Acceleration down an inclined plane?

Question

I need to know how I can calculate the acceleration of a momentum trolley down an inclined plane. i know it has something to do with gravity and sin of the angle from the ground but can anyone give me the definite correct formula? thanks

Answer 1

Use the fundamental definitions of the trig functions from Pythagoras and not only will you have the formula but you will also understand where it comes from:

The sine of an angle in a right triangle is defined as the length of the opposite side divided by the length of the hypoteneuse. It should be obvious from this that the sine of zero degrees is zero, which is what you get when the plane is horizontal. Raising the plane to form an incline increases both the angle and the length of the opposite side (the plane itself is the hypoteneuse).

As the angle increases to 90 degrees the sine increases to a maximum value of 1, and then decreases if the plane tilts back the other way, which should also be obvious.

A plane tilted 90 degrees is vertical so anything 'rolling' down it will actually just be falling at the acceleration of gravity. A horizontal plane in effect means your trolley has nowhere to fall so it stays still, but as it tilts upwards there is a bigger and bigger vertical component to its velocity - found by multiplying g times the sine of the angle.

Answer 2

a = g*sin(angle) = (9.81 m/s^2)*sin(angle)

That's neglecting friction and the angular momentum of the wheels.

Take care,

David