Question

A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of 32 m/s, the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 140 m), the block swings toward the outside of the curve. Then the string makes an angle θ with the vertical. Find θ.

Answer 1

The vertical component of string tension, T sinè, equals the weight, M g.

The horizontal component of string tension, T cosè, is the centripetal force, m V^2/R.

Note that the horizontal/vertical force ratio is tan è

V^2/(Rg) = tan è

Solve for è