Conservation of energy problems involving moving particles and systems

(See attached file for full problem description)

19. The graphs attached show the force acting on a particle as the particle moves along the positive x axis from the origin to x = x1. The force is parallel to the x axis and is conservative. The maximum magnitude F1 has the same value for all graphs. Rank the situations according to the change in the potential energy associated with the force, least (or most negative) to greatest (or most positive).

20. A ball is held at a height H above a floor. It is then released and falls to the floor. If air resistance can be ignored, which of the five graphs below correctly gives the mechanical energy E of the Earth-ball system as a function of the altitude y of the ball?

21. An elevator is rising at constant speed. Consider the following statements:

I. the upward cable force is constant.
II. the kinetic energy of the elevator is constant
III. the gravitational potential energy of the Earth-elevator system is constant.
IV. the acceleration of the elevator is zero
V. the mechanical energy of the Earth-elevator system is constant

22. For a block of mass m to slide without friction up the rise of height h shown, it must have a minimum initial speed of:

23. A 2.2 kg block starts from rest on a rough inclined plane that makes an angle of 25 degrees with the horizontal. the coefficient of kinetic friction is 0.25. As the block goes 2.0m down the plane, the mechanical energy of the Earth-block system changes by:

24. A 0.20 kg particle moves along the x axis under the influence of a stationary object. The potential energy is given by U(x) = 8x^2 + 2x^4, where U is in joules and x is in meters. If the particle has a speed of 5.0m/s when it is at x = 1.0m, its speed when it is at the origin is:

25. A 0.50 kg block attached to an ideal spring with a spring constant of 80 H/m oscillates on a horizontal frictionless surface. When the spring is 4.0cm shorter than its equilibrium length, the speed of the block is 0.50 m/s. the greatest speed of the block is: