Ballistic Pendulum!

fomenkoa

Hi all

We are doing a physics lab where we lift a pendulum to a certain height, let go of it, and the pendulum strikes a physics cart on a track. A lightgate then measures the velocity of the cart.

We need to figure out the speed of the cart given the distance the pendulum is raised by

I think you do it like this:
At the top, the pendulum's energy is all mgh
at the bottom of the swing, the pendulum's energy is all kinetic, so it is now all 0.5 m v^2 from this, we can figure out its speed at the bottom

The pendulum's mass and speed at the bottom of swing is now known. The cart's mass is known and it starts from rest.

Then you just plug values into the formula for elastic collisions:

(2 * m1 / (m1+m2) )* speed of pendulum at bottom) = speed of cart




Is this correct? It seems too simple since the lab is supposed to be harder than this. Can one actually use the elastic collision formula?
Thanks

Integral

First, please read this thread so to better format your equation.

Anytime I see the expression (m₁ + m₂) in an expression about a collision I think inelastic. Could you please show us the derivation of your final velocity expression?

EDIT: Did your experimental numbers agree with your expression?

andrevdh

I would guess that one would rather use conservation of momentum. You have an isolated system assuming that the pendulum hits the cart on the same height as its center of mass and the cart has negligible friction. Therefore momentum will be conserved. The pendulum will probably swing back upwards after the collision. You need to measure the amount by which it swung upwards in order to calculate the momentum of the pendulum after the collision.