When you lift a bowling ball with a force of 61.1 N, the ball accelerates upward with an acceleration a. If you lift with a force of 70.9 N, the ball's acceleration is 2.07a. Calculate the weight of the bowling ball.

the weight of the ball is w = 51.94 N (mass = 5.3 kg)

Explanation:

Following Newton's second law:

net force = mass * acceleration = weight/gravity * acceleration

then denoting 1 and 2 as the first and second lift

F₁ - w = w/g * a₁

F₂ - w = w/g * a₂ = w/g * 2.07a

dividing both equations

(F₂ - w) / (F₁ - w) = 2.07

(F₂ - w) = 2.07 * (F₁ - w)

1.07*w = 2.07*F₁ - F₂

w = (2.07*F₁ - F₂) / 1.07

replacing values

w = (2.07*61.1 N - 70.9 N) / 1.07 = 51.94 N

then the weight of the ball is w = 51.94 N (mass = 5.3 kg)