A rollercoaster car, 300 kg with passengers, accelerates down a 65° hill. We will assume that friction is small enough that it can be ignored.

Question

A) Determine the value of the component pf the gravitational force parallel to the hill

B)What is the acceleration oof the rollercoaster down the hill?

C)If they are traveling 4 m/s, how fast will they be traveling at the end of the straight stretch 20 m later?

Answer 1

A) F_gx = mg*sin(65) = (300 kg)(9.8 m/s/s)*sin(65) = 577.3 N

B) F_gx = ma = mg*sin(65) --> masses cancel

a = (9.8 m/s/s)*sin(65)

a = 8.88 m/s/s

C) v_f² = v₀² + 2aΔx

v_f² = (4 m/s)² + 2(8.88 m/s/s)(20 m)

v_f² = sqrt(371.2 m²/s²)

v_f = 19.3 m/s