Physics Chapter 8

At what point does the mass have the most potential energy?

Far Left

Block 1 and block 2 have the same mass, m, and are released from the top of two inclined planes of the same height making 30° and 60° angles with the horizontal direction, respectively. If the coefficient of friction is the same in both cases, which of the blocks is going faster when it reaches the bottom of its respective incline?

Block 2 is faster.

Two identical balls are thrown from the top of a building with the same speed. Ball 1 is thrown horizontally, while ball 2 is thrown at an angle θ above the horizontal. Neglecting air resistance, which ball will have the greatest speed when hitting the ground below?

Both balls reach the ground with the same speed.

You and your friend want to go to the top of the Eiffel Tower. Your friend takes the elevator straight up. You decide to walk up the spiral stairway, taking longer to do so. Compare the gravitational potential energy (U) of you and your friend, after you both reach the top.

Both of you have the same amount of potential energy.

At what point does the mass have its highest speed?

Directly downward

At what point does the mass have the most kinetic energy?

Directly downward

How do the escape velocities for two rockets, the first weighing 20 N and the second weighing 20,000 N compare?

The escape velocity for the lighter rocket is the same as that for the heavier rocket.

A potential energy function for a certain system is given by U1(x) =Cx2+Bx3. The potential energy function for a second system is given by U2(x) =A+Cx2+Bx3, where A is a positive quantity. How does the force on system 1 relate to the force in system 2 at a given position?

The force is identical in the two systems.

A particle is moving in three-dimensions and is not acted on by any non-conservative forces. The particle is moving with velocity V when it is located at point O. When the particle returns to point O at a later time, which statement is vrtrue about its velocity?

The magnitude of the velocity when the particle returns is the magnitude of V.

A potential energy function for a certain system is given by U1(x) =Cx2+Bx3. The potential energy function for a second system is given by U2(x) =A+Cx2+Bx3, where A is a positive quantity. If an object begins at the same initial position with the same initial velocity in both systems, how is the motion in the two systems related?

The motion in the two systems is identical.

An object of mass m is held at a vertical height h from ground level. It is then released and falls under the influence of gravity. Which of the following statements is true in this situation? (Neglect air resistance.)

The potential energy of the object is decreasing and the kinetic energy is increasing.

Two inclined planes A and B have the same height but different angles of inclination with the horizontal. Inclided plane A has a steeper angle of inclination than inclined plane B. An object is released at rest from the top of each of the inclined planes. How does the speed of the object at the bottom of inclined plane A compare with that of the speed at the bottom of inclined plane B?

The speed of the object is the same for both inclined planes.

Neglecting air resistance, when you toss a stone straight up in the air from Earth's surface, which of the following statements is true for the upward motion of the stone.

The stone's kinetic energy decreases while its gravitational potential energy increases.

A lightweight object and a very heavy object are sliding with equal speeds along a level frictionless surface. They both slide up the same frictionless hill. Which rises to a greater height?

They both slide to the same height.

ou need to load a crate of mass m onto the bed of a truck. One possibility is to lift the crate straight up over a height h, equal to height of the truck's bed. The work done in this case is W1. The other possibility is to slide the crate up the frictionless ramp of length L as shown in Fig. 8-1. In this case you perform work W2. What statement is true?

W1= W2

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

Yes, since the choice of the zero of potential energy is arbitrary.

The total mechanical energy of a system

is constant, if only conservative forces act.

A ball drops some distance and loses 30 J of gravitational potential energy. Do not ignore air resistance. How much kinetic energy did the ball gain?

less than 30 J

A ball drops some distance and gains 30 J of kinetic energy. Do not ignore air resistance. How much gravitational potential energy did the ball lose?

more than 30 J

If an object is located in a region over which its potential energy is constant, the object is said to be in

neutral equilibrium.

A minimum in the potential energy curve represents a point of

stable equilibrium.

A maximum in the potential energy curve represents a point of

unstable equilibrium.

Swimmers at a water park have a choice of two frictionless water slides (see Fig. 8-3). Although both slides drop over the same height, h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the end of slide 1 compares with v2, the speed of a swimmer reaching the end of slide 2?

v1= v2