Consider a mass and spring system. If the mass is pulled by distance x, stretching the spring by x, write the expression for the potential energy

A 28 kg child jumps on a spring-driven pogo stick. At one point, the child stands on the stick so that only their weight pushes the spring down. If the spring compresses by 8 cm,  a) What is the spring constant of the pogo stick?b) What is the spring potential energy?

A 12.0 kg box is given an initial push that starts it sliding across the floor. It eventually comes to a stop. If the box has an initial velocity of 3.5 m/s, how much work is done by friction to cause it to come to a stop? (Yes, you are correct, you do not know the coefficient of friction.)

The force law for a non-linear spring is F(x) = -60x1.15 N. Find the work required to compress the spring 30 cm from its resting length.

Suppose that 60 J of work is done to stretch a bow a distance of 0.5 m.  (a)  What is the increase in potential energy of the bow?  (b)  If the spring constant of the bow is 1200 Nt/m, what distance was the bow stretched?

A certain spring is found not to obey Hooke's law; it exerts a restoring force F(x) = -ax² - 6x³ if it is stretched or compressed, where: a = 10.0N/m², B = 300.0N/m³ The mass of the spring is negligible. Calculate the potential energy function U(x) for this spring, if U(x=0) = 0. Find the spring potential energy at x = 0.500 m

.  A pogo stick has a spring with a spring constant of 2.5×104N/m,, which can be compressed 12.0 cm. To what maximum height from the uncompressed spring can a child jump on the stick using only the energy in the spring, if the child and stick have a total mass of 40 kg?

On Earth with a gravational acceleration g, the potential energy stored in an object varies directly with its mass m and its vertical height h. What is the equations of the potential energy of a 2kg skateboard that is sliding down a ramp?

Your answer is partially correct. The figure shows an 7.8 kg stone at rest on a spring. The spring is compressed 9.9 cm by the stone. (a) What is the spring constant? (b) The stone is pushed down an additional 26 cm and released.What is the elastic potential energy of the compressed spring just before that release? (c) What is the change in the gravitational potential energy of the stone-Earth system when the stone moves from the release point to its maximum height? (d) What is that maximum height, measured from the release point? (a) Number 172 Units N/m (b) Number 49.75 Units J (c) Number 79.75 Units (d) Number 64.7 Units cm