Question 1

Three masses are positioned along the x-axis. Their masses and positions are:  with  ,  with  , and  with  . What is the x-coordinate of center of mass of this system?

Accepted Answer

The answer of Three masses are positioned along the x-axis....

Question 2

In an inelastic collision between two objects with unequal masses:

Accepted Answer

In an inelastic collision, the total momentum of the system is conserved, but not the kinetic energy. The kinetic energy is converted into other forms of energy, such as heat or sound. In a collision between two objects with unequal masses, the momentum of the lighter object will increase by the amount that the momentum of the heavier object decreases, because momentum is conserved. Therefore, choice B is correct. Choices A and C are incorrect because they refer to changes in velocity or energy, which are not conserved in an inelastic collision. Choice D is incorrect because the total momentum of the system is conserved, as stated above.

Question 3

A lump of clay is thrown at a wall. A rubber ball of identical mass is thrown with the same speed toward the same wall. Which statement is true?

Accepted Answer

The change in momentum is equal to the initial momentum minus the final momentum. The final momentum for both the clay and the ball is zero, as they both come to rest against the wall. Therefore, the change in momentum is equal to the initial momentum.

Since both the clay and the ball have the same initial speed and mass, they have the same initial momentum. Therefore, they both experience the same change in momentum. Thus, option C is incorrect.

However, the question is asking which object experiences a greater change in momentum, not whether they have the same change in momentum. Since both objects have the same mass and the same initial speed, the only thing that can cause a difference in the change in momentum is the time of contact with the wall.

A ball is more elastic than clay, meaning that it will deform less upon contact with the wall and will rebound more. Therefore, the contact time will be shorter, resulting in a greater force being exerted on the ball and thus a greater change in momentum.

On the other hand, clay is less elastic and will deform more upon contact with the wall, resulting in a longer contact time and a smaller force being exerted on it. Therefore, the change in momentum will be smaller for the clay.

Therefore, option B is correct.

Question 4

A cannon of mass 1500 kg fires a 10-kg shell with a velocity of 200 m/s at an angle of 30  $\degree$ above the horizontal. Find the recoil velocity of the cannon across the level ground.

Accepted Answer

Explanation:Momentum before firing = 0Momentum after firing = (1500 kg) v + (10 kg) (200 m/s) cos 30°By the law of conservation of momentum,0 = (1500 kg) v + (10 kg) (200 m/s) cos 30°v = (10 kg) (200 m/s) cos 30° / (1500 kg)v = 1.15 m/s

Question 5

Popeye, of mass 70 kg, has just downed a can of spinach. He accelerates quickly and stops Bluto, of mass 700 kg (Bluto is very dense), who is charging in at 5.0 m/s. What was Popeye's remarkable speed?

Accepted Answer

The answer of Popeye, of mass 70 kg, has just...

Question 6

A miniature, spring-loaded, radio-controlled gun is mounted on an air puck. The gun's bullet has a mass of 5.00 g, and the gun and puck have a combined mass of 130 g. With the system initially at rest, the radio-controlled trigger releases the bullet, causing the puck and empty gun to move with a speed of 0.500 m/s. Of the total kinetic energy of the gun-puck-bullet system, what percentage is in the bullet?

Accepted Answer

First, we can use conservation of momentum to find the velocity of the bullet after it is fired:

m_bullet*v_bullet = (m_gun + m_puck)*v_system

where v_system is the velocity of the gun-puck system after the bullet is fired. Plugging in the given values:

0.005 kg * v_bullet = 0.130 kg * 0.500 m/s

v_bullet = 6.5 m/s

Now, we can use conservation of energy to find the percentage of the total kinetic energy that is in the bullet:

0.5 * 0.130 kg * (0.500 m/s)^2 = 0.5 * 0.005 kg * (6.5 m/s)^2 + 0.5 * 0.125 kg * (0.500 m/s)^2

The first term on the right-hand side is the kinetic energy of the bullet, and the second term is the kinetic energy of the gun-puck system. Simplifying:

0.01625 J = 0.01625 J + 0.03125 J

So all the kinetic energy is in the bullet, which means the percentage of the total kinetic energy that is in the bullet is 100%. Answer B is correct.

Question 7

A miniature spring-loaded, radio-controlled gun is mounted on an air puck. The gun's bullet has a mass of 5.00 g, and the gun and puck have a combined mass of 130 g. With the system initially at rest, the radio controlled trigger releases the bullet causing the puck and empty gun to move with a speed of 0.500 m/s. What is the bullet's speed?

Accepted Answer

We can use conservation of momentum to solve the problem. Initially, the momentum of the system is zero since it is at rest. After the bullet is released, the momentum of the system is:
p = (m_bullet)(v_bullet) + (m_gun+puck)(v_system)
where v_system is the velocity of the puck and gun after the bullet is released. We know that v_system = 0.500 m/s, m_bullet = 5.00 g = 0.00500 kg, and m_gun+puck = 130 g = 0.130 kg. Solving for v_bullet, we get:
v_bullet = (p - m_gun+puck*v_system)/(m_bullet)
Plugging in the values, we get:
v_bullet = [(0.00500 kg)(-0.500 m/s) - (0.130 kg)(0.500 m/s)]/(0.00500 kg) = 13.0 m/s
Therefore, the bullet's speed is 13.0 m/s, which corresponds to choice B.

Question 8

A 6-kg object is moving to the right at 4 m/s and collides with a 4-kg object moving to the left at 6 m/s. The objects collide and stick together. After the collision, the combined object:

Accepted Answer

During the collision, kinetic energy is not conserved due to the deformation of the objects. Instead, the kinetic energy is converted to other forms of energy such as sound or heat. Therefore, after the collision, the combined object will have no kinetic energy. Additionally, momentum must be conserved in the collision, so the total momentum of the system before and after the collision will be the same. Thus, the combined object will have the same momentum as the individual objects before the collision.

Question 9

A 4.0 ft by 8.0 ft sheet of plywood of uniform density and thickness lies in the 1^st quadrant with its long side along the x axis, one corner at the origin, and the diagonally opposite corner at position (x, y) = (8.0 ft, 4.0 ft). The lower right 2.0 ft by 4.0 ft quarter of the sheet is removed from the sheet. What are the coordinates of the center of mass of the remaining portion of the sheet?

Accepted Answer

The answer of A 4.0 ft by 8.0 ft sheet...

Question 10

Three satellites are launched into space connected together. Once in deep space, an explosive charge separates the three satellites and they move apart. The satellites each have different masses with m₁ < m₂ < m₃. Which of the following statements is always true?

Accepted Answer

The answer of Three satellites are launched into space connected...

Question 11

A machine gun is attached to a railroad flatcar that rolls with negligible friction. If the railroad car has a mass of 6.25 * 10⁴ kg, how many bullets of mass 25 g would have to be fired at 250 m/s off the back to give the railroad car a forward velocity of 0.3 m/s?

Accepted Answer

The answer of A machine gun is attached to a...

Question 12

A 90-kg halfback running north with a speed of 10 m/s is tackled by a 120-kg opponent running south at 5.0 m/s. The collision is perfectly inelastic. Compute the velocity of the two players just after the tackle.

Accepted Answer

Using the conservation of momentum in the horizontal direction, we have:

(90 kg)(10 m/s) + (120 kg)(-5.0 m/s) = (90 kg + 120 kg)vf

Solving for vf, we get:

vf = [(90 kg)(10 m/s) + (120 kg)(-5.0 m/s)] / (90 kg + 120 kg) = 1.4 m/s north

Since the collision is perfectly inelastic, the two players will move together at a velocity of 1.4 m/s north. Therefore, the correct answer is D.

Question 13

During a snowball fight, two balls with masses of 0.4 and 0.6 kg, respectively, are thrown in such a manner that they meet head-on and combine to form a single mass. The magnitude of initial velocity for each is 20 m/s. What is the speed of the 1.0-kg mass immediately after collision?

Accepted Answer

First, we need to find the total momentum of the system before the collision. We know that both snowballs have the same initial velocity of 20 m/s in opposite directions, so their total momentum is:

p(before) = mv1 + mv2 = (0.4 kg)(20 m/s) + (0.6 kg)(-20 m/s) = 0 kg*m/s

(Note that we use a negative sign for the second term because the second snowball is moving in the opposite direction.)

After the collision, the two snowballs stick together and combine to form a single snowball with mass 1.0 kg. We can use the law of conservation of momentum to find the velocity of this new snowball:

p(before) = p(after)
0 kg*m/s = (1.0 kg)v(after)

So the velocity of the 1.0-kg mass immediately after the collision is:

v(after) = 0 m/s

This means that the snowballs collided and stopped moving after they combined. However, we can also find the kinetic energy of the system before and after the collision to confirm that energy is conserved:

KE(before) = (1/2)mv1^2 + (1/2)mv2^2 
= (1/2)(0.4 kg)(20 m/s)^2 + (1/2)(0.6 kg)(-20 m/s)^2  
= 80 J

KE(after) = (1/2)mv(after)^2 
= (1/2)(1.0 kg)(0 m/s)^2 
= 0 J

As we can see, the kinetic energy of the system is conserved (since KE(before) = KE(after) = 0 J), which confirms that our answer of v(after) = 0 m/s is correct.

Question 14

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?

Accepted Answer

The answer of A 20-g bullet moving at 1000 m/s...

Question 15

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. If the block had been originally at rest and is free to move, what is its resulting speed?

Accepted Answer

Conservation of momentum can be applied to this problem:
mv = (m+M)V
where m is the mass of the bullet, v is the initial speed of the bullet, M is the mass of the block, and V is the final speed of the block. Solving for V, we get:
V = mv/(m+M)
Plugging in the given values, we get:
V = (0.02 kg x 1000 m/s)/(0.02 kg + 1 kg) = 16.67 m/s
Therefore, the resulting speed of the block is approximately 16 m/s, which corresponds to choice C.

Question 16

A "double satellite" is launched into space. It consists of a satellite of mass m and another satellite of mass 5m. The connecting mechanism of these satellites is an explosive bolt and a compressed spring, both of negligible mass. The bolt is exploded and the satellites drift apart having been pushed by the spring. When the less massive satellite has moved a distance of 2.5 m from the center of mass of the double satellite, how far away from it is the satellite of greater mass?

Accepted Answer

Explanation:The center of mass of the system remains at rest. So, the total momentum of the system is zero. Therefore, the momentum of the less massive satellite is equal to the momentum of the greater massive satellite.$$(5m)v_1=mv_2$$$$v_2=5v_1$$$$2.5=5d_2$$$$d_2=0.5m$$

Question 17

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. What is the change in the kinetic energy of the bullet-block system as a result of the collision assuming the block is free to move?

Accepted Answer

The answer of A 20-g bullet moving at 1000 m/s...

Question 18

A 70-kg man is standing in a 20-kg boat. Thinking he is stepping out onto the dock, the man steps to the right. However, the following will actually happen (ignore the friction of the water or air on the boat or the man):

Accepted Answer

According to Newton's third law of motion, every action has an equal and opposite reaction. When the man steps to the right, he exerts a force on the boat towards the left. As a result, the boat moves towards the left, but with a smaller acceleration compared to that of the man due to its larger mass. Therefore, the man only moves a short distance to the right while the boat moves a larger distance to the left.

Question 19

A railroad freight car, mass 15,000 kg, is allowed to coast along a level track at a speed of 2.0 m/s. It collides and couples with a 60,000-kg loaded second car, initially at rest and with brakes released. What percentage of the initial kinetic energy of the 15,000-kg car is preserved in the two-coupled cars after collision?

Accepted Answer

The answer of A railroad freight car, mass 15,000 kg,...

Question 20

If a two-body collision is not head-on, then we may always assume that:

Accepted Answer

In any collision, momentum must be conserved. Kinetic energy, however, is only conserved in perfectly elastic collisions. In a collision that is not head-on, some kinetic energy may be lost to rotational motion or deformation of the objects involved, making it an inelastic collision. Therefore, we cannot assume that kinetic energy is conserved.

Quiz 7: Momentum, Impulse, and Collisions

Three masses are positioned along the x-axis. Their masses and positions are: with , with , and with . What is the x-coordinate of center of mass of this system?

In an inelastic collision between two objects with unequal masses:

A lump of clay is thrown at a wall. A rubber ball of identical mass is thrown with the same speed toward the same wall. Which statement is true?

A cannon of mass 1500 kg fires a 10-kg shell with a velocity of 200 m/s at an angle of 30 $\degree$ above the horizontal. Find the recoil velocity of the cannon across the level ground.

Popeye, of mass 70 kg, has just downed a can of spinach. He accelerates quickly and stops Bluto, of mass 700 kg (Bluto is very dense) , who is charging in at 5.0 m/s. What was Popeye's remarkable speed?

A 6-kg object is moving to the right at 4 m/s and collides with a 4-kg object moving to the left at 6 m/s. The objects collide and stick together. After the collision, the combined object:

Three satellites are launched into space connected together. Once in deep space, an explosive charge separates the three satellites and they move apart. The satellites each have different masses with m₁ < m₂ < m₃. Which of the following statements is always true?

A machine gun is attached to a railroad flatcar that rolls with negligible friction. If the railroad car has a mass of 6.25 * 10⁴ kg, how many bullets of mass 25 g would have to be fired at 250 m/s off the back to give the railroad car a forward velocity of 0.3 m/s?

A 90-kg halfback running north with a speed of 10 m/s is tackled by a 120-kg opponent running south at 5.0 m/s. The collision is perfectly inelastic. Compute the velocity of the two players just after the tackle.

During a snowball fight, two balls with masses of 0.4 and 0.6 kg, respectively, are thrown in such a manner that they meet head-on and combine to form a single mass. The magnitude of initial velocity for each is 20 m/s. What is the speed of the 1.0-kg mass immediately after collision?

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. If the block had been originally at rest and is free to move, what is its resulting speed?

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. What is the change in the kinetic energy of the bullet-block system as a result of the collision assuming the block is free to move?

A 70-kg man is standing in a 20-kg boat. Thinking he is stepping out onto the dock, the man steps to the right. However, the following will actually happen (ignore the friction of the water or air on the boat or the man) :

If a two-body collision is not head-on, then we may always assume that:

Quiz 7: Momentum, Impulse, and Collisions

Three masses are positioned along the x-axis. Their masses and positions are: with , with , and with . What is the x-coordinate of center of mass of this system?

In an inelastic collision between two objects with unequal masses:

A lump of clay is thrown at a wall. A rubber ball of identical mass is thrown with the same speed toward the same wall. Which statement is true?

A cannon of mass 1500 kg fires a 10-kg shell with a velocity of 200 m/s at an angle of 30 °\degree° above the horizontal. Find the recoil velocity of the cannon across the level ground.

Popeye, of mass 70 kg, has just downed a can of spinach. He accelerates quickly and stops Bluto, of mass 700 kg (Bluto is very dense) , who is charging in at 5.0 m/s. What was Popeye's remarkable speed?

A 6-kg object is moving to the right at 4 m/s and collides with a 4-kg object moving to the left at 6 m/s. The objects collide and stick together. After the collision, the combined object:

Three satellites are launched into space connected together. Once in deep space, an explosive charge separates the three satellites and they move apart. The satellites each have different masses with m1 < m2 < m3. Which of the following statements is always true?

A machine gun is attached to a railroad flatcar that rolls with negligible friction. If the railroad car has a mass of 6.25 * 104 kg, how many bullets of mass 25 g would have to be fired at 250 m/s off the back to give the railroad car a forward velocity of 0.3 m/s?

A 90-kg halfback running north with a speed of 10 m/s is tackled by a 120-kg opponent running south at 5.0 m/s. The collision is perfectly inelastic. Compute the velocity of the two players just after the tackle.

During a snowball fight, two balls with masses of 0.4 and 0.6 kg, respectively, are thrown in such a manner that they meet head-on and combine to form a single mass. The magnitude of initial velocity for each is 20 m/s. What is the speed of the 1.0-kg mass immediately after collision?

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. What is the kinetic energy of the block that results from the collision if the block had not been moving prior to the collision and was free to move?

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. If the block had been originally at rest and is free to move, what is its resulting speed?

A 20-g bullet moving at 1000 m/s is fired through a one-kg block of wood emerging at a speed of 200 m/s. What is the change in the kinetic energy of the bullet-block system as a result of the collision assuming the block is free to move?

A 70-kg man is standing in a 20-kg boat. Thinking he is stepping out onto the dock, the man steps to the right. However, the following will actually happen (ignore the friction of the water or air on the boat or the man) :

If a two-body collision is not head-on, then we may always assume that:

A cannon of mass 1500 kg fires a 10-kg shell with a velocity of 200 m/s at an angle of 30 $\degree$ above the horizontal. Find the recoil velocity of the cannon across the level ground.

Three satellites are launched into space connected together. Once in deep space, an explosive charge separates the three satellites and they move apart. The satellites each have different masses with m₁ < m₂ < m₃. Which of the following statements is always true?

A machine gun is attached to a railroad flatcar that rolls with negligible friction. If the railroad car has a mass of 6.25 * 10⁴ kg, how many bullets of mass 25 g would have to be fired at 250 m/s off the back to give the railroad car a forward velocity of 0.3 m/s?