Chapter 7 physics

Two objects have the same mass. Object one is initially at rest, and object two initially moves to the east at 2 m/s. The two objects undergo an elastic collision. If the final velocity of object one is (1.732 m/s, 30 degrees north of east), then what is the final velocity of object two?

(1 m/s, 60 degrees south of east)

If the impulse is 200 N⋅s in the negative direction and the time interval is 10 s, then what is the average net force?

-20 N

A football player leaps at a speed of 3.0 m/s toward a second football player, who is moving at 0.5 m/s toward the first player. The two players collide and then move together at 1.2 m/s. If the player moving originally at 0.5 m/s has a mass of 175 kg, what is the other player's mass?

165 kg?

Two cars, A and B, are traveling along the x-axis. Car B has half the mass and half the speed of car A. What is the ratio of the magnitudes of their momenta, pA/pB?

4

Fnet = (10 N/s)t is the magnitude of a nonconstant force that increases linearly with time, where t is measured in seconds. If this net force acts from ti = 0 s until tf = 10 s, then what is the magnitude of the impulse?

500 N⋅s

What can cause a change in the velocity of the center of mass of a system?

A nonzero net external force

What is the direction of the total impulse?

Direction of the net force

True or false: The center of mass of a two-particle system can lie anywhere in space.

False

How can impulse be determined graphically?

The area under the force versus time graph

What is the rate of change of momentum of an object with respect to time?

The net force acting on the object

Two bars, each 30 cm long, are placed end to end. The bar on the left has a mass of 2 kg, and the bar on the right has a mass of 3 kg. Find how far from the place where they meet, and in which direction, the center of mass of the two-bar system is located.

Toward the right 3 cm

When dealing with a two-dimensional elastic collision it can be easiest to set the total kinetic energies equal, because in an elastic collision the total kinetic energy is __________ .

conserved

Rank the following according to the magnitude of the impulse with the largest magnitude at the top and the smallest at the bottom.

Average Net Force = 10N in the negative direction, time interval = 50s Average Net Force = 20N in the positive direction, time interval = 20s Average Net Force = 10N in the negative direction, time interval = 20s Average Net Force = 10N in the positive direction, time interval = 10s

A catapult launches a firework into the air, but it does not explode. It travels in projectile motion and lands in an empty field. A second identical firework is launched in an identical way, but this time it explodes. If we ignore air resistance, where is the center of mass of the second firework after the pieces land?

At the same place as the first firework

The four figures below show the before and after velocities of a ball bouncing off a vertical wall. Rank the 4 cases below from greatest on the top to least on the bottom based on the magnitude of the change in momentum.

Case A,C,B,D

Select all of the following that are equal to the total impulse.

Change in momentum Product of net force and time interval

Particle A has a mass of 10 kg and particle B has a mass of 20 kg. Where is the center of mass located?

Closer to particle B

Rank the following according to the magnitude of the average net force with the largest magnitude at the top and the smallest at the bottom.

Impulse= 400 N-s in the Negative direction, Time Interval= 10 s Impulse= 300 N-s in the Positive direction, Time Interval= 10 s Impulse= 400 N-s in the Positive direction, Time Interval= 20 s Impulse= 500 N-s in the Negative direction, Time Interval= 50 s

If the ends of two identical bars are put together so that they make an L-frame, where is the center of mass located?

In the empty space between the two bars and diagonal from the corner

According to the law of conservation of momentum, in the absence of external forces, for two objects, what is the change in momentum of one object?

It has the same magnitude as the change in momentum of the other object, but it is in the opposite direction.

Select all of the following that are always conserved in an elastic collision. Assume the net external force is zero.

Kinetic energy Momentum

The units of momentum are

ML/T.

What is conserved if a vector quantity is conserved?

Magnitude and direction Magnitude and components

If a vector's magnitude is constant, then is the vector always conserved? Select all answers that are correct.

No, because the vector's components could change. No, because the vector's direction could change.

Select all of the following that are equal to the SI units of impulse.

N⋅s kg⋅m/s

What is the term for when two objects stick together after the collision?

Perfectly inelastic

Select all of the following statements that are true for an elastic collision. Assume the net external force is zero.

The initial kinetic energy of the system is equal to the final kinetic energy of the system. The initial momentum of the system is equal to the final momentum of the system.

A 1000-kg car moving at 20 m/s in the positive direction collides head on with a 2000-kg truck moving at 10 m/s in the negative direction. After the collision, the car and the truck are stuck together, so their final velocities are the same. How do their initial and final speeds compare?

The initial speed of the car is greater than its final speed. The initial speed of the truck is greater than its final speed.

A 10-kg fox is initially moving in the negative direction at 10 m/s. Later it is moving in the positive direction at 20 m/s. By how much did its momentum change?

+300 kg⋅m/s

A 10-kg bird is initially moving in the positive direction at 20 m/s. Later it is moving in the positive direction at 10 m/s. By how much did its momentum change?

-100 kg.m/s

What is conserved in a perfectly inelastic collision?

Momentum only

Object one has twice the mass of object two. Object one initially moves to the right at 5 m/s, and object two initially moves to the left at 4 m/s. The two objects undergo an elastic collision. If the final velocity of object one is 1 m/s to the left, then what is the final velocity of object two?

8 m/s to the right

Object one has twice the mass of object two. Object one initially moves to the north at 3 m/s, and object two initially moves to the east at 6 m/s. The two objects undergo a perfectly inelastic collision. What is their final velocity?

(2.828 m/s, to the northeast)

An ice puck of mass 1.0 kg moving to the right at an initial speed of 1.0 m/s at t = 0 s on a frictionless surface is subject to the net force shown in the graph. What is the impulse given to the ice puck between 0 s and 5.0 s?

+15 kg⋅m/s

A firework is launched from the ground at a speed of 50 m/s at an angle of 60 degrees from the horizontal. When it reaches its highest point, it explodes into two pieces of equal mass. Immediately after the explosion, one piece moves horizontally to the right at 50 m/s. What is the velocity of the other piece immediately after the explosion? All velocities are measured with respect to the ground. Ignore air resistance.

0 m/s

A 4.00 kg object is moving at 3.00 m/s WEST. It catches up to and strikes a 6.00 kg that is moving WEST at 2.00 m/s. The objects undergo an elastic collision in the EAST-WEST direction. The velocity of the 4.00 kg object after the collision is

1.80 m/s WEST.

Two cars, A and B, are traveling along the x-axis. Car B has half the mass and the same speed as car A. What is the ratio of the magnitudes of the momenta pA/pB?

2

Two cars, A and B, are traveling along the x-axis. Car B has the same mass and half the speed as car A. What is the ratio of the magnitudes of the momenta pA/pB?

2

Two objects have the same mass. Object one initially moves to the right at 2 m/s, and object two initially moves to the left at 7 m/s. The two objects collide. If the final velocity of object one is 3 m/s to the left, then what is the final velocity of object two?

2 m/s to the left

Two objects of equal mass undergo an elastic collision. Object one initially moves to the right at 2 m/s, and object two initially moves to the left at 4 m/s. If the final velocity of object one is 4 m/s to the left, then what is the final velocity of object two?

2 m/s to the right

A 4.00 kg object is moving at 5.00 m/s NORTHWEST. It strikes a 6.00 kg object that is moving SOUTHWEST at 2.00 m/s. The objects collide perfectly inelastically (stick together). The velocity of the 6.00 kg object after the collision is

2.33 m/s at an angle of 14.0 degrees NORTH of WEST.

A 4.00 kg object is moving at 5.00 m/s EAST. It strikes a 6.00 kg object that is at rest. The objects collide elastically. The velocity of 4.00 kg object after the collision is in the SOUTHWEST direction. The speed of the 6.00 kg object after the collision is

2.38 m/s.

In an elastic collision, one ball has initial velocity v when it collides head-on with another, much less massive ball, initially at rest. The velocity of the second ball after the collision is approximately equal to

2v

A uniform cube has 12 edges, and each edge has a length of 3.464 cm. One corner of the cube is located at the origin. What is the distance from the origin to the center of mass of the cube?

3 cm

Object one has twice the mass of object two. Object one initially moves to the right at 8 m/s, and object two initially moves to the left at 4 m/s. The two objects undergo a perfectly inelastic collision. What is their final velocity?

4 m/s to the right

Two objects have the same mass. Object one initially moves to the right at 5 m/s, and object two initially moves to the left at 4 m/s. The two objects collide. If the final velocity of object one is 3 m/s to the left, then what is the final velocity of object two?

4 m/s to the right

If the momentum of a ball is doubled, then the kinetic energy is

4 times larger.

A 10-kg object initially traveling in the positive direction at 5.0 m/s is subjected to a net force as represented in the graph. What is the final speed?

7.0 m/s

How is the net impulse determined?

By calculating the vector sum of the impulses from individual forces

True or false: The rate of change of the momentum of an object is equal to its acceleration.

False

Two objects of equal mass of 10 kg undergo a one-dimensional collision. Rank the following scenarios according to the magnitude of the total momentum of the system, with the largest magnitude at the top and the smallest at the bottom.

Initial Velocity of object A = (10m/s, north) and initial velocity of object B = (30m/s, north) Initial Velocity of object A = (50m/s, north) and initial velocity of object B = (20 m/s, south) Initial Velocity of object A = (70 m/s, south) and initial velocity of object B = (50m/s, north) Initial Velocity of object A = (10 m/s, north) and initial velocity of object B = 0 m/s

Select all of the following that are equal to impulse.

The change in momentum The product of force and time interval

What is the direction of impulse?

The direction of the force

Two objects are held together by pushing against a strong spring, as shown. The objects are released simultaneously from rest. The mass of object 1 is m1 and the mass of object 2 is m2. Select all of the following that are correct.

The final momentum of the system is zero. The initial momentum of the system is zero. v2/v1 = m1/m2

Select all of the following that are always features of perfectly inelastic collisions.

The final velocities of all of the objects are the same. The decrease in kinetic energy is as large as possible. The objects stick together.

A 1000-kg car moving at 10 m/s in the positive direction collides head on with a 2000-kg truck moving at 35 m/s in the negative direction. After the collision, the car and the truck are stuck together, so their final velocities are the same. How do their initial and final speeds compare?

The initial speed of the car is less than its final speed. The initial speed of the truck is greater than its final speed.

Select all of the following that are always features of perfectly inelastic collisions.

The objects stick together. The final velocities of all of the objects are the same. The decrease in kinetic energy is as large as possible.

One particle has a mass of 10 kg and is located at the origin (x = 0). Rank the following situations according to the center of mass of the two-particle system with the largest center of mass at the top and the smallest at the bottom.

The other particle has a mass of 70 kg and is located at x= 80 m The other particle has a mass of 10 kg and is located at x= 90 m The other particle has a mass of 90 kg and is located at x= 10 m

If a heavy object traveling toward the north has an elastic collision with a light object traveling toward the east, choose all of the true statements below.

The relative speeds of the two objects are unchanged. The total kinetic energy of the system is the same after the collision as before.

True or false: If the net external force is zero, then momentum is always conserved in an elastic collision.

True

When is momentum conserved?

When the net external force is zero

A net external __________ acting on a system will cause the center of mass to accelerate.

force

A 100 kg mass, initially at rest, is blown apart into a 60 kg piece and a 40 kg piece. After the blast, the two masses are moving apart with a relative velocity of 60 m/s. The speed of the 60 kg mass is

24 m/s.

The momentum of an object changes from 3 N⋅s i + 4 N⋅s j to being at rest in 1 second. What is the magnitude of the average net force?

5 N⋅s

A 2.0-kg hockey puck is initially at rest on a frictionless ice surface when it is subject to the net force shown in the graph. What is the speed of the puck at 10 s?

7.5 m/s

When dealing with a two-dimensional collision, because momentum is a ____________, it is usually best to split it up into components.

vector

A 10-kg object initially traveling in the positive direction at 7.0 m/s is subjected to a net force as represented in the graph. What is the final speed?

4.5 m/s

A 3.0 kg object is moving to the right at 4.0 m/s. It collides in a perfectly inelastic collision with a 6.0 kg object moving to the left at 2.0 m/s. What is the total kinetic energy after the collision?

0.0 J

Object two has twice the mass of object one. Object one initially moves to the right at 3 m/s, and object two initially moves to the left at 6 m/s. The two objects undergo a perfectly inelastic collision. What is their final velocity?

3 m/s to the left

Two objects have the same mass. Object one initially moves to the right at 4 m/s, and object two initially moves to the left at 4 m/s. The two objects collide. If the final velocity of object one is 3 m/s to the left, then what is the final velocity of object two?

3 m/s to the right

True or false: The law of conservation of momentum states that in the absence of external forces, the momentum of a system remains constant.

True

An object with a mass of 1 kg is moving toward the right at 3 m/s when it collides with a stationary mass of 2 kg. After the collision, the 1 kg mass is moving toward the left at 1 m/s, and the 2 kg mass is moving toward the right at 2 m/s. Was this collision elastic?

Yes

A 1000-kg car moving at 40 m/s in the positive direction collides head on with a 2000-kg truck moving at 5 m/s in the negative direction. After the collision, the car and the truck are stuck together, so their final velocities are the same. How do their initial and final speeds compare?

The initial speed of the car is greater than its final speed. The initial speed of the truck is less than its final speed.

Two objects collide and stick together. Which of the following is false?

kinetic energy is conserved

A perfectly inelastic collision is one in which only __________ is always conserved.

momentum

If a heavy object traveling toward the north has a completely inelastic collision with a light object traveling toward the east, choose all the true statements from below.

After the collision, the two objects will both move with the same velocity vector as the center of mass did before the collision. The two objects stick together.