A 0.18-kg ball on a stick is whirled on a vertical circle at a constant speed. When the ball is at the three o'clock position, the stick's tension is 19 N. Find the tension in the stick when the ball is (a) at the twelve o'clock and (b) at the six o'clock positions.

a) 17 N

b) 21 N

Explanation:

At the 3 o'clock position, the sum of the forces towards the center is:

∑F = ma

T = m v² / r

19 = m v² / r

At the 12 o'clock position, the sum of the forces towards the center is:

∑F = ma

T + mg = m v² / r

T + (0.18) (9.8) = 19

T = 17.2 N

At the 6 o'clock position, the sum of the forces towards the center is:

∑F = ma

T - mg = m v² / r

T - (0.18) (9.8) = 19

T = 20.8 N

Rounding to two significant figures, the tensions are 17 N and 21 N.