When you lift a bowling ball with a force of 71.6 N, the ball accelerates upward with an acceleration a. If you lift with a force of 82.3 N, the ball's acceleration is 1.91a. Calculate the weight of the bowling ball.

59.84 N

Explanation:

The net force is responsible for the upward acceleration of the bowling ball.

The net force acting on a body accelerates the body in the same direction as that in which the resultant is applied.

Net force = ma

ma = F - mg

In the first case,

F = 71.6 N, a = a m/s²

ma = 71.6 - mg (eqn 1)

In the second case,

F = 82.3 N, a = 1.91a m/s²

m(1.91a) = 82.3 - mg

1.91 ma = 82.3 - mg (eqn 2)

Substitute for ma in (eqn 2)

1.91 (71.6 - mg) = 82.3 - mg

136.756 - 1.91 mg = 82.3 - mg

136.756 - 82.3 = 1.91 mg - mg

0.91 mg = 54.456

mg = 54.456/0.91

mg = 59.84 N

Hence, the weight of the bowling ball = 59.84 N

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