Question 1

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?

Accepted Answer

B

Question 2

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?

Accepted Answer

A

Question 3

In a perfectly ELASTIC collision between two perfectly rigid objects

Accepted Answer

In a perfectly elastic collision, both the momentum and the kinetic energy of the system are conserved since no kinetic energy is lost to other forms of energy such as heat or sound. This means that both A and B are true, but the correct answer is D as it includes both A and B. C and E are incorrect as they suggest that either momentum or kinetic energy is not conserved, which is not true for perfectly elastic collisions.

Question 4

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

Accepted Answer

The answer of In the figure,determine the character of the...

Question 5

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?

Accepted Answer

The answer of How much energy is needed to change...

Question 6

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?

Accepted Answer

By Newton's Third Law, the force applied by Jacques on George's canoe is equal in magnitude and opposite in direction to the force applied by George on Jacques' canoe. Therefore, the net external force on the system (the two canoes) is zero, and the total momentum of the system remains constant. Since the initial momentum of the system was zero (the two canoes were at rest), the final momentum of the system must also be zero. However, since Jacques applied a force on George's canoe to separate them, there was work done on the system, and thus the total kinetic energy of the system was not conserved. Therefore, the final kinetic energy of the system is zero, which means that the canoes come to a complete stop. Thus, the correct choice is B, which states that the final momentum is in the direction opposite of the force applied, and the final kinetic energy is zero.

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?

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Question 8

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:

Accepted Answer

The total energy stored in the spring is given by:

$E_{spring}=\frac{1}{2}kx^2$

Where k represents the spring constant and x represents the displacement of the spring from its equilibrium position. We can solve for k by setting the energy stored in the spring equal to the given value of 75.0 J:

$75.0 J=\frac{1}{2}kx^2$

$k=\frac{2E_{spring}}{x^2}=\frac{2(75.0 J)}{(0.200 m)^2}=1875 N/m$

Since the blocks are pressed together against the spring, their initial displacement from equilibrium is 0.200 m (the length of the compressed spring), and the total mass of the system is 5.00 kg, the force on the spring can be calculated as:

$F=kx=1875 N/m \cdot 0.200 m=375 N$

This will be the maximum force experienced by the blocks as they move away from the spring. Initially, this force will accelerate the blocks together, until they are no longer in contact and the spring is fully extended. At this point, the blocks will be moving together with some velocity, which we can find using conservation of energy:

$E_{total}=E_{kinetic}+E_{potential}$

Initially, the blocks are at rest and all of the energy is stored in the spring, so $E_{total}=75.0 J$. At the maximum velocity, all of the energy will be in the form of kinetic energy, so $E_{kinetic}=\frac{1}{2}mv^2$, where m is the mass of each block. Since both blocks are moving together with the same velocity, we can write:

$75.0 J=2 \cdot \frac{1}{2}m v^2$

Simplifying:

$v=\sqrt{\frac{75 J}{m}}$

Plugging in m=2.00 kg gives:

$v_A=\sqrt{\frac{75 J}{2.00 kg}}=6.71 m/s$

Plugging in m=3.00 kg gives:

$v_B=\sqrt{\frac{75 J}{3.00 kg}}=4.47 m/s$

Therefore, the correct answer is A) 6.71 m/s (A), 4.47 m/s (B).

Question 9

In an INELASTIC collision between two objects

Accepted Answer

In an inelastic collision, the momentum of the system is conserved but the kinetic energy of the system is not conserved. This means that the total momentum of the objects before the collision is equal to the total momentum of the objects after the collision, but some of the kinetic energy is transformed into other forms of energy, such as heat or sound. Therefore, choices A, B, D, and E are incorrect.

Question 10

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

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The answer of In the figure,determine the character of the...

Question 11

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?

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Question 12

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

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Question 13

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

The answer of A 10.0-kg shell is traveling horizontally to...

Question 14

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?

Accepted Answer

The answer of A car of mass 1689 kg collides...

Question 15

A shell explodes into two fragments,one fragment 25 times heavier than the other.If any gas from the explosion has negligible mass,then

Accepted Answer

The law of conservation of momentum states that the total momentum of a closed system is constant if no external forces act on it. In the case of the shell explosion, the system is the two fragments. Since they are part of the same system and no external forces are considered, the momentum change of one fragment must be equal and opposite to the momentum change of the other, regardless of their masses. This means the momentum change of the lighter fragment is exactly the same as the momentum change of the heavier fragment, but in the opposite direction.

Quiz 5: Energy