Chapter 9

Object A strikes the stationary object B head-on in an elastic collision. The mass of A is fixed, you may choose the mass of B appropriately. Then:

for B to have the greatest recoil kinetic energy, choose mB = mA

What magnitude impulse will give a 2.0-kg object a momentum change of magnitude + 50kg· m/s?

+50N*s

Block A, with a mass of 2.0kg, moves along the x axis with a velocity of 5.0m/s in the positive x direction. It suffers an elastic collision with block B, initially at rest, and the blocks leave the collision along the x axis. If B is much more massive than A, the speed of A after the collision is:

-5.0 m/s

Two spacemen are floating together with zero speed in a gravity-free region of space. The mass of spaceman A is 120kg and that of spaceman B is 90kg. Spaceman A pushes B away from him with B attaining a final speed of 0.5m/s. The final recoil speed of A is:

.38 m/s

A 3.00-g bullet traveling horizontally at 400m/s hits a 3.00-kg wooden block, which is initially at rest on a smooth horizontal table. The bullet buries itself in the block without passing through. The speed of the block after the collision is:

.40 m/s

Blocks A and B are moving toward each other along the x axis. A has a mass of 2.0kg and a velocity of 50m/s, while B has a mass of 4.0kg and a velocity of −25m/s. They suffer an elastic collision and move off along the x axis. The kinetic energy transferred from A to B during the collision is:

0

A 2.0-kg mass is attached to one end of a spring with a spring constant of 100N/m and a 4.0-kg mass is attached to the other end. The masses are placed on a horizontal frictionless surface and the spring is compressed 10cm. The spring is then released with the masses at rest and the masses oscillate. When the spring has its equilibrium length for the first time the 2.0-kg mass has a speed of 0.36m/s. The mechanical energy that has been lost to the instant is:

0.31

Cart A, with a mass of 0.20kg, travels on a horizontal air track at 3.0m/s and hits cart B, which has a mass of 0.40kg and is initially traveling away from A at 2.0m/s. After the collision the center of mass of the two cart system has a speed of:

0.33m/s

A 5-kg object can move along the x axis. It is subjected to a force F in the positive x direction; a graph of F as a function of time t is shown below. Over the time the force is applied the change in the velocity of the object is:

0.8m/s

For a completely inelastic two-body collision the kinetic energy retained by the objects is the same as:

1 2Mv2com, where M is the total mass and vcom is the velocity of the center of mass

A machinist starts with three identical square plates but cuts one corner from one of them, two corners from the second, and three corners from the third. rank the 3 plates according the x coordinate of their centers of mass, from smallest to largest

1 and 3 ties, then 2

A 4.0-N puck is traveling at 3.0m/s. It strikes a 8.0-N puck, which is stationary. The two pucks stick together. Their common final speed is:

1.0 m/s

Block A, with a mass of 4kg, is moving with a speed of 2.0m/s while block B, with a mass of 8kg, is moving in the opposite direction with a speed of 3m/s. The center of mass of the two block-system is moving with a velocity of:

1.3m/s in the same direction as B

the and y coordinates of the COM of the three particle system shown below are

1.4m, 1.9m

At one instant of time a rocket is traveling in outer space at 2500m/s and is exhausting fuel at a rate of 100kg/s. If the speed of the fuel as it leaves the rocket is 1500m/s, relative to the rocket, the thrust is

1.5×105 N

A block moves at 5.0m/s in the positive x direction and hits an identical block, initially at rest. A small amount of gunpowder had been placed on one of the blocks. The explosion does not harm the blocks but it doubles their total kinetic energy. After the explosion the blocks move along the x axis and the incident block has a speed in of:

1.8 m/s

A 0.2-kg rubber ball is dropped from the window of a building. It strikes the sidewalk below at 30m/s and rebounds up at 20m/s. The impulse on the ball during the collision is:

10N·s upward

Two objects, X and Y, are held at rest on a horizontal frictionless surface and a spring is compressed between them. The mass of X is 2/5 times the mass of Y. Immediately after the spring is released, X has a kinetic energy of 50J and Y has a kinetic energy of:

125J

At the same instant that a 0.50-kg ball is dropped from 25m above Earth, a second ball, with a mass of 0.25kg, is thrown straight upward from Earth's surface with an initial speed of 15m/s. They move along nearby lines and pass without colliding. At the end of 2.0s the velocity of the center of mass of the two-ball system is:

15 m/s, down

A particle moves along the x axis. Its momentum is graphed below as a function of time. Rank the numbered regions according to the magnitude of the force acting on the particle, least to greatest.

2, 3, 4, 1

A 500-kg sack of coal is dropped on a 2000-kg railroad flatcar which was initially moving at 3m/s as shown. After the sack rests on the flatcar, the speed of the flatcar is:

2.4 m/s

A very massive object traveling at 10m/s strikes a very light object, initially at rest, and the light object moves off in the direction of travel of the heavy object. If the collision is elastic, the speed of the lighter object is:

20 m/s

Two 4.0-kg blocks are tied together with a compressed spring between them. They are thrown from the ground with an initial velocity of 35m/s, 45◦ above the horizontal. At the highest point of the trajectory they become untied and spring apart. About how far below the highest point is the center of mass of the two-block system 2.0s later, before either fragment has hit the ground?

20m

A rocket exhausts fuel with a velocity of 1500m/s, relative to the rocket. It starts from rest in outer space with fuel comprising 80 per cent of the total mass. When all the fuel has been exhausted its speed is:

2400m/s

Bullets from two revolvers are fired with the same velocity. The bullet from gun #1 is twice as heavy as the bullet from gun #2. Gun #1 weighs three times as much as gun #2. The ratio of the momentum imparted to gun #1 to that imparted to gun #2 is:

2:1

A stream of gas consists of n molecules. Each molecule has mass m and speed v. The stream is reflected elastically from a rigid surface as shown. The magnitude of the change in the total momentum of the stream is:

2mnvsin30◦

A large wedge with a mass of 10kg rests on a horizontal frictionless surface, as shown. A block with a mass of 5.0kg starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block's velocity is 3.0m/s and the horizontal component is 6.0m/s. At that instant the velocity of the wedge is:

3.0 m/s to the right

A 640-N hunter gets a rope around a 3200-N polar bear. They are stationary, 20m apart, on frictionless level ice. When the hunter pulls the polar bear to him, the polar bear will move

3.3 m

A 1.0-kg ball moving at 2.0m/s perpendicular to a wall rebounds from the wall at 1.5m/s. The change in the momentum of the ball is:

3.5N· s away from wall

Blocks A and B are moving toward each other. A has a mass of 2.0kg and a velocity of 50m/s, while B has a mass of 4.0kg and a velocity of −25m/s. They suffer a completely inelastic collision. The kinetic energy lost during the collision is:

3750 J

Two bodies, A and B, have equal kinetic energies. The mass of A is nine times that of B. The ratio of the momentum of A to that of B is

3:1

A 1000-kg space probe is motionless in space. To start moving, its main engine is fired for 5s during which time it ejects exhaust gases at 5000m/s. At the end of this process it is moving at 20m/s. The approximate mass of the ejected gas is:

4 kg

A 3.0-kg and a 2.0-kg cart approach each other on a horizontal air track. They collide and stick together. After the collision their total kinetic energy is 40J. The speed of their center of mass is:

4.0m/s

A 2-kg cart, traveling on a horizontal air track with a speed of 3m/s, collides with a stationary 4-kg cart. The carts stick together. The impulse exerted by one cart on the other has a magnitude of:

4N*s

Two boys, with masses of 40kg and 60kg, respectively, stand on a horizontal frictionless surface holding the ends of a light 10-m long rod. The boys pull themselves together along the rod. When they meet the 60-kg boy will have moved what distance?

4m

A 75-kg man is riding in a 30-kg cart at 2.0m/s. He jumps off in such a way as to land on the ground with no horizontal velocity. The resulting change in speed of the cart is:

5.0m/s

At the same instant that a 0.50-kg ball is dropped from 25m above Earth, a second ball, with a mass of 0.25kg, is thrown straight upward from Earth's surface with an initial speed of 15m/s. They move along nearby lines and pass each other without colliding. At the end of 2.0s the height above Earth's surface of the center of mass of the two-ball system is:

7.1 m

A 3-g bullet is fired horizontally into a 10-kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 3mm above its lowest position. The velocity of the bullet was:

8.0×10^2 m/s

A man is marooned at rest on level frictionless ice. In desperation, he hurls his shoe to the right at 15m/s. If the man weighs 720N and the shoe weighs 4.0N, the man moves to the left with a speed of:

8.3×10^−2 m/s

A 2.5-kg stone is released from rest and falls toward Earth. After 4.0s, the magnitude of its momentum is:

98kg·m/s

A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Starting from rest the heavier object moves downward and the lighter object moves upward with the same magnitude acceleration. Which of the following statements is true for the system consisting of the two masses?

None of the above statements are true

The center of mass of a system of particles obeys an equation similar to Newton's second law F = m acom, where:

F is the net external force and m is the total mass of the system

Momentum may be expressed in

N*s

For a two-body collision involving objects with different masses, a frame of reference which has the same velocity relative to the laboratory as does the center of mass of the two objects is:

a frame for which the total momentum of the two objects is zero

If the total momentum of a system is changing

a net external force must be acting on the system

The momentum of an object at a given instant is independent of its

acceleration

A 10-kg block of ice is at rest on a frictionless horizontal surface. A 1.0-N force is applied in an easterly direction for 1.0s. During this time interval, the block:

acquires a momentum of 1.0 kg * m/s

the COM of a uniform disk of radius R is located

at the center

which of the following statements are true

none of the above

Force:

equals the time rate of change of momentum

A student's life was saved in an automobile accident because an airbag expanded in front of his head. If the car had not been equipped with an airbag, the windshield would have stopped the motion of his head in a much shorter time. Compared to the windshield, the airbag:

exerts a much smaller force

At the same instant that a 0.50-kg ball is dropped from 25m above Earth, a second ball, with a mass of 0.25kg, is thrown straight upward from Earth's surface with an initial speed of 15m/s. They move along nearby lines and pass without colliding. At the end of 2.0s the magnitude of the acceleration of the center of mass of the two-ball system is:

g

Two identical carts travel at 1m/s in opposite directions on a common horizontal surface. They collide head-on and are reported to rebound, each with a speed of 2m/s. Then

if some other form of energy were changed to kinetic during the collision, the report could be true

A 640-N acrobat falls 5.0m from rest into a net. The net tosses him back up with the same speed he had just before he hit the net. The magnitude of the average upward force exerted on him by the net during this collision is:

impossible to determine from given data

A man sits in the back of a canoe in still water. He then moves to the front of the canoe and sits there. Afterwards the canoe:

is rearward of its original position and not moving

The center of mass of a system of particles remains at the same place if:

is rearward of its original position and not moving

A projectile in flight explodes into several fragments. The total momentum of the fragments immediately after this explosion:

is the same as the momentum of the projectile immediately before the explosion

An elastic collision is one in which

kinetic energy and momentum are both conserved

A 64-kg woman stands on frictionless level ice with a 0.10-kg stone at her feet. She kicks the stone with her foot so that she acquires a velocity of 0.0017m/s in the forward direction. The velocity acquired by the stone is:

m/s backward

The physical quantity "impulse" has the same dimensions as that of:

momentum

An inelastic collision is one in which

momentum is conserved but kinetic energy is not conserved

A uniform narrow bar, resting on ice, is given a transverse horizontal impulse J at one end as shown. The center of mass of the bar COM will then:

move in a straight line

A golf ball of mass m is hit by a golf club so that the ball leaves the tee with speed v. The club is in contact with the ball for time T. The magnitude of the average force on the club on the ball during the time T is:

mv/T

The center of mass of Earth's atmosphere is:

near the center of Earth

Whenever an object strikes a stationary object of equal mass:

none of the above

Two objects, P and Q, have the same momentum. Q has more kinetic energy than P if it:

s moving faster than P

the center of mass of the system consisting of Earth, the Sun, and the planet Mars is:

the closer to the Sun than to either of the other bodies

The center of mass of a system of particles has a constant velocity if:

the external forces acting on particles of the system sum to zero

When you step on the accelerator to increase the speed of your car, the force that accelerates the car is:

the force of friction of the road on the tires

the thrust of a rocket

the force of the exiting fuel gases on the rocket

When a particle suffers a head-on elastic collision with another particle, initially at rest, the greatest fraction of kinetic energy is transferred if:

the incident and target particle have the same mass

Two carts (A and B), having spring bumpers, collide as shown. Cart A has a mass of 2kg and is initially moving to the right. Cart B has a mass of 3kg and is initially stationary. When the separation between the carts is a minimum:

the kinetic energy of the system is at a minimum

A thick uniform wire is bent into the shape of the letter "U" as shown. Which point indicates the location of the center of mass of this wire?

the lower dot

A 2.0-kg block is attached to one end of a spring with a spring constant of 100N/m and a 4.0-kg block is attached to the other end. The blocks are placed on a horizontal frictionless surface and set into motion. At one instant the 2.0-kg block is observed to be traveling to the right with a speed of 0.50m/s and the 4.0-kg block is observed to be traveling to the left with a speed of 0.30m/s. Since the only forces on the blocks are the force of gravity, the normal force of the surface, and the force of the spring, we conclude that:

the motion was started with at least one of masses moving

The law of conservation of momentum applies to a system of colliding objects only if

the net external impulse is zero

Sphere X, of mass 2kg, is moving to the right at 10m/s. Sphere Y, of mass 4kg, is moving to the left at 10m/s. The two spheres collide head-on. The magnitude of the impulse of X on Y is

the same as the magnitude of the impulse of Y on X

Two bodies of unequal mass, placed at rest on a frictionless surface, are acted on by equal horizontal forces for equal times. Just after these forces are removed, the body of greater mass will have

the same momentum as the other body

A cart loaded with sand slides forward along a horizontal frictionless track. As the cart moves, sand trickles out at a constant rate through a hole in the back of the cart. The acceleration of the cart is:

zero

A ball hits a wall and rebounds with the same speed, as diagramed below. The changes in the components of the momentum of the ball are:

∆px = 0,∆py > 0

A rifle of mass M is initially at rest but free to recoil. It fires a bullet of mass m and velocity v (relative to the ground). After firing, the velocity of the rifle (relative to the ground) is:

−mv/M

Sphere A has mass m and is moving with velocity v. It makes a head-on elastic collision with a stationary sphere B of mass 2m. After the collision their speeds (vA and vB) are:

−v/3, 2v/3