Question

A sphere travels down a ramp and falls a distance before landing on a plane, bouncing once, and then colliding with a domino. The domino then falls and collides with the next and so on and so forth. The last domino falls onto the side of a sphere, causing it to roll.

A. Provide the equations that can be used to describe the change in type and amount of energy across the step.

B. Calculate the amount of energy that is converted from one form to another form using the changes in mass and height. For example, if appropriate for your selected step, you could calculate the transformation of potential energy to kinetic energy.

Answer 1

a) When the sphere travels down the ramp and falls a distance then its gravitational potential energy is converted into kinetic energy. Given as:

where mass of the first sphere falling the distance under the gravitational acceleration

Now this mass when collides with the next domino of mass which falls a height of .

using conservation of momentum:

b) Now its final velocity after falling can be given by equation of motion:

hence its final kinetic energy be: