Motion on an inclined plane

Question:

What are the factors affecting the motion of a trolley on an inclined plane, and how is the angle of the plane linked to the acceleration of the trolley?

Answer:

The motion of a trolley on a slope will be affected by:
(a) the friction
(i) between the trolley and the slope (this will depend on the nature of the slope and the wheels and the mass of the trolley (m))
(ii) in the wheel bearings
(iii) due to air resistance
(b) the angle of the plane to the horizontal
(c) the value of the gravitational acceleration at that point (g)

If the trolley is running more or less freely down the slope (i.e. unpowered) the acceleration of the trolley will depend on the component of the trolley's weight down the slope.
If the weight if the trolley is W and the plane is inclined at an angle A to the horizontal the component of the weight down the slope will be:

Accelerating force = component of weight = W sin (A)

The acceleration is therefore = F/m = [W sin (A)]/m = [mg sin (A)]/m