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

Hope this Helps!!!

not too sure thinking all accelerations are pointed down

initial speed when it is dropped is 150 ft/s

now at the same moment the acceleration due to gravity is perpendicular to its velocity

so as we know that

now we have centripetal acceleration a = 32 ft/s^2 as its perpendicular to velocity

while tangential acceleration at the same moment will be zero

so

now radius of curvature is given as

so the radius of curvature just after it is dropped is 703.125 ft