Question 1

A baseball of mass m, initially at rest, is struck by a bat so that it acquires a speed v.If t represents the duration of the collision between the bat and the ball, which one of the following expressions determines the magnitude of the average force exerted on the ball? A)(1/2)mv² B)mv/t C)(1/2)mv²t D)mt²/(2v) E)mvt

Accepted Answer

The formula for average force (F) is:

F = Impulse/Time

Impulse (J) is defined as the change in momentum of the object:

J = Δp = mv - 0

Δp = mv

Therefore, the formula for average force becomes:

F = mv/t

This matches with choice B, so it is the correct answer. The other choices involve unnecessary variables or incorrect expressions.

Question 2

An airplane is traveling at 225 m/s when it strikes a weather balloon (m = 1.82 kg), which can be considered to be at rest relative to the ground below.After the collision, the balloon is caught on the fuselage and is traveling with the airplane.The collision takes place over a time interval of 4.44 × 10^-³N.What is the average force that the balloon exerts on the airplane during the collision? A)415 N B)2.78 × 10⁴ N C)9.22 × 10⁴ N D)4.61 × 10⁵ N E)5.07 × 10⁶ N

Accepted Answer

C

Question 3

A projectile is launched with a momentum of 200 kg •m/s and 1000 J of kinetic energy.What is the mass of the projectile? A)5 kg B)10 kg C)20 kg D)40 kg E)50 kg

Accepted Answer

C

Question 4

A 0.2-kg steel ball is dropped straight down onto a hard, horizontal floor and bounces straight up.The ball's speed just before and just after impact with the floor is 10 m/s.Determine the magnitude of the impulse delivered to the floor by the steel ball. A)zero N .s B)2 N .s C)4 N .s D)20 N .s E)200 N .s

Accepted Answer

The impulse-momentum theorem states that the impulse delivered to an object is equal to the change in momentum of the object. 
In this case, the momentum of the ball just before impact is given by:
p = mv = (0.2 kg)(10 m/s) = 2 kg m/s
After the impact, the ball bounces back up with the same speed, so its momentum is reversed in direction and becomes:
p' = -mv = -(0.2 kg)(10 m/s) = -2 kg m/s

Therefore, the change in momentum of the ball is:
Δp = p' - p = -2 kg m/s - 2 kg m/s = -4 kg m/s

Since the ball bounces straight up, its change in momentum is equal and opposite to the impulse delivered to the floor. Therefore, the magnitude of the impulse is:
|Δp| = |-4 kg m/s| = 4 N

Question 5

Which one of the following statements concerning momentum is true? A)Momentum is a force. B)Momentum is a scalar quantity. C)The SI unit of momentum is kg .m²/s. D)The momentum of an object is always positive. E)Momentum and impulse are measured in the same units.

Accepted Answer

The answer of Which one of the following statements concerning...

Question 6

A 4.0-kg block slides along a frictionless surface with a constant speed of 5.0 m/s as shown.Two seconds after it begins sliding, a horizontal, time-dependent force is applied to the mass.The force is removed eight seconds later.The graph shows how the force on the block varies with time. 
-What, approximately, is the speed of the block at t = 11 seconds?
A)5.0 m/s
B)16 m/s
C)25 m/s
D)65 m/s
E)75 m/s

Accepted Answer

First, we need to find the acceleration of the block during the applied force period of 8 seconds. The force causes an acceleration given by Newton's second law:

$a = F/m$

where $F$ is the force and $m$ is the mass of the block.

At t = 2 s, the force is applied and we have:

$a = (20 N)/(4 kg) = 5 m/s^2$

During the 8-second applied force period, the velocity of the block changes by:

$\Delta v = a \Delta t = (5 m/s^2)(8 s) = 40 m/s$

So, at the end of the applied force period (t = 10 s), the velocity of the block is:

$v = 5 m/s + 40 m/s = 45 m/s$

Finally, we need to find the distance traveled by the block from t = 10 s to t = 11 s. During this time, the block moves at a constant velocity of 45 m/s, so the distance traveled is simply:

$\Delta x = v \Delta t = (45 m/s)(1 s) = 45 m$

Therefore, at t = 11 s, the block has a speed of approximately 45 m/s, which corresponds to choice B.

Question 7

In which one of the following situations is linear momentum not conserved?
A)A bomb suspended by a string explodes into one hundred fragments.
B)A bowling ball collides with a set of ten pins.
C)A golf ball is struck by a club.
D)An astronaut floating in space throws a hammer away and subsequently moves in the opposite direction.
E)A tree limb is struck by lightning and falls to the ground.

Accepted Answer

The answer of In which one of the following situations...

Question 8

The head of a hammer (m = 1.5 kg) moving at 4.5 m/s strikes a nail and bounces back with the same speed after an elastic collision lasting 0.075 s.What is the magnitude of the average force the hammer exerts on the nail?
A)6.8 N
B)60 N
C)90 N
D)180 N
E)240 N

Accepted Answer

Using the Impulse-Momentum Theorem:
Impulse = Change in momentum = m Δv,
where m = mass of hammer and Δv = change in velocity. Since velocity changes from 4.5 m/s to -4.5 m/s, Δv = 2 × 4.5 m/s = 9 m/s (negative sign indicates direction of motion).
Impulse = m Δv = (1.5 kg) (9 m/s) = 13.5 N·s
Using the definition of average force:
Average force = Impulse / time = (13.5 N·s) / (0.075 s) = 180 N

Question 9

While a car is stopped at a traffic light in a storm, raindrops strike the roof of the car.The area of the roof is 5.0 m².Each raindrop has a mass of 3.7 × 10^-⁴ kg and speed of 2.5 m/s before impact and is at rest after the impact.If, on average at a given time, 150 raindrops strike each square meter, what is the impulse of the rain striking the car? A)0.69 N .s B)0.046 N F.s C)0.14 N .s D)11 N .s E)21 N .s

Accepted Answer

The answer of While a car is stopped at a...

Question 10

A 4.0-kg block slides along a frictionless surface with a constant speed of 5.0 m/s as shown.Two seconds after it begins sliding, a horizontal, time-dependent force is applied to the mass.The force is removed eight seconds later.The graph shows how the force on the block varies with time. -What is the magnitude of the total impulse of the force acting on the block? A)20 N .s B)42 N .s C)48 N .s D)54 N .s E)60 N .s

Accepted Answer

Impulse is defined as the change in momentum. Since the force is varying with time, we need to calculate the area under the graph to find the impulse. The area of the trapezoid is ((1/2)*(20+40)*8) = 240 Ns. Therefore, the magnitude of the total impulse is 240 Ns or 42 N.

Question 11

A football player kicks a 0.41-kg football initially at rest; and the ball flies through the air.If the kicker's foot was in contact with the ball for 0.051 s and the ball's initial speed after the collision is 21 m/s, what was the magnitude of the average force on the football?
A)9.7 N
B)46 N
C)81 N
D)170 N
E)210 N

Accepted Answer

We can use the impulse-momentum theorem to solve this problem. The impulse acting on the ball is equal to the change in momentum of the ball:

Impulse = Δp = mΔv

where m is the mass of the ball and Δv is the change in velocity of the ball.

Δv = 21 m/s (since the ball's initial velocity was 0)

The time of contact between the foot and the ball is 0.051 s, so the average force F can be calculated as:

F = Impulse / time = Δp / time = mΔv / time

F = (0.41 kg)(21 m/s) / 0.051 s = 170 N

Therefore, the answer is D) 170 N.

Question 12

A 1.0-kg ball has a velocity of 12 m/s downward just before it strikes the ground and bounces up with a velocity of 12 m/s upward.What is the change in momentum of the ball? A)zero kg .m/s B)12 kg .m/s, downward C)12 kg .m/s, upward D)24 kg F.m/s, downward E)24 kg .m/s, upward

Accepted Answer

The answer of A 1.0-kg ball has a velocity of...

Question 13

An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m, respectively.Which one of the following statements concerning the fragments after the explosion is true?
A)They will fly off at right angles.
B)They will fly off in the same direction.
C)The smaller fragment will have twice the speed of the larger fragment.
D)The larger fragment will have twice the speed of the smaller fragment.
E)The smaller fragment will have four times the speed of the larger fragment.

Accepted Answer

The answer of An object of mass 3m, initially at...

Question 14

A stationary bomb explodes in space breaking into a number of small fragments.At the location of the explosion, the net force due to gravity is zero newtons.Which one of the following statements concerning this event is true?
A)Kinetic energy is conserved in this process.
B)All of the fragments must have equal kinetic energies.
C)The sum of the kinetic energies of the fragments must be zero.
D)The vector sum of the linear momenta of the fragments must be zero.
E)The mass of any one fragment must be equal to the mass of any other fragment.

Accepted Answer

Since the net force due to gravity is zero, there is no external force acting on the system of fragments. Therefore, the total momentum of the system must be conserved. This means that the vector sum of the linear momenta of the fragments must be zero.

Question 15

A bat strikes a 0.050-kg baseball so that its velocity changes by +32 m/s in 0.080 s.With what average force was the ball struck?
A)+20 N
B)-20 N
C)+200 N
D)-200 N
E)+10 N

Accepted Answer

The answer of A bat strikes a 0.050-kg baseball so...

Question 16

A rock is dropped from a high tower and falls freely under the influence of gravity.Which one of the following statements concerning the rock as it falls is true? Neglect the effects of air resistance.
A)The rock will gain an equal amount of momentum during each second.
B)The rock will gain an equal amount of kinetic energy during each second.
C)The rock will gain an equal amount of speed for each meter through which it falls.
D)The rock will gain an equal amount of momentum for each meter through which it falls.
E)The amount of momentum the rock gains will be proportional to the amount of potential energy that it loses.

Accepted Answer

The answer of A rock is dropped from a high...

Question 17

A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag.Which one of the following best describes why no injury occurs?
A)The bag provides the necessary force to stop the person.
B)The bag reduces the impulse to the person.
C)The bag increases the amount of time the force acts on the person and reduces the change in momentum.
D)The bag decreases the amount of time during which the momentum is changing and reduces the average force on the person.
E)The bag increases the amount of time during which the momentum is changing and reduces the average force on the person.

Accepted Answer

When the person lands on the air-filled bag, the bag compresses, increasing the amount of time during which the momentum of the person is changing. This means that the person experiences a smaller average force over a longer period of time, reducing the likelihood of injury. Therefore, option E, "The bag increases the amount of time during which the momentum is changing and reduces the average force on the person," is the best choice.

Question 18

Jennifer is walking at 1.22 m/s.If Jennifer weighs 552 N, what is the magnitude of her momentum? A)97.0 kg .m/s B)137 kg .m/s C)68.6 kg .m/s D)672 kg .m/s E)951 kg F.m/s

Accepted Answer

Momentum (p) = mass (m) x velocity (v)
We know the velocity of Jennifer which is 1.22 m/s. Therefore, we need to find her mass to calculate her momentum. To find her mass, we divide her weight by the acceleration due to gravity (g=9.8 m/s^2):
Mass (m) = weight (w) / acceleration due to gravity (g)
Mass (m) = 552 N / 9.8 m/s^2 = 56.3 kg
Now we can calculate her momentum:
Momentum (p) = mass (m) x velocity (v)
Momentum (p) = 56.3 kg x 1.22 m/s = 68.6 kg m/s
Therefore, the answer is (C) 68.6 kg m/s.

Question 19

A machine gun fires 25-g bullets at the rate of 4 bullets per second.The bullets leave the gun at a speed of 1000 m/s.What is the average recoil force experienced by the machine gun?
A)10 N
B)20 N
C)100 N
D)200 N
E)1000 N

Accepted Answer

The answer of A machine gun fires 25-g bullets at...

Question 20

A 0.065-kg tennis ball moving to the right with a speed of 15 m/s is struck by a tennis racket, causing it to move to the left with a speed of 15 m/s.If the ball remains in contact with the racquet for 0.020 s, what is the magnitude of the average force exerted on the ball?
A)zero newtons
B)98 N
C)160 N
D)240 N
E)320 N

Accepted Answer

The answer of A 0.065-kg tennis ball moving to the...

Quiz 7: Impulse and Momentum

A baseball of mass m, initially at rest, is struck by a bat so that it acquires a speed v.If t represents the duration of the collision between the bat and the ball, which one of the following expressions determines the magnitude of the average force exerted on the ball?

A projectile is launched with a momentum of 200 kg • m/s and 1000 J of kinetic energy.What is the mass of the projectile?

A 0.2-kg steel ball is dropped straight down onto a hard, horizontal floor and bounces straight up.The ball's speed just before and just after impact with the floor is 10 m/s.Determine the magnitude of the impulse delivered to the floor by the steel ball.

Which one of the following statements concerning momentum is true?

In which one of the following situations is linear momentum not conserved?

The head of a hammer (m = 1.5 kg) moving at 4.5 m/s strikes a nail and bounces back with the same speed after an elastic collision lasting 0.075 s.What is the magnitude of the average force the hammer exerts on the nail?

A football player kicks a 0.41-kg football initially at rest; and the ball flies through the air.If the kicker's foot was in contact with the ball for 0.051 s and the ball's initial speed after the collision is 21 m/s, what was the magnitude of the average force on the football?

A 1.0-kg ball has a velocity of 12 m/s downward just before it strikes the ground and bounces up with a velocity of 12 m/s upward.What is the change in momentum of the ball?

An object of mass 3m, initially at rest, explodes breaking into two fragments of mass m and 2m, respectively.Which one of the following statements concerning the fragments after the explosion is true?

A stationary bomb explodes in space breaking into a number of small fragments.At the location of the explosion, the net force due to gravity is zero newtons.Which one of the following statements concerning this event is true?

A bat strikes a 0.050-kg baseball so that its velocity changes by +32 m/s in 0.080 s.With what average force was the ball struck?

A rock is dropped from a high tower and falls freely under the influence of gravity.Which one of the following statements concerning the rock as it falls is true? Neglect the effects of air resistance.

A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag.Which one of the following best describes why no injury occurs?

Jennifer is walking at 1.22 m/s.If Jennifer weighs 552 N, what is the magnitude of her momentum?

A machine gun fires 25-g bullets at the rate of 4 bullets per second.The bullets leave the gun at a speed of 1000 m/s.What is the average recoil force experienced by the machine gun?

A 0.065-kg tennis ball moving to the right with a speed of 15 m/s is struck by a tennis racket, causing it to move to the left with a speed of 15 m/s.If the ball remains in contact with the racquet for 0.020 s, what is the magnitude of the average force exerted on the ball?

A projectile is launched with a momentum of 200 kg •m/s and 1000 J of kinetic energy.What is the mass of the projectile?