Chapter 9 physics

A 2.0-kg ball moving eastward at 3.0 m/s suddenly collides with and sticks to a 4.0-kg ball moving northward at 2.0 m/s. What is the magnitude of the momentum of this system just after the collision?

10 kg

If you want to double the momentum of a gas molecule, by what factor must you increase its kinetic energy?

)4

A 3.0-kg mass is located at (0.0 m, 8.0 m), and a 1.0-kg mass is located at (12 m, 0.0 m). You want to add a 4.0-kg mass so that the center of mass (or center of gravity) of the three-mass system will be at the origin. What should be the coordinates of the 4.0-kg mass?

(-3.0 m, -6.0 m)

Three masses are located in the x-y plane as follows: a mass of 6 kg is at (0 m, 0 m), a mass of 4 kg is at (3 m, 0 m), and a mass of 2 kg is at (0 m, 3 m). Where is the center of mass (or center of gravity) of the system?

(1 m, 0.5 m)

The graph in the figure shows the x component F of the net force that acts for 10 s on a 100-kg crate. What is the change in the momentum of the crate during the 10 s that this force acts?

) -75 kg

Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved 12m?

) 28 m

Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. How far has the heavier astronaut moved when the lighter astronaut has moved 12 m?

) 9.0 m

Three objects are moving along a straight line as shown in the figure. Taking the positive direction to be to the right, what is the total momentum of this system?

-14.0 kg

Two air track carts move along an air track towards each other. Cart A has a mass of 450 g and moves toward the right with a speed of 0.850 m/s. Cart B has a mass of 300 g and moves toward the left with a speed of 1.12 m/s. What is the total momentum of the two-cart system?

0.047 kg

A 320-g air track cart traveling at 1.25 m/s suddenly collides elastically with a stationary 270-g cart. What is the speed of the 320-g cart just after the collision?

0.11 m/s

A 2.0-m rope is lying on a table. You pick up one end and start raising it vertically. How high above the table is the center of mass (or center of gravity) of the rope when half of the rope has lifted off the table?

0.25 m

A 0.330-kg volleyball is thrown vertically downward with a speed of 0.150 m/s in a place where g = 9.81 m/s2. It takes it 0.0655 s to reach the ground. What is the magnitude of its momentum just before it hits the ground?

0.262 kg

A 0.140-kg baseball is dropped and reaches a speed of 1.20 m/s just before it hits the ground and bounces. It rebounds with an upward velocity of 1.00 m/s. What is the change of the ball's momentum during the bounce?

0.308 kg

A 0.14-kg baseball is dropped from rest from a height of 2.0 m above the ground. What is the magnitude of its momentum just before it hits the ground if we neglect air resistance?

0.88 kg

A 60.0-kg man stands at one end of a 20.0-kg uniform 10.0-m long board. How far from the man is the center of mass (or center of gravity) of the man-board system?

1.25 m

Three masses, 1.0 kg, 2.0 kg, and 3.0 kg, are located at (0.0 m, 0.0 m), (1.0 m, 1.0 m), 60) and (2.0 m, -2.0 m), respectively. What is the location of the center of mass (or center of gravity) of this system?

1.3 m, -0.67 m)

A 340-g air track cart traveling at 1.25 m/s suddenly collides elastically with a stationary 300-g cart. What is the speed of the 300-g cart just after the collision?

1.33 m/s

A 100-g ball falls from a window that is 12 m above ground level and experiences no significant air resistance as it falls. What is its momentum when it strikes the ground?

1.5 kg

Three small masses are positioned as follows: 2.0 kg at (0.0 m, 0.0 m), 2.0 kg at (2.0 m, 0.0 m), and 4.0 kg at (2.0 m, 1.0 m). Determine the coordinates of the center of mass (or center of gravity) of this system.

1.5 m, 0.50 m)

In a police ballistics test, a 10.0-g bullet moving at 300 m/s is fired into a 1.00-kg block at rest. The bullet goes through the block almost instantaneously and emerges with 50.0% of its original speed. What is the speed of the block just after the bullet emerges?

1.50 m/s

A 0.140-kg baseball is dropped from rest from a height of 2.20 m above the ground and experiences negligible air resistance as it falls. It rebounds to a height of 1.60 m. What change in the ball's momentum occurs as it rebounds from the ground?

1.70 kg

A 0.140-kg baseball is thrown with a velocity of 27.1 m/s.It is struck by the bat with an average force of 5000 N, which results in a velocity of 37.0 m/s in the opposite direction from the original velocity. How long were the bat and ball in contact?

1.79 × 10-3 s

Two vehicles approach a right angle intersection and then suddenly collide. After the collision, they become entangled. If their mass ratios were 1:4 and their respective speeds as they approached the intersection were both 13 m/s, find the magnitude and direction of the final velocity of the wreck.

11 m/s at 76° with respect to the original direction of the lighter car

In a certain nuclear reactor, neutrons suddenly collide with carbon nuclei, which have 12 times the mass of neutrons. In a head-on elastic collision with a stationary carbon nucleus, what fraction of its initial speed does the neutron have after the collision?

11/13

A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together after the collision. What is the speed of the wreckage just after the collision?

12.2 m/

An 8.0-g bullet is suddenly shot into a 4.0-kg block, at rest on a frictionless horizontal surface, as shown in the figure. The bullet remains lodged in the block. The block then moves against a spring and compresses it by 8.9 cm. The force constant (spring constant) of the spring is 1400 N/m. What is the magnitude of the impulse on the block (including the bullet inside) due to the spring during the entire time interval during which the block compresses the spring?

13 N

A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the speed of the cars after collision?

14 m/s

A car heading north suddenly collides at an intersection with a truck of the same mass heading east. If they lock together and travel at 28 m/s at 15° north of east just after the collision, how fast was the car initially traveling?

14 m/s D) 7 m/s

A 328-kg car moving at 19.1 m/s in the +x direction hits from behind a second car moving at 13.0 m/s in the same direction. If the second car has a mass of 790 kg and a speed of 15.1 m/s right after the collision, what is the velocity of the first car after this sudden collision?

14.0 m/s

A 600-kg car makes a 90° turn. Its speed before the turn is 21.0 m/s and after the turn it is 24.0 m/s. What is the magnitude of the change in the car's momentum during the turn?

19.1 × 10^3 kgm/s

In the figure, four point masses are placed as shown. Assume that all the numbers in the figure are accurate to two significant figures. What are the x and y coordinates of the center of mass (or center of gravity) of this arrangement?

2.3 m, 2.8 m)

A 1200-kg cannon suddenly fires a 100-kg cannonball at 35 m/s.What is the recoil speed of the cannon? Assume that frictional forces are negligible and the cannon is fired horizontally.

2.9 m/s

A firecracker breaks up into two pieces, one of which has a mass of 200 g and flies off along the +x-axis with a speed of 82.0 m/s. The second piece has a mass of 300 g and flies off along the +y-axis with a speed of 45.0 m/s. What is the total momentum of the two pieces?

21.2 kg

A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 320-g piece moves along the +x-axis with a speed of 2.00 m/s and a 355-g piece moves along the +y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction relative to the +x-axis does the third piece move?

219.8° from the +x-axis

A 0.140-kg baseball is dropped from rest. It has a speed of 1.20 m/s just before it hits the ground, and it rebounds with an upward speed of 1.00 m/s. The ball is in contact with the ground for 0.0140 s. What is the average force exerted by the ground on the ball during the time of contact?

22.0 N upwards

A 1200-kg pick-up truck traveling south at 15 m/s suddenly collides with a 750-kg car that is traveling east. The two vehicles stick together and slide along the road after colliding. A highway patrol officer investigating the accident determines that the final position of the wreckage after the collision is 25 m, at an angle of 50° south of east, from the point of impact. She also determines that the coefficient of kinetic friction between the tires and the road at that location was 0.40. What was the speed of the car just before the collision?

23 m/s

A fire hose is turned on the door of a burning building in order to knock the door down. This requires a force of 1000 N. If the hose delivers 40 kg of water per second, what is the minimum velocity of the stream needed to knock down the door, assuming the water doesn't bounce back?

25 m/s

Two dogs, Rover and Fido, run on a level frictionless surface. Rover runs eastward with a momentum of 24 kg . m/s, and Fido runs northward with momentum 10 kg . m/s. They make a sudden perfectly inelastic collision. What is the magnitude of their combined momentum after the collision?

26 kg . m/s

An object initially at rest suddenly explodes in two fragments of masses 2.6 kg and 3.3 kg that move in opposite directions. If the speed of the first fragment is 3.6 m/s, find the internal energy of the explosion.

30 J

A very small 51-g steel ball is released from rest and falls vertically onto a steel plate. The ball strikes the plate and is in contact with it for 0.50 ms. The ball rebounds elastically and returns to its original height. The total time interval for a round trip is 3.00 s. What is the magnitude of the average force exerted on the ball by the plate during contact with the plate?

3000 N

A 14-cm diameter champagne bottle rests on its side on top of a frictionless horizontal table. Suddenly, the cork pops and the bottle slides backward, covering a distance of 22.0 cm in 0.44 s. If the mass of the bottle is 500 times the mass of the cork, find the distance from the original position that the cork will land on the table. Neglect air resistance and assume that the cork is very small compared to the bottle.

3000 cm

Ablockofmassm=34kgandspeedVisbehindablockofmassM=81kgandspeed of 0.50 m/s, as shown in the figure. The surface is frictionless and the blocks collide and couple. After the collision, the blocks have a common speed of 0.90 m/s. What is the magnitude of the impulse on the 34-kg block due to the collision?

32 N

A tiger is running in a straight line. If we double both the mass and speed of the tiger, the magnitude of its momentum will increase by what factor?

4

0.10-kg ball, traveling horizontally at 25 m/s, strikes a wall and rebounds at 19 m/s. What is the magnitude of the change in the momentum of the ball during the rebound?

4.4 kg

A golf club exerts an average horizontal force of 1000 N on a 0.045-kg golf ball that is initially at rest on the tee. The club is in contact with the ball for 1.8 ms. What is the speed of the golf ball just as it leaves the tee?

40 m/s

As shown in the figure, a bullet of mass 0.010 kg moving horizontally suddenly strikes a block of wood of mass 1.5 kg that is suspended as a pendulum. The bullet lodges in the wood, and together they swing upward a vertical distance of 0.40 m. The length of the string is 2.0 m. What was the speed of the bullet just before it struck the wooden block?

420 m/s

An 8.0-g bullet is suddenly shot into a 4.0-kg block that is at rest on a frictionless horizontal surface, as shown in the figure. The bullet remains lodged in the block. The block then moves against a spring and compresses it by 3.7 cm. The force constant (spring constant) of the spring is 2500 N/m. What was the initial speed v of the bullet?

460 m/s

A 900-kg car traveling east at 15.0 m/s suddenly collides with a 750-kg car traveling north at 20.0 m/s. The cars stick together after the collision. In what direction does the wreckage move just after the collision?

48.0° N of E

A 1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds fast. What is the speed of these two sea creatures just after their collision? You can neglect any drag effects of the water during the collision.

5.0 m/s

A dinner plate falls vertically to the floor and breaks up into three pieces, which slide horizontally along the floor. Immediately after the impact, a 200-g piece moves along the +x-axis with a speed of 2.00 m/s, a 235-g piece moves along the +y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. What is the speed of the third piece?

5.33 m/s

Astronaut Jennifer's lifeline to her spaceship comes loose and she finds herself stranded, " floating" 100 m from the mothership. She suddenly throws her 2.00-kg wrench at 20 m/s in a direction away from the ship. If she and her spacesuit have a combined mass of 200 kg, how long does it take her to coast back to her spaceship?

500 s

In a police ballistics test, a 2.00-g bullet suddenly hits and becomes embedded in a 5.00-kg wood block which is hanging from a 1.20-m long string. This causes the block to swing through an arc of 3.50°. What was the speed of the bullet just before it hit the block?

524 m/s

A 1500-kg car traveling at 90 km/h toward the east suddenly collides with a 3000-kg car traveling at 60 km/h toward the south. The two cars stick together after the collision. What is the direction of motion of the cars after collision?

53.1° S of E

A golf ball of mass 0.050 kg is at rest on the tee. Just after being struck, it has a velocity of 102 m/s. If the club and ball were in contact for 0.81 ms, what is the average force exerted on the ball by the club?

6.3 kN

Calculate the impulse due to a force of 4.5 N that lasts for 1.4 s.

6.3 kg

A 1200-kg ore cart is rolling at 10.8 m/s across a flat friction-free surface. A crane suddenly drops 858 kg of ore vertically into the cart. How fast does the cart move just after being loaded with the ore?

6.30 m/s

A block of mass m = 3.6 kg, moving on a frictionless surface with a speed vi = 9.3 m/s, makes a sudden perfectly elastic collision with a stationary block of mass M, as shown in the figure. Just after the collision, the 3.6-kg block recoils with a speed of vf = 2.7 m/s.What is the speed V of the other block?

6.6 m/s

A super dart of mass 20 g, traveling at 350 m/s, strikes a steel plate at an angle of 30° with the plane of the plate, as shown in the figure. It bounces off the plate at the same angle but at a speed of 320 m/s. What is the magnitude of the impulse that the plate gives to the bullet?

6.7 N

A 1200-kg car moving at 15.6 m/s suddenly collides with a stationary car of mass 1500 kg. If the two vehicles lock together, what is their combined velocity immediately after the collision?

6.9 m/s

1000-kg whale swims horizontally to the right at a speed of 6.0 m/s. It suddenly collides directly with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds fast. What is the momentum of these two sea creatures just after their collision? You can neglect any drag effects of the water during the collision.

6000 kg

A batter hits a foul ball. The 0.14-kg baseball that was approaching him at 40 m/s leaves the bat at 30 m/s in a direction perpendicular to the line between the batter and the pitcher. What is the magnitude of the impulse delivered to the baseball?

7.0 N

A 900-kg car traveling 30.0° south of east at 12.0 m/s suddenly collides with a 750-kg car traveling north at 17.0 m/s. The cars stick together after colliding. What is the speed of the wreckage just after the collision?

7.21 m/s

A block of mass m = 4.4 kg, moving on frictionless surface with a speed vi = 9.2 m/s, makes a sudden perfectly elastic collision with a second block of mass M, as shown in the figure. The second block is originally at rest. Just after the collision, the 4.4-kg block recoils with a speed of vf = 2.5 m/s. What is the mass M of the second block?

7.7 kg

In a certain nuclear reactor, neutrons suddenly collide with deuterons, which have twice the mass of neutrons. In a head-on elastic collision with a stationary deuteron, what fraction of the initial kinetic energy of a neutron is transferred to the deuteron?

8-9

A steady horizontal force lasting for 2.1 s gives a 1.25 kg object an acceleration of 3.2 m/s2 on a frictionless table. What impulse does this force give to the object?

8.4 kg

Ablockofmassm= 9.0 kg and speed V and is behind a block of mass M = 27 kg and speed of 0.50 m/s, as shown int the figure. The surface is frictionless, and the blocks suddenly collide and couple. After the collision, the blocks have a common speed of 0.90 m/s. How much kinetic energy of the blocks is lost due to the collision?

8.6 J

A girl of mass 55 kg throws a ball of mass 0.80 kg against a wall. The ball strikes the wall horizontally with a speed of 25 m/s, and it bounces back with this same speed. The ball is in contact with the wall 0.050 s. What is the magnitude of the average force exerted on the wall by the ball?

800 N

A puck with a mass m1 = 50 g moving at 1.0 m/s approaches a stationary puck with a mass m2 = 100 g on a frictionless air table, and they undergo a sudden two-dimensional elastic collision. After the collision, both pucks have identical speeds, but travel in different directions. What is the angle between the original and final paths of puck with mass m1?

90°

You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You have two choices about what to do with the ball: either catch the ball or deflect it back toward your friend with the same speed as it was originally thrown. Which choice should you make in order to maximize your speed on the skateboard?

Deflect the ball back.

If you want to double the kinetic energy of a gas molecule, by what factor must you increase its momentum?

Square root of 2

A firecracker explodes in midair and breaks up into many fragments. Which of the following statements are true regarding conditions immediately before and immediately after the explosion? I. The total momentum of the fragments is equal to the original momentum of the firecracker. II. The total kinetic energy of the fragments is equal to the original kinetic energy of the firecracker.

Statement I only

A 5-kg ball collides inelastically head-on with a 10-kg ball, which is initially stationary. Which of the following statements is true? (There could be more than one correct choice.)

The magnitude of the change of the momentum of the 5-kg ball is equal to the magnitude of the change of momentum of the 10-kg ball. AND The magnitude of the change of velocity the 5-kg ball experiences is greater than that of the 10-kg ball.

A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the momentum during the collision are correct? (There could be more than one correct choice.)

The momentum of the car-truck system is conserved, but the momentum of each one separately is not conserved.

A rocket explodes into two fragments, one 25 times heavier than the other. The magnitude of the momentum change of the lighter fragment is

The same as the momentum change of the heavier fragment.

A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the magnitude of the average force during the collision is correct?

The small car and the truck experience the same average force.

A small car meshes with a large truck in a head-on collision. Which of the following statements concerning the magnitude of the momentum change during the collision is correct? (There could be more than one correct choice.)

The small car and the truck experience the same magnitude momentum change.

Three cars, car X, car Y, and car Z, begin accelerating from rest at the same time. Car X is more massive than car Y, which is more massive than car Z. The net accelerating force exerted on each car is identical. After 10 seconds, which car has the most amount of momentum?

They all have the same amount of momentum.

In a collision between two unequal masses, which mass receives a greater magnitude impulse?

They receive equal impulses.

In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is

completely inelastic.

In a game of pool, the white cue ball hits the #5 ball and stops, while the #5 ball moves away with the same velocity as the cue ball had originally. Both balls have the same mass. This type of collision is

elastic

Identical forces act for the same length of time on two different objects. The magnitude of the change in momentum of the lighter object is

exactly equal to the magnitude of the change in momentum of the larger mass.

The momentum of an isolated system is conserved

in both elastic and inelastic collisions

A railroad car collides with and sticks to an identical railroad car that is initially at rest. After the collision, the kinetic energy of the system

is half as much as before.

Which of the following quantities are units of impulse? (There could be more than one correct choice.)

kg

Which of the following quantities are units of momentum? (There could be more than one correct choice.)

kg

) If a quantity you calculated had units of kg

momentum AND impulse

In the figure showing an isolated system, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is

not possible because momentum is not conserved.

An egg falls from a bird's nest in a tree and feels no effects due to the air. As it falls,

only its mechanical energy is conserved.

On a horizontal frictionless air table, a puck runs into an ideal horizontal spring that is fastened to the table. The puck compresses the spring by 15 cm before coming to rest.

only the mechanical energy (kinetic plus potential) of the puck

In the figure, determine the character of the collision. The masses of the blocks, and the velocities before and after, are shown. The collision is

perfectly elastic.

Two friends are standing on opposite ends of a canoe that is initially at rest with respect to a frictionless lake. The person in the front throws a very massive ball toward the back, and the person in the back catches it. After the ball is caught, the canoe is

stationary

A rubber ball and a lump of clay have equal mass. They are thrown with equal speed against a wall. The ball bounces back with nearly the same speed with which it hit. The clay sticks to the wall. Which one of these objects experiences the greater momentum change?

the ball

A rubber ball bounces off of a wall with an initial speed v and reverses its direction so its speed is v right after the bounce. As a result of this bounce, which of the following quantities of the ball are conserved? (There could be more than one correct choice.)

the kinetic energy of the ball

Two objects of different masses have momentum of equal, non-zero magnitude. Which object has more kinetic energy?

the lighter object

During World War I, Germany used a "Big Bertha" cannon to hurl shells into Paris 30 miles away. This gun also had a very long barrel. What was the reason for using a long barrel in these guns?

to allow the force of the expanding gases from the gunpowder to act for a longer time