1. An engineer working at an industrial spring company designs a spring that obeys a force law F(x) = -c(x – Xeq)³ where c is a positive constant and xeq is the equilibrium position of the spring. a. What are the units of the constant c? Explain. b. Let the equilibrium position xeq potential energy as a function of position. = 0 and derive an expression for the system's c. Make a graph of the force F(x) function and the potential energy U(x) function.

A 0.750kg mass is attached to a spring, as shown. The surface that the mass is on is frictionless. A force of 25.0N is used to stretch the spring 0.450m. Then the mass is released from rest to oscillate. spring mass friction less surface a. What is the spring constant? b. What is the period of oscillation? c. What is the total mechanical energy in the oscillating system?

A spring has a length of 0.270 m when a 0.300 kg mass hangs from it, and a length of 0.750 m when a 2.10 kg mass hangs from it.   a. What is the force constant (in N/m) of the spring? ____ N/m   b. What is the unloaded length (in m) of the spring? ____ m

10 cm long spring, with a spring constant of 27 N/m, is used to reload the ball in a pinball machine. The spring is compressed by 4.0 cm by a mechanism in the machine and then let go. a. Calculate the elastic potential energy stored in the spring A new spring is fitted into the machine. It only needs to be compressed by 3.0 cm to store the same amount of elastic potential energy as the previus spring. b. Calculate the spring constant of this new spring The owner of the game wants to double the potential energy stored in this new spring. c. Calculate the compression of the spring needed in order to achieve this

A wooden box of mass 6.0 kg slides on a frictionless tabletop with a speed of 3.0 m/s. It is brought to rest by a compressing spring. The spring content is 1250 N/m. a. Calculate the maximum distance the spring is compressed. b. Determine the speed and acceleration of the block who the spring is compressed a distance of 14 cm.

A 3.59 kg ball is held at rest exactly 3.7 meters in the air. Assume their is no spring in this problem. A. How much gravitational potential energy does the ball currently have? Joules B. How much kinetic energy does the ball currently have? Joules C. How much total mechanical energy does the ball have currently? Joules The ball is than allowed to fall to the ground. As the ball falls It gravitational potential energy gets converted into Kinetic Energy. The moment before hits the ground all of its energy is in the form of kinetic energy. D. How much G.P.E does the ball have the moment before it hits the ground? Joules E. How much kinetic energy does the ball have the moment before it hits the ground? Joules F. what is the ball's speed the instant before it hits the ground? m/s