Question

A rollercoaster starts from a height of 45.0 m. The car on the rollercoaster has a mass of 1200 kg. When it starts, the ramp makes an angle of 60.0° above the horizontal. The coefficient of friction between the ramp and the car is 0.15. What is the acceleration of the car with and without friction? Draw the free-body diagram.

Single line text.

Answer 1

1)

$$ma=mg\sin{60}\\a=g\sin{60}\\a=9.8\sin{60}=8.5\frac{m}{s^2}$$

2)

$$ma=mg\sin{60}-\mu mg\cos{60}\\a=g(\sin{60}-\mu \cos{60})\\a=9.8(\sin{60}-0.15\cos{60})=7.8\frac{m}{s^2}$$