Physics Lab #10

 

Hooke’s Law: Spring Force Lab

Theory

A spring at its equilibrium point gives rise to no force, but if it is stretched or compressed from that equilibrium state a force is generated to try to push or pull the spring back to equilibrium (this is called a restitution, or restorative, force).   The force of restitution, F, will act in opposition to the displacement from equilibrium, x.  Further, the size of the force will be proportional to the displacement, and thus we write:

F = -kx

Where k is called the “spring constant” and has units of N/m.  (The minus sign is there to indicate that the restorative force and the displacement are in opposite directions.

The equation is named after its discoverer, Robert Hooke, so is known as Hooke’s Law.  It works well for springs and okay for other materials, as long as the displacement is kept relatively small and the material dose not rupture.

The period, P, for a mass, m, suspended from a spring is given by:

P = 2π √(m/k)

Procedure

Part 1

1. Hang the spring tight end up from a clamp on the ring stand.  Suspend the mass carrier from the bottom of the spring if you have one.
2. Using different masses and meter stick fill in the table below.  (Don’t forget to add the mass of the spring carrier, if you are using one.)

3. Draw a free body diagram for the suspended mass and use it, Hooke’s Law, and the fact that weight is mg, to get a relationship between the mass and the displacement. 
4. Draw the appropriate graph and use it to argue for the validity of Hooke’s law and calculate your spring constant if it appears to be valid.

Part 2

1. Using the same set up as in part 1 hang a mass from the spring and use a stop watch to find the period for ten oscillations of the masses.  (Don’t forget to add the mass of the spring carrier, if you are using one.)
2. Calculate the period of one oscillation and use that result and the equation from the theory section to find the spring constant.
3. Compare your results to those of part 1.