When you lift a bowling ball with a force of 60.7 N, the ball accelerates upward with an acceleration a. If you lift with a force of 69.3 N, the ball's acceleration is 1.99a. Calculate the weight of the bowling ball.
To calculate the weight of the bowling ball, we need to understand the relationship between force, acceleration, and weight.
Weight is a force that is determined by the mass and the gravitational pull on an object. The formula to calculate weight is:
Weight = mass × acceleration due to gravity
Now, in the given scenario, we have two different forces and their corresponding accelerations. Let's assign variables to our unknowns:
Force 1 (F1) = 60.7 N
Force 2 (F2) = 69.3 N
Acceleration 1 (a1) = a
Acceleration 2 (a2) = 1.99a
Weight of the bowling ball (W) = ?
From Newton's second law of motion, we know that force is equal to mass multiplied by acceleration:
Force = mass × acceleration
Using this law, we can write the equations based on the given information:
Equation 1: F1 = M × a
Equation 2: F2 = M × 1.99a
We need to find the weight W, which is equal to mass multiplied by the acceleration due to gravity. So, let's solve for mass first.
Rearrange Equation 1 to solve for mass:
M = F1 / a
Substitute the value of M in Equation 2:
F2 = (F1 / a) × 1.99a
Simplify the equation:
F2 = F1 × 1.99
Now, we have the relationship between the two forces:
69.3 N = 60.7 N × 1.99
Solve for F1:
F1 = 69.3 N / 1.99
Calculate F1:
F1 ≈ 34.77 N
We now have the force F1 and acceleration a.
To find the weight W, we can substitute this information into the weight formula:
W = mass × acceleration due to gravity
W = F1 / a × acceleration due to gravity
Acceleration due to gravity is approximately 9.8 m/s².
Finally, we can calculate the weight:
W = (34.77 N / a) × 9.8 m/s²
Therefore, the weight of the bowling ball is approximately (34.77 N / a) × 9.8 m/s².