Question

You go out to the barn and start up the egg collecting machine. Eggs slide down a 30 degree ramp with a coefficient of kinetic friction of 0.2. What is the acceleration of the egg as it moves down the ramp?

If the ramp is two meters long, how fast are the eggs moving when they hit the bottom?

If we assume that the eggs are spherical with a radius of 3 cm, mass 200 grams and roll down the ramp instead of sliding, now recalculate how fast they are moving when they reach the bottom.

Answer 1

Given the inclination of the ramp is and the coefficient of kinetic friction is = 0.2

a) Let m be the mass of the egg. The forces acting on the egg is shown in the figure below.

The second law equation for the egg is given by,

So the acceleration of the egg as it moves down the ramp is 3.20m/s2.

b) Given the length of the ramp is L = 2m. Assume that the egg is at rest at the top of the ramp. Then,

So the velocity of the egg when they hit the bottom of the ramp is 3.58m/s.

c) Here the egg is considered as a solid sphere of radius R = 3cm = 0.03m and mass m = 200g = 0.2kg. Now the egg is rolling instead of sliding. Applying law of conservation of energy,

But,

Therefore,

For a solid sphere,

So if the egg was rolling instead of sliding, the speed at the bottom of the ramp will be 3.74m/s.