Question

A rollercoaster car, 300 kg with passengers, accelerates down a 65 degree hill. we will assume that friction is small enough that it can be ignored. 1) determine the value of the component of the gravitational force parallel to the hill. 2) what is the acceleration of the rollercoaster down t

Answer 1

Refer to the diagram shown below.

m = 300 kg, the mass of the rollercoaster
θ = 60°
g = 9.8 m/s²
Friction is ignored.

The component of the weight acting down the incline (no friction) is
F = mg sinθ
   = (300 kg)*(9.8 m/s²)*sin(65°)
   = 2664.5 N

If the acceleration down the incline, then
(300 kg)*(a m/s²) = 2664.5 N
a = 2664.5/300 = 8.882 m/s²

Answers:
(1) F = 2664.5 N acting down the hill
(2) a = 8.882 m/s²