Three parts to this problem. Questions for both parts and additional info listed in "Description" below.

Question

A pair of fuzzy dice is attached to the rearview mirror of a car with a short string. When the car accelerates forward, the string makes an angle of 7.17 degrees from the vertical.

Part a) Sketch a Free body diagram.

Part b) What direction is the net force?

Part c) What is the magnitude of the accleration?

Answer 1

The only forces acting on the fuzzy dice are gravitational force (mg) and the tension of the string (T).

a) θ = 7.17°, T_x = ma where a is the acceleration of the car; T_y = mg

b) The direction of the net force is the same as the direction the car is accelerating.

c) T_x/T_y = ma/mg = a/g = tan(7.17°)

a = g tan(7.17°) = 9.8 tan(7.17°) ≈ 1.23 m/s²