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?


Momentum During Collisions

• When the bumper cars collide,F1 = -F2 so F1t = -F2t, and therefore p1 = -p2 .

• The change in momentum for one object is equal and opposite to the change in momentum for the other object.

• Total momentum is neither gained not lost during collisions.


Conservation of Momentum

• Total momentum remains constant during collisions.• The momentum lost by one object equals the momentum

gained by the other object.• Conservation of momentum simplifies problem solving.



Visual Concept

Conservation of Momentum



• A 62.0 kg astronaut on a spacewalk tosses a 0.145 kg baseball at 26.0 m/s out into space. With what speed does the astronaut recoil?– Step 1: Find the initial momentum of both astronaut

and baseball.• Answer: zero because vi = 0 for both

– Step 2: Since pi = 0, then pf, astronaut= -pf, baseball

– Step 3: Substitute and solve for vf,astronaut

• Answer: -0.0608 m/s or -6.08 cm/s

• Does a pitcher recoil backward like the astronaut when throwing the ball? Explain.


Classroom Practice Problem

• Gerard is a quarterback and Tyler is a defensive lineman. Gerard’s mass is 75.0 kg and he is at rest. Tyler has a mass of 112 kg, and he is moving at 8.25 m/s when he tackles Gerard by holding on while they fly through the air. With what speed will the two players move together after the collision?

• Answer: 4.94 m/s



• Two skaters have equal mass and are at rest. They are pushing away from each other as shown.• Compare the forces on the two girls.• Compare their velocities after the push.

• How would your answers change if the girl on the right had a greater mass than her friend?

• How would your answers change if the girl on the right was moving toward her friend before they started pushing apart?


What do you think?

• Collisions are sometimes described as elastic or inelastic. To the right is a list of colliding objects. Rank them from most elastic to most inelastic.

• What factors did you consider when ranking these collisions?

1. A baseball and a bat

2. A baseball and a glove

3. Two football players

4. Two billiard balls

5. Two balls of modeling clay

6. Two hard rubber toy balls

7. An automobile collision


Perfectly Inelastic Collisions

• Two objects collide and stick together.– Two football players– A meteorite striking the earth

• Momentum is conserved.• Masses combine.


Classroom Practice Problems• An 2.0 x 105 kg train car moving east at 21 m/s

collides with a 4.0 x 105 kg fully-loaded train car initially at rest. The two cars stick together. Find the velocity of the two cars after the collision.– Answer: 7.0 m/s to the east

• Now calculate the kinetic energy of the two cars before and after the collision. Was kinetic energy conserved?– Answer: KEbefore= 4.4 x 107 J, KEafter= 1.5 x 107 J

• KE is not conserved. It is less after the collision.


Inelastic Collisions

• Kinetic energy is less after the collision.– It is converted into other forms of energy.

• Internal energy - the temperature is increased.• Sound energy - the air is forced to vibrate.

• Some kinetic energy may remain after the collision, or it may all be lost.


Elastic Collisions

• Objects collide and return to their original shape.• Kinetic energy remains the same after the collision.• Perfectly elastic collisions satisfy both conservation laws

shown below.


Elastic Collisions

• Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of momentum?– vf,A = 2.0 m/s, vf,B = 2.0 m/s

– vf,A = 0 m/s, vf,B = 4.0 m/s

– vf,A = 1.5 m/s, vf,B = 2.5 m/s

• Answer: all three

m = 0.35 kg m = 0.35 kg

v = 4.0 m/s v = 0 m/s


Elastic Collisions

• Two billiard balls collide head on, as shown. Which of the following possible final velocities satisfies the law of conservation of kinetic energy?– vf,A = 2.0 m/s, vf,B = 2.0 m/s

– vf,A = 0 m/s, vf,B = 4.0 m/s

– vf,A = 1.5 m/s, vf,B = 2.5 m/s

• Answer: only vf,A = 0 m/s, vf,B = 4.0 m/s

m = 0.35 kg m = 0.35 kg

v = 4.0 m/s v = 0 m/s



Visual Concept

Types of Collisions


Types of Collisions



• To the right is a list of colliding objects. Rank them from most elastic to most inelastic.

• What factors did you consider when ranking these collisions?

1. A baseball and a bat

2. A baseball and a glove

3. Two football players

4. Two billiard balls

5. Two balls of modeling clay

6. Two hard rubber toy balls

7. An automobile collision


Preview

• Multiple Choice

• Short Response

• Extended Response


Multiple Choice, continued

2. The vector below represents the momentum of a car traveling along a road.

The car strikes another car, which is at rest, and the result is an inelastic collision. Which of the following vectors represents the momentum of the first car after the collision?F.G.H.J.



3. What is the momentum of a 0.148 kg baseball thrown with a velocity of 35 m/s toward home plate?

A. 5.1 kg • m/s toward home plate

B. 5.1 kg • m/s away from home plate

C. 5.2 kg • m/s toward home plate

D. 5.2 kg • m/s away from home plate



Use the passage below to answer questions 4–5.After being struck by a bowling ball, a 1.5 kg bowling pin slides to the right at 3.0 m/s and collides head-on with another 1.5 kg bowling pin initially at rest.

4. What is the final velocity of the second pin if the first pin moves to the right at 0.5 m/s after the collision?F. 2.5 m/s to the leftG. 2.5 m/s to the rightH. 3.0 m/s to the leftJ. 3.0 m/s to the right



Use the passage below to answer questions 4–5.After being struck by a bowling ball, a 1.5 kg bowling pin slides to the right at 3.0 m/s and collides head-on with another 1.5 kg bowling pin initially at rest.

5. What is the final velocity of the second pin if the first pin stops moving when it hits the second pin?A. 2.5 m/s to the leftB. 2.5 m/s to the rightC. 3.0 m/s to the leftD. 3.0 m/s to the right



6. For a given change in momentum, if the net force that is applied to an object increases, what happens to the time interval over which the force is applied?

F. The time interval increases.

G. The time interval decreases.

H. The time interval stays the same.

J. It is impossible to determine the answer from the given information.



8. Two shuffleboard disks of equal mass, one of which is orange and one of which is yellow, are involved in an elastic collision. The yellow disk is initially at rest and is struck by the orange disk, which is moving initially to the right at 5.00 m/s. After the collision, the orange disk is at rest. What is the velocity of the yellow disk after the collision? Think energy!

F. zero

G. 5.00 m/s to the left

H. 2.50 m/s to the right

J. 5.00 m/s to the right



Use the information below to answer questions 9–10.

A 0.400 kg bead slides on a straight frictionless wire and moves with a velocity of 3.50 cm/s to the right, as shown below. The bead collides elastically with a larger 0.600 kg bead that is initially at rest. After the collision, the smaller bead moves to the left with a velocity of 0.70 cm/s.

9. What is the large bead’s velocity after the collision?

A. 1.68 cm/s to the right

B. 1.87 cm/s to the right

C. 2.80 cm/s to the right

D. 3.97 cm/s to the right



Use the information below to answer questions 9–10.

A 0.400 kg bead slides on a straight frictionless wire and moves with a velocity of 3.50 cm/s to the right, as shown below. The bead collides elastically with a larger 0.600 kg bead that is initially at rest. After the collision, the smaller bead moves to the left with a velocity of 0.70 cm/s.

10. What is the total kinetic energy of the system after the collision?

F. 1.40 10–4 J

G. 2.45 10–4 J

H. 4.70 10 –4 J

J. 4.90 10 –4 J


Short Response

11. Is momentum conserved when two objects with zero initial momentum push away from each other?


Short Response, continued

An 8.0 g bullet is fired into a 2.5 kg pendulum bob, which is initially at rest and becomes embedded in the bob. The pendulum then rises a vertical distance of 6.0 cm.

13. What was the initial speed of the bullet? Show your work.


Short Response, continued

Base your answers to questions 13–14 on the information below.

An 8.0 g bullet is fired into a 2.5 kg pendulum bob, which is initially at rest and becomes embedded in the bob. The pendulum then rises a vertical distance of 6.0 cm.

14. What will be the kinetic energy of the pendulum when the pendulum swings back to its lowest point? Show your work.


Extended Response

15. An engineer working on a space mission claims that if momentum concerns are taken into account, a spaceship will need far less fuel for the return trip than for the first half of the mission.Write a paragraph to explain and support this hypothesis.

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