Question 1

A 10.0-kg shell is traveling horizontally to the right at 25.0 m/s relative to the ground when it explodes into two fragments,one of mass 3.00 kg and the other of mass 7.00 kg.The lighter fragment goes directly forward,and the explosion releases 1.50 × 10³ J of mechanical energy to the fragments.Find the magnitude and direction of the velocity of the heavier fragment relative to the ground just after the explosion.Ignore the effect of any ejected gases.

Accepted Answer

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Question 2

A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them.They are not attached to the spring.After they are released and have both moved free of the spring
A) the lighter block will have more kinetic energy than the heavier block.
B) the heavier block will have more kinetic energy than the lighter block.
C) both blocks will both have the same amount of kinetic energy.
D) both blocks will have equal speeds.
E) the magnitude of the momentum of the heavier block will be greater than the magnitude of the momentum of the lighter block.

Accepted Answer

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Question 3

A 310-g air track cart is traveling at 1.25 m/s and a 260-g cart traveling in the opposite direction at 1.33 m/s.What is the speed of the center of mass of the two carts?
A) 2.80 m/s
B) 0.0732 m/s
C) 0.131 m/s
D) 1.47 m/s
E) 1.29 m/s

Accepted Answer

The speed of the center of mass can be calculated using the formula: $v_{cm} = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$, where $m_1$ and $m_2$ are the masses of the carts, and $v_1$ and $v_2$ are their velocities. Given that one cart is moving in the opposite direction, its velocity is considered negative. Thus, $v_{cm} = \frac{(0.31 \times 1.25) + (0.26 \times -1.33)}{0.31 + 0.26} = \frac{0.3875 - 0.3458}{0.57} = 0.0731 \, m/s$, which rounds to 0.0732 m/s, making option B correct.

Question 4

The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface.For an object with a coefficient of 0.78,what fraction of the object's kinetic energy is lost during a single collision?
A) 39%
B) 16%
C) 47%
D) 61%

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Question 5

In the figure,determine the character of the collision.The masses of the blocks,and the velocities before and after are given.The collision is 
A) perfectly elastic.
B) partially inelastic.
C) completely inelastic.
D) characterized by an increase in kinetic energy.
E) not possible because momentum is not conserved.

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Question 6

In the figure,determine the character of the collision.The masses of the blocks,and the velocities before and after are given,and no other unbalanced forces act on these blocks.The collision is 
A) perfectly elastic.
B) partially inelastic.
C) completely inelastic.
D) characterized by an increase in kinetic energy.
E) not possible because momentum is not conserved.

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Question 7

A 1000.0 kg car is moving at 15 km/h.If a 2000.0 kg truck has 18 times the kinetic energy of the car,how fast is the truck moving?
A) 45 km/h
B) 63 km/h
C) 54 km/h
D) 36 km/h

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Question 8

A plane flies directly between two cities,A and B,which are separated by 2300 mi.From A to B,the plane flies into a 65 mi/h headwind.On the return trip from B to A,the wind velocity is unchanged.The trip from B to A takes 65 min less than the trip from A to B.What is the airspeed of the plane,assuming it is the same in both directions?
A) 530 mi/h
B) 400 mi/h
C) 480 mi/h
D) 610 mi/h

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Question 9

A car of mass 1689 kg collides head-on with a parked truck of mass 2000 kg. Spring mounted bumpers ensure that the collision is essentially elastic.If the velocity of the truck is 17 km/h (in the same direction as the car's initial velocity)after the collision,what was the initial speed of the car?
A) 19 km/h
B) 38 km/h
C) 29 km/h
D) 10 km/h

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Question 10

A 620-g object traveling at 2.1 m/s collides head-on with a 320-g object traveling in the opposite direction at 3.8 m/s.If the collision is perfectly elastic,what is the change in the kinetic energy of the 620-g object?
A) It loses 0.23 J.
B) It gains 0.69 J.
C) It loses 0.47 J.
D) It loses 1.4 J.
E) It doesn't lose any kinetic energy because the collision is elastic.

Accepted Answer

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Question 11

A 2.00-m rod of negligible mass connects two very small objects at its ends. The mass of one object is 1.00 kg and the mass of the other is unknown. The center of mass of this system is on the rod a distance 1.60 m from the 1.00-kg mass object. What is the mass of the other object?
A) 4.11 kg
B) 3.22 kg
C) 4.00 kg
D) 0.250 kg
E) 0.800 kg

Accepted Answer

We can use the formula for the center of mass of a two-object system:
$$x_{cm}=\frac{m_1x_1+m_2x_2}{m_1+m_2}$$
where $m_1$ and $m_2$ are the masses of the objects, $x_1$ is the distance from the center of mass to the 1.00 kg mass object, and $x_2$ is the distance from the center of mass to the other object.

We are given $m_1=1.00$ kg, $x_1=0.4$ m, and $x_{cm}=1.60$ m. We can rearrange the formula to solve for $m_2$:
$$m_2=\frac{x_{cm}(m_1+m_2)-m_1x_1}{x_2}$$
Plugging in the given values, we have:
$$m_2=\frac{(1.60)(1.00+m_2)-(1.00)(0.40)}{1.60}$$
Simplifying this expression:
$$m_2=2.40-0.625m_2$$
$$1.625m_2=2.40$$
$$m_2=1.477\approx \boxed{	extbf{(C) } 4.00 kg}$$

Question 12

A baseball is thrown vertically upward and feels no air resistance.As it is rising
A) both its momentum and its mechanical energy are conserved.
B) its momentum is not conserved, but its mechanical energy is conserved.
C) both its momentum and its kinetic energy are conserved.
D) its kinetic energy is conserved, but its momentum is not conserved.
E) its gravitational potential energy is not conserved, buts its momentum is conserved.

Accepted Answer

When the baseball is thrown vertically upward, only gravity is acting on it. Therefore, there is no external force acting on it and its mechanical energy is conserved. However, the baseball's momentum is not conserved, as it is constantly changing direction due to the force of gravity.

Question 13

A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s.If the collision is perfectly elastic,what is the final speed of the 2.3-kg object?
A) 0.48 m/s
B) 7.1 m/s
C) 3.8 m/s
D) 4.3 m/s
E) 6.6 m/s

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Question 14

Jacques and George meet in the middle of a lake while paddling in their canoes.They come to a complete stop and talk for a while.When they are ready to leave,Jacques pushes George's canoe with a force  to separate the two canoes.What is correct to say about the final momentum and kinetic energy of the system if we can neglect any resistance due to the water?
A) The final momentum is in the direction of  but the final kinetic energy is zero.
B) The final momentum is in the direction opposite of  but the final kinetic energy is zero.
C) The final momentum is in the direction of  and the final kinetic energy is positive.
D) The final momentum is zero and the final kinetic energy is zero.
E) The final momentum is zero but the final kinetic energy is positive.

Accepted Answer

According to the law of conservation of momentum, the total momentum of the system (the two canoes) before and after the push must be equal. Since Jacques pushes George's canoe in the direction opposite of the initial momentum, the final momentum must be in the opposite direction. However, since the canoes come to a complete stop, the final kinetic energy is zero. Thus, choice B is correct.

Question 15

An airplane flies between two points on the ground that are 500 km apart. The destination is directly north of the origination of the flight. The plane flies with an air speed of 120 m/s. If a constant wind blows at 10.0 m/s due west during the flight,what direction must the plane fly relative to north to arrive at the destination?
A) 4.78° east of north
B) 4.76° east of north
C) 85.2° west of north
D) 4.78° west of north
E) 4.76° west of north

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Question 16

Is it possible for a system to have negative potential energy?
A) Yes, as long as the kinetic energy is positive.
B) Yes, as long as the total energy is positive.
C) Yes, since the choice of the zero of potential energy is arbitrary.
D) No, because the kinetic energy of a system must equal its potential energy.
E) No, because this would have no physical meaning.

Accepted Answer

Potential energy is defined as the energy possessed by an object due to its position or configuration relative to other objects. The choice of the zero of potential energy is arbitrary and can be chosen by convention. Therefore, it is possible for a system to have negative potential energy if the reference point is chosen such that the system's current configuration has a negative potential energy. The kinetic energy of the system does not necessarily need to be positive or equal to the potential energy.

Question 17

On a smooth horizontal floor,an object slides into a spring which is attached to another mass that is initially stationary.When the spring is most compressed,both objects are moving at the same speed.Ignoring friction,what is conserved during this interaction?
A) momentum and mechanical energy
B) momentum only
C) kinetic energy only
D) momentum and kinetic energy
E) momentum and potential energy

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Question 18

How much energy is needed to change the speed of a 1600 kg sport utility vehicle from 15.0 m/s to 40.0 m/s?
A) 1.10 MJ
B) 10.0 kJ
C) 20.0 kJ
D) 40.0 kJ
E) 0.960 MJ

Accepted Answer

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Question 19

There must be equal amounts of mass on both side of the center of mass of an object.

Accepted Answer

The center of mass is determined by the distribution of mass, not the amount of mass on each side. It is possible for one side to have more mass than the other and still have the center of mass at the geometric center of the object.

Question 20

On a frictionless horizontal table,two blocks (A of mass 2.00 kg and B of mass 3.00 kg)are pressed together against an ideal massless spring that stores 75.0 J of elastic potential energy.The blocks are not attached to the spring and are free to move free of it once they are released from rest.The maximum speed achieved by each block is closest to:
A) 6.71 m/s (A), 4.47 m/s (B)
B) 4.47 m/s (A), 6.71 m/s (B)
C) 5.48 m/s for both
D) 6.12 m/s (A), 5.00 m/s (B)
E) 5.00 m/s (A), 6.12 m/s (B)

Accepted Answer

The maximum speed of each block can be found using the conservation of energy principle. The total elastic potential energy stored in the spring is converted into the kinetic energy of the two blocks. The kinetic energy ($KE$) is given by $KE = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity of the block. Since the total energy is conserved, the sum of the kinetic energies of both blocks equals the initial potential energy stored in the spring, i.e., $75.0 J$.For two blocks of different masses, the block with the smaller mass (A, 2.00 kg) will achieve a higher speed than the block with the larger mass (B, 3.00 kg) because the same amount of energy results in a higher velocity for the lighter object. The correct speeds, as calculated using the conservation of energy and taking into account the mass of each block, are 6.71 m/s for block A and 4.47 m/s for block B, making option A the correct choice.

Quiz 1: A: Foundations

A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them.They are not attached to the spring.After they are released and have both moved free of the spring

A 310-g air track cart is traveling at 1.25 m/s and a 260-g cart traveling in the opposite direction at 1.33 m/s.What is the speed of the center of mass of the two carts?

The coefficient of the restitution of an object is defined as the ratio of its outgoing to incoming speed when the object collides with a rigid surface.For an object with a coefficient of 0.78,what fraction of the object's kinetic energy is lost during a single collision?

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

In the figure,determine the character of the collision.The masses of the blocks,and the velocities before and after are given,and no other unbalanced forces act on these blocks.The collision is

A 1000.0 kg car is moving at 15 km/h.If a 2000.0 kg truck has 18 times the kinetic energy of the car,how fast is the truck moving?

A car of mass 1689 kg collides head-on with a parked truck of mass 2000 kg. Spring mounted bumpers ensure that the collision is essentially elastic.If the velocity of the truck is 17 km/h (in the same direction as the car's initial velocity) after the collision,what was the initial speed of the car?

A 620-g object traveling at 2.1 m/s collides head-on with a 320-g object traveling in the opposite direction at 3.8 m/s.If the collision is perfectly elastic,what is the change in the kinetic energy of the 620-g object?

A 2.00-m rod of negligible mass connects two very small objects at its ends. The mass of one object is 1.00 kg and the mass of the other is unknown. The center of mass of this system is on the rod a distance 1.60 m from the 1.00-kg mass object. What is the mass of the other object?

A baseball is thrown vertically upward and feels no air resistance.As it is rising

A 2.3-kg object traveling at 6.1 m/s collides head-on with a 3.5-kg object traveling in the opposite direction at 4.8 m/s.If the collision is perfectly elastic,what is the final speed of the 2.3-kg object?

Is it possible for a system to have negative potential energy?

On a smooth horizontal floor,an object slides into a spring which is attached to another mass that is initially stationary.When the spring is most compressed,both objects are moving at the same speed.Ignoring friction,what is conserved during this interaction?

How much energy is needed to change the speed of a 1600 kg sport utility vehicle from 15.0 m/s to 40.0 m/s?

There must be equal amounts of mass on both side of the center of mass of an object.