As your bus rounds a flat curve at constant speed, a package with mass .5 kg, suspended from the luggage compartment of the bus by a string 45 cm long, is found to hang at rest relative to the bus, with the string making an angle of 30 degrees with the vertical. In this position, the package is 50 m from the center of curvature of the curve. What is the speed of the bus?

Question

Anonymous · Accepted Answer

Thanks! My answer was 16.8 m/s. Is that correct?

drwls · Answer

Let T be the tension force in the string.
Apply vertical and horizontal force balances.

T cos 30 = weight = M g
T sin 30 = centripetal force = M V^2/R

Divide one equation by the other. This will eliminate the unknown T

tan 30 = V ^2/(Rg)

Solve for V