When you lift a bowling ball with a force of 69.3 N, the ball accelerates upward with an acceleration a. If you lift with a force of 77.2 N, the ball's acceleration is 2.00a. Calculate the weight of the bowling ball.

For this should I add both force together to find a?

To find the weight of the bowling ball, you do not need to add the forces. Weight is actually a force, and it is given by the equation:

Weight = mass × acceleration due to gravity

In this problem, we are given the force applied to lift the ball and the corresponding accelerations. However, we don't have the mass or gravitational acceleration directly. We need to use the relationship between force, mass, and acceleration to solve for the weight.

The relationship between force, mass, and acceleration is given by Newton's Second Law of Motion, which states:

Force = mass × acceleration

We can rearrange this equation to solve for mass:

mass = Force / acceleration

Now, let's analyze the problem step by step:

1. First, let's consider the force of 69.3 N and the corresponding acceleration, which we'll call "a1". Using Newton's Second Law, we can write:

69.3 N = mass × a1

2. Next, let's consider the force of 77.2 N and the corresponding acceleration, which is 2 times the previous acceleration (2.00a1). Using Newton's Second Law, we can write:

77.2 N = mass × (2.00a1)

3. Now, we have two equations with two unknowns: mass and a1. Let's solve the equations simultaneously:

69.3 N = mass × a1 ----(1)
77.2 N = mass × (2.00a1) ----(2)

To eliminate the mass, we can divide equation (2) by equation (1):

77.2 N / 69.3 N = (mass × (2.00a1)) / (mass × a1)

Simplifying, we have:

1.113 = 2.00

Now, if we simplify further, we see that the equations do not agree. This means there is no consistent solution for mass and acceleration a1. Therefore, it is not possible to determine the weight of the bowling ball with the given information.

In summary, you cannot calculate the weight of the bowling ball based on the forces and accelerations provided.

Use F=ma.

69.3-mg = ma
77.2-mg = 2ma

Eliminate a from the equation and solve for m. g=acc.due to gravity = 9.8 m/s/s.