Question

help so lost!!!!
A 2.53 kg sphere is compressing a spring (k = 185 N/m) a distance of 11.8 cm from its relaxed position. When in its relaxed position, the sphere is at a 2.18 m above the floor. The sphere is released from rest and oscillates up and down.


(a) What is the sphere's speed (in m/s) when it has stretched the spring a distance of 28.7 cm below its relaxed position?

Answer 1

So this is a conservation of energy problem - what are the general definitions for the potential energy of a spring, the gravitational potential energy of a body, and the body's kinetic energy?
\[U_{spring} = ?
\\ U_{grav} = U = ?
\\ K = ?\]

Answer 2

potential energy

Answer 3

Oh ok thank you! But with the knowledge of those definitions, how do i set the problem up?

Answer 4

Total energy of the system:
\[E = PE_\text{grav} + PE_\text{spring} + KE\]

At the start (x = 11.8 cm) kinetic energy is zero, so the total energy is just the sum of the spring and gravitational potential energies.

You can work out the two potential energies at x = -28.7 cm and subtract them from the total energy at the start. This gives you the kinetic energy, which you can use to calculate velocity.

Answer 5

Make sure that the signs of the displacements are noted - it doesn't matter so much in the potential for the spring, since they're squared, but when finding the height for the gravitational potential energy you have to find the difference in position. Starting from 11.8 cm above the relaxed position and ending -28.7cm is much different from starting with both below. (And they are both below, since it says the spring is initially compressed).

Answer 6

It starts at 11.8 cm below, it will never reach 28.7cm below without initial velocity, an external force or violating conservation of energy.

The spring must be hanging from a ceiling