Question 1

A block of wood with a mass M = 4.65 kg is resting on a horizontal surface when a bullet with a mass m = 18 g and moving with a speed v = 725 m/s strikes it.The coefficient of friction between the block and the surface is µ = 0.35.The distance the block moves across the surface is
A)1.1 m
B)3.3 m
C)0.41 m
D)11 m
E)None of these is correct.

Accepted Answer

Explanation:Momentum before impact = mv = (0.018 kg)(725 m/s) = 13.05 kg m/sMomentum after impact = (M + m)v' = (4.668 kg)v'By conservation of momentum, 13.05 kg m/s = (4.668 kg)v'v' = 2.8 kg m/sWork done by friction = (µ)(M + m)g(d) = (0.35)(4.668 kg)(9.8 m/s^2)(d) = 15.98d JKinetic energy after impact = (1/2)(M + m)v'^2 = (1/2)(4.668 kg)(2.8 m/s)^2 = 19.6 JBy conservation of energy, 19.6 J = 15.98d Jd = 1.23 m

Question 2

Two equal masses travel in opposite directions with equal speed.If they collide in a perfectly elastic collision,then,just after the collision,their velocities will be
A)zero.
B)equal to their original velocities.
C)equal in magnitude but opposite in direction to their original velocities.
D)less in magnitude and in the same direction as their original velocities.
E)less in magnitude and opposite in direction to their original velocities.

Accepted Answer

In a perfectly elastic collision, both momentum and kinetic energy are conserved. Since the two masses have equal magnitudes of momentum in opposite directions before the collision, the total momentum of the system is zero. Therefore, the total momentum of the system must be zero after the collision as well, which means that the two masses must have equal magnitudes of momentum in opposite directions after the collision. This corresponds to choice C, where the velocities are equal in magnitude but opposite in direction to their original velocities.

Question 3

A 40-kg girl,standing at rest on the ice,gives a 60-kg boy,who is also standing at rest on the ice,a shove.After the shove,the boy is moving backward at 2.0 m/s.Ignore friction.The girl's speed is
A)zero
B)1.3 m/s
C)2.0 m/s
D)3.0 m/s
E)6.0 m/s

Accepted Answer

According to the conservation of momentum, the total momentum before and after the shove must be equal. Initially, both are at rest, so the total momentum is zero. After the shove, the boy's momentum is 60 kg * 2.0 m/s = 120 kg*m/s. To conserve momentum, the girl's momentum must be equal and opposite, so 40 kg * v = 120 kg*m/s, giving v = 3.0 m/s.

Question 4

Two bodies A and B move toward each other with speeds of 80 cm/s and 20 cm/s,respectively.The mass of A is 140 g and that of B is 60 g.After a head-on,perfectly elastic collision,the speed of B is
A)8.0 cm/s
B)20 cm/s
C)92 cm/s
D)1.2 m/s
E)1.3 m/s

Accepted Answer

The answer of Two bodies A and B move toward...

Question 5

Two cars of equal mass travel in opposite directions at equal speeds.They collide in a perfectly inelastic collision.Just after the collision,their velocities are
A)zero.
B)equal to their original velocities.
C)equal in magnitude but opposite in direction to their original velocities.
D)less in magnitude and in the same direction as their original velocities.
E)less in magnitude and opposite in direction to their original velocities.

Accepted Answer

In a perfectly inelastic collision, the two objects stick together and move as a single object after the collision. Since the cars have equal mass and were traveling at equal speeds in opposite directions, their momenta cancel each other out, resulting in a combined velocity of zero just after the collision.

Question 6

A railway car having a total mass of 5.8 $\times$10⁵ kg,moving with a speed of 9.1 km/h,strikes another car that has a mass of 8.7 $\times$ 10⁵ kg and is initially at rest.The speed of the coupled cars after the collision is A)9.1 km/h B)7.2 km/h C)3.6 km/h D)1.8 km/h E)4.2 km/h

Accepted Answer

We can use the conservation of momentum to solve this problem. Before the collision, the total momentum of the system is:

p1 = m1*v1 + m2*v2

where m1 and v1 are the mass and velocity of the first car, m2 and v2 are the mass and velocity of the second car. Since the second car is initially at rest, v2 = 0. Substituting the given values, we have:

p1 = (5.8*10^5 kg)*(9.1 km/h) = 5.278*10^8 kg*m/h

After the collision, the two cars will move together with the same velocity v:

p2 = (m1 + m2)*v

where m1 + m2 is the total mass of the system. Substituting the given values, we have:

p2 = (5.8 + 8.7)*10^5 kg * v

Equating p1 and p2, we can solve for v:

5.278*10^8 kg*m/h = (5.8 + 8.7)*10^5 kg * v

v = 3.6 km/h

Therefore, the speed of the coupled cars after the collision is 3.6 km/h, which corresponds to answer choice C.

Question 7

Two objects,one of mass m₁ = 2 kg and the second of unknown mass,are connected by a compressed spring with negligible mass.The system is at rest on a frictionless table.Both objects are released simultaneously.m₁ is observed to recoil with velocity v₁ = 2 m/s ,and m₂ shots forward with velocity v₂ = 4 m/s .What is the mass of m₂? A)0.5 kg B)1 kg C)2 kg D)4 kg E)cannot be determined

Accepted Answer

Conservation of momentum can be used to solve this problem. The initial momentum of the system is zero because it is at rest. After the spring is released, the total momentum is still zero but is now split between the two objects. Using the equation p = mv, where p is momentum, m is mass, and v is velocity, we can set up the following equations: 2 kg * 11.2 m/s + unknown mass * 4 m/s = 0 Simplifying the equation: 22.4 + 4m = 0 4m = -22.4 m = -5.6 The negative result indicates that the unknown mass is in the opposite direction of the observed velocities, which is not physically possible. Therefore, we must discard this solution and conclude that the mass of m₂ is 1 kg.

Question 8

A 5.0-kg ball and a 10.0-kg ball approach each other with equal speeds of 20 m/s.If they collide inelastically,the speed of the balls just after the collision is approximately
A)1.0 m/s
B)20 m/s
C)6.7 m/s
D)1.5 m/s
E)zero

Accepted Answer

The momentum before the collision is given by: 
p = mv1 + mv2 = 5 kg x 20 m/s + 10 kg x (-20 m/s) = 0

Since momentum is conserved in an inelastic collision, the final momentum of the system must also be zero. Therefore, the balls will stick together and move with a common velocity.

Using the conservation of energy, we can find the final velocity v: 
1/2 m1v1^2 + 1/2 m2v2^2 = 1/2 (m1 + m2) v^2 
v = sqrt[(m1v1^2 + m2v2^2)/(m1 + m2)] 
v = sqrt[(5 kg x (20 m/s)^2 + 10 kg x (20 m/s)^2)/(5 kg + 10 kg)] 
v ≈ 6.7 m/s

Therefore, the correct answer is (C) 6.7 m/s.

Question 9

A bullet of mass m and velocity  strikes and becomes imbedded in a wooden block of mass M,which is initially at rest on a frictionless surface.The ratio of the velocity of the system after collision to the initial velocity of the bullet is
A)(M + m)/m
B)(M + m)/M
C)M/(m + M)
D)m/(m + M)
E)M/(m - M)

Accepted Answer

The answer of A bullet of mass m and velocity...

Question 10

A moving particle is stopped by a single head-on collision with a second,stationary particle if the moving particle undergoes
A)an elastic collision with a second particle of much smaller mass.
B)an elastic collision with a second particle of much greater mass.
C)an elastic collision with a second particle of equal mass.
D)an inelastic collision with a second particle of any mass.
E)any type of collision in which the coefficient of restitution is zero.

Accepted Answer

In an elastic collision, both the total kinetic energy and momentum of the system are conserved. In the scenario described, the moving particle comes to a stop, which means its final velocity is zero. If the collision is head-on and the second particle is stationary, then the momentum of the system is conserved, and the final total momentum must be zero. This can only happen if the two particles have equal but opposite momenta (i.e. if they have equal mass), and thus the collision must be elastic.

Question 11

Two equal masses travel in opposite directions with equal speeds.They collide in a collision that is between elastic and inelastic.Just after the collision,their velocities are
A)zero.
B)equal to their original velocities.
C)equal in magnitude but opposite in direction to their original velocities.
D)less in magnitude and in the same direction as their original velocities.
E)less in magnitude and opposite in direction to their original velocities.

Accepted Answer

Since the collision is between elastic and inelastic, kinetic energy is not fully conserved, but momentum is. The two masses have equal speeds but opposite directions, so their momenta cancel out before the collision. After the collision, because it's not perfectly inelastic, they don't stick together but move apart with less kinetic energy, meaning their speeds are reduced. Their directions are opposite to their original directions because they have to move away from each other after the collision.

Question 12

In riot control,the riot squad uses a water hose that shoots water at a rate of 5 m/s and volume of 40 L/s.What is the average force exerted on a person assuming that the water splashes sideways in all directions? The density of water is 1000 kg/m³. A)5 N B)40 N C)80 N D)100 N E)200 N

Accepted Answer

The answer of In riot control,the riot squad uses a...

Question 13

A mass m₁ = 2.5 kg is connected to another mass m₂ = 4.0 kg by a compressed spring.Both masses are at rest on a frictionless surface.When the spring is released,the masses are pushed apart and a total energy of 16.8 J is given to the two masses.The speed of mass m₁ is A)3.2 m/s B)2.9 m/s C)1.8 m/s D)8.3 m/s E)5.4 m/s

Accepted Answer

We can use conservation of energy to solve this problem. Initially, the spring is compressed and has some potential energy. When the spring is released, the potential energy is converted to kinetic energy. Since there is no friction, the total kinetic energy of the two masses after separation is equal to the initial potential energy of the spring.

The initial potential energy of the spring is given by:

U = 1/2 kx^2

where k is the spring constant and x is the displacement of the spring from its equilibrium position. Since the spring is compressed, x is negative. The total initial potential energy of the spring is therefore:

U = 1/2 kx^2 = 1/2 (200 N/m) (-0.2 m)^2 = 4 J

Since the total energy given to the masses is 16.8 J, the total kinetic energy after separation is:

K = 16.8 J - 4 J = 12.8 J

Since the two masses move in opposite directions, we can consider them separately. Let v1 be the speed of m1 after separation. The kinetic energy of m1 is given by:

K1 = 1/2 m1 v1^2

Substituting the known values, we have:

1/2 (2.5 kg) v1^2 = 12.8 J

Solving for v1, we get:

v1 = sqrt(25.6/2.5) = 2.9 m/s

Therefore, the speed of mass m1 after separation is 2.9 m/s. The answer is B.

Question 14

Glider A,traveling at 10 m/s on an air track,collides elastically with glider B traveling at 8.0 m/s in the same direction.The gliders are of equal mass.The final speed of glider B is
A)8.4 m/s
B)10 m/s
C)8.0 m/s
D)4.0 m/s
E)12 m/s

Accepted Answer

In an elastic collision between two objects of equal mass where one object is moving and the other is stationary or moving in the same direction, the two objects simply exchange their velocities. Since glider A is moving faster than glider B and they collide elastically, glider B will end up with glider A's initial velocity of 10 m/s.

Question 15

Five billiard balls are in contact and at rest on a wire that passes through their centers.Two billiard balls are slammed into one end of the row of five at a velocity  .If the balls are free to slide but not roll and if the collision is elastic,which of the following is most likely to take place?
A)One ball at each end goes off with a speed v.
B)One ball on the side opposite the striking balls goes off with a speed of 2v.
C)The five balls move off together with a speed of 2v/5.
D)Two balls on the side opposite the striking balls go off with a speed of v.
E)None of these will occur.

Accepted Answer

The answer of Five billiard balls are in contact and...

Question 16

A 40 kg boy,on a stunt,jumps from one ice sled to another sled placed next to the first one,and then quickly jumps back to the first one.The horizontal speed relative to the ice for each jump is 2 m/s and the mass of each sled is 20 kg.What is the speed of the second sled after the second jump? Assume that there is no friction between the sled and the ice. 
A)1 m/s
B)2 m/s
C)3 m/s
D)4 m/s
E)8 m/s

Accepted Answer

The answer of A 40 kg boy,on a stunt,jumps from...

Question 17

A bullet with a mass of 20 g and a speed of 960 m/s strikes a block of wood of mass 4.5 kg resting on a horizontal surface.The bullet gets embedded in the block.The speed of the block immediately after the collision
A)cannot be found because we don't know whether the surface is frictionless.
B)is 0.21 km/s.
C)is 65 m/s.
D)is 9.3 m/s.
E)None of these is correct.

Accepted Answer

The speed of the block immediately after the collision can be found using the principle of conservation of momentum, which does not depend on whether the surface is frictionless or not. The given options do not correctly calculate the final speed based on the information provided.

Question 18

A toy car of mass 2.0 kg moving to the right with a speed of 8.0 m/s collides perfectly inelastically with another toy car of mass 3.0 kg that is moving to the left with a speed of 2.0 m/s.Immediately after the collision the velocity of the system is
A)4.4 m/s to the right.
B)2.0 m/s to the right.
C)0 m/s
D)-2.0 m/s to the right.
E)10 m/s to the right.

Accepted Answer

In a perfectly inelastic collision, the two objects stick together after the collision. The total momentum before the collision equals the total momentum after the collision. The initial momentum is $ (2.0\, \text{kg} \times 8.0\, \text{m/s}) + (3.0\, \text{kg} \times -2.0\, \text{m/s}) = 16.0\, \text{kg}\cdot\text{m/s} - 6.0\, \text{kg}\cdot\text{m/s} = 10.0\, \text{kg}\cdot\text{m/s} $. The total mass after the collision is $2.0\, \text{kg} + 3.0\, \text{kg} = 5.0\, \text{kg}$. Therefore, the velocity of the system after the collision is $ \frac{10.0\, \text{kg}\cdot\text{m/s}}{5.0\, \text{kg}} = 2.0\, \text{m/s} $ to the right.

Question 19

Consider an inelastic collision between balls of mass m₁ and m₂.The velocities before the collision are ₁ and ₂,respectively,and the velocities after the collision are ₁ and ₂,respectively.Which of the following statements concerning this collision is true? A)m₁ ₁ + m₁ ₁ = m₂ ₂ + m₂ ₂ B) ₂ - ₁ > ₁ - ₂ C) ₂ - ₁ = ₁ - ₂ D) ₂ - ₁ < ₁ - ₂ E) m₁( ₁)² + m₂( ₂)² = m₁( ₁)² + m₂( ₂)²

Accepted Answer

The given velocities before and after the collision indicate that the collision is inelastic since the velocities of the two balls change after the collision. 
Option A is incorrect as the sum of the velocities before and after the collision should be conserved by the law of conservation of momentum, which is not the case. 
Option C is incorrect as the velocities before the collision and the velocities after the collision are not equal. 
Option D is incorrect as it gives an inequality that violates the law of conservation of momentum. 
Option E involves the conservation of both momentum and kinetic energy, which is not necessary to answer the given question. Therefore, option B is the best choice as it is the only statement that is feasible based on the information given.

Question 20

An object of mass M₁ is moving with a speed v on a straight,level,frictionless track when it collides with another mass M₂ that is at rest on the track.After the collision,M₁ and M₂ stick together and move with a speed of A)v B)M₁v C)(M₁ + M₂)v/M₁ D)M₁v/(M₁ + M₂) E)M₁v/M₂

Accepted Answer

This is a conservation of momentum problem. The total momentum before the collision (mass of the first object times its velocity) must equal the total momentum after the collision (combined mass of both objects times their new velocity). The correct formula that represents this situation is $ \frac{m_1v}{(m_1 + m_2)} $, where $ m_1 $ is the mass of the first object, $ m_2 $ is the mass of the second object, and $ v $ is the initial velocity of the first object.

Quiz 8: Systems of Particles and Conservation of Linear Momentum

A block of wood with a mass M = 4.65 kg is resting on a horizontal surface when a bullet with a mass m = 18 g and moving with a speed v = 725 m/s strikes it.The coefficient of friction between the block and the surface is µ = 0.35.The distance the block moves across the surface is

Two equal masses travel in opposite directions with equal speed.If they collide in a perfectly elastic collision,then,just after the collision,their velocities will be

A 40-kg girl,standing at rest on the ice,gives a 60-kg boy,who is also standing at rest on the ice,a shove.After the shove,the boy is moving backward at 2.0 m/s.Ignore friction.The girl's speed is

Two bodies A and B move toward each other with speeds of 80 cm/s and 20 cm/s,respectively.The mass of A is 140 g and that of B is 60 g.After a head-on,perfectly elastic collision,the speed of B is

Two cars of equal mass travel in opposite directions at equal speeds.They collide in a perfectly inelastic collision.Just after the collision,their velocities are

A railway car having a total mass of 5.8 $\times$ 10⁵ kg,moving with a speed of 9.1 km/h,strikes another car that has a mass of 8.7 $\times$ 10⁵ kg and is initially at rest.The speed of the coupled cars after the collision is

A 5.0-kg ball and a 10.0-kg ball approach each other with equal speeds of 20 m/s.If they collide inelastically,the speed of the balls just after the collision is approximately

A bullet of mass m and velocity strikes and becomes imbedded in a wooden block of mass M,which is initially at rest on a frictionless surface.The ratio of the velocity of the system after collision to the initial velocity of the bullet is

A moving particle is stopped by a single head-on collision with a second,stationary particle if the moving particle undergoes

Two equal masses travel in opposite directions with equal speeds.They collide in a collision that is between elastic and inelastic.Just after the collision,their velocities are

In riot control,the riot squad uses a water hose that shoots water at a rate of 5 m/s and volume of 40 L/s.What is the average force exerted on a person assuming that the water splashes sideways in all directions? The density of water is 1000 kg/m³.

A mass m₁ = 2.5 kg is connected to another mass m₂ = 4.0 kg by a compressed spring.Both masses are at rest on a frictionless surface.When the spring is released,the masses are pushed apart and a total energy of 16.8 J is given to the two masses.The speed of mass m₁ is

Glider A,traveling at 10 m/s on an air track,collides elastically with glider B traveling at 8.0 m/s in the same direction.The gliders are of equal mass.The final speed of glider B is

Five billiard balls are in contact and at rest on a wire that passes through their centers.Two billiard balls are slammed into one end of the row of five at a velocity .If the balls are free to slide but not roll and if the collision is elastic,which of the following is most likely to take place?

A bullet with a mass of 20 g and a speed of 960 m/s strikes a block of wood of mass 4.5 kg resting on a horizontal surface.The bullet gets embedded in the block.The speed of the block immediately after the collision

A toy car of mass 2.0 kg moving to the right with a speed of 8.0 m/s collides perfectly inelastically with another toy car of mass 3.0 kg that is moving to the left with a speed of 2.0 m/s.Immediately after the collision the velocity of the system is

Consider an inelastic collision between balls of mass m₁ and m₂.The velocities before the collision are ₁ and ₂,respectively,and the velocities after the collision are ₁ and ₂,respectively.Which of the following statements concerning this collision is true?

An object of mass M₁ is moving with a speed v on a straight,level,frictionless track when it collides with another mass M₂ that is at rest on the track.After the collision,M₁ and M₂ stick together and move with a speed of