A particle with mass 2.55 kg is moving in one dimension subject to a potential energy function that is a 4th-order polynomial. There are equilibrium points at x = -2 m, x = 1 m, and x = 3 m. The potential energy is zero at the origin. When the particle is located at x = -2 m, it has a potential energy of 22.3 J and is moving with a speed of 5.4 m/s. What is the speed of the particle when it is located at x = 2 m?

Consider an object of mass m = 4 kg on a frictionless table. The object experiences a repulsive force F = a/x2 + b/x, where F is in newtons and x is the position of the object relative to the origin. Write an expression for the work done by the repulsive force on the object as it moves from an initial position of x1 to a final position of x2.    If the object starts at a position of x1 = 8.5 m apart, how much work, in joules, is required by an external force to bring it to a position of x2 = 2.5 m apart when a = 19 and b = 11?    If the object starts at rest at a position x3 = 1.3 m and is released, at what speed v, in meters per second, will the object be moving when it is at position x4 = 12.5 m?

A particle with a mass of 2.00 kg moves along the x axis. Initially, the particle's position is x = 1.00 m and its speed is 4.00 m/s. The graph below shows the potential energy of the particle vs. position. Assume that the total mechanical energy of the particle is conserved throughout its motion. + U (Joules) 20.0 (a) What is the total mechanical energy of the particle (E = K + U), in units of Joules (J)? 15.0 – 10.0 5.00 x (meters) 1.00 2.00 3.00 4.00 -5.00 (b) What is the speed of the particle when it is located at x = 2.00 meters? Give your answer in meters per second (m/s). (c) What are the equilibrium positions of the particle? For each equilibrium position, determine whether it is stable or unstable.

A ball with a mass of 500 g is thrown directly upward by a boy standing over a 5 m hole in the ground. The ball leaves the boys hand at a height of 1 m above the ground and with a speed of 10 m/s. What is the total mechanical energy of the ball when it hits the bottom of the hole? Take ground level to be the zero of gravitational potential energy. Assume air resistance is negligible.

The Elf on the Shelf has mass 0.500 kg and is sitting on a shelf some height y above the ground.The gravitational potential energy is 49.0 J? The Elf is bumped and falls off the shelf. How fast will the Elf be moving just before it strikes the ground?

A spring has a natural length of 0.2350 m and a spring constant of 584 N/m. At what TWO lengths would the spring have a potential energy of 21.4 J? Are both of these lengths feasible?

An object with mass 3 kg is moving with a speed of 5 m/s at a height of 2.5 m above the  ground. Using the ground as the zero Potential Energy point, what is the total mechanical energy of the particle?

A roller coaster car with mass m and initial velocity v is at height h above the ground. Calculate the potential energy, kinetic energy and velocity for the following values:   h(m) m(kg) v(m/s) 1.00E+02 5.00E+02 0.00E+00

A mass of 10.0 kg is attached to a spring on a frictionless horizontal surface. The spring constant k = 504 Newtons / meters. The spring is stretched a distance of 0.500 meters. At that point, what is the Potential Energy (in Joules) stored in the spring?