Exam 8: Potential Energy and Conservation of Energy

In this graph of potential energy vs. x, the horizontal line represents the total mechanical energy of a particle. Approximately what is its kinetic energy at x = 15 m?

A small object slides along the frictionless loop-the-loop with a diameter of 3 m. What minimum speed must it have at the top of the loop in order to remain in contact with the loop?

Which one of the following five quantities CANNOT be used as a unit of potential energy?

The potential energy of a particle moving along the x axis is given by U(x) = (8.0 J/m²)x² + (2.0 J/m⁴)x⁴. If the total mechanical energy is 9.0 J, the limits of motion are:

A particle is released from rest at the point x = a and moves along the x axis subject to the potential energy function U(x) shown. The particle:

Given a potential energy function U(x), the corresponding force is in the positive x direction if:

A 0.5-kg block slides along a horizontal frictionless surface at 2 m/s. It is brought to rest by compressing a very long spring of spring constant 800 N/m. The maximum spring compression is:

A toy cork gun contains a spring whose spring constant is 10.0 N/m. The spring is compressed 5.00 cm and then used to propel a 6.00-g cork. The cork, however, sticks to the spring for 1.00 cm beyond its unstretched length before separation occurs. The muzzle velocity of this cork is:

Two objects interact with each other and with no other objects. Initially object A has a speed of 5 m/s and object B has a speed of 10 m/s. In the course of their motion they return to their initial positions. Then A has a speed of 4 m/s and B has a speed of 7 m/s. We can conclude:

No kinetic energy is possessed by:

A 0.20-kg particle moves along the x axis under the influence of a conservative force. The potential energy is given by U(x) = (8.0 J/m²)x² + (2.0 J/m⁴)x⁴, Where x is in coordinate of the particle. If the particle has a speed of 5.0 m/s when it is at x = 1.0 m, its speed when it is at the origin is:

The first graph shows the potential energy U(x) for a particle moving on the x axis. Which of the following five graphs correctly gives the force F exerted on the particle?

A force on a particle is conservative if:

The potential energy of a body of mass m is given by U = -mgx + 1/2kx². The corresponding force is:

The wound spring of a clock possesses:

Objects A and B interact with each other via both conservative and nonconservative forces. Let K_A and K_B be the kinetic energies, U be the potential energy, and E_int be the internal energy. If no external agent does work on the objects then:

A 0.75-kg block slides on a rough horizontal table top. Just before it hits a horizontal ideal spring its speed is 3.5 m/s. It compresses the spring 5.7 cm before coming to rest. If the spring constant is 1200 N/m, the thermal energy of the block and the table top must have:

A nonconservative force:

A 25-g ball is released from rest 80 m above the surface of the Earth. During the fall the total thermal energy of the ball and air increases by15 J. Just before it hits the surface its speed is

Three identical blocks move either on a horizontal surface, up a plane, or down a plane, as shown below. They all start with the same speed and continue to move until brought to rest by friction. Rank the three situations according to the mechanical energy dissipated by friction, least to greatest.