Question

Boxes A and B are connected to each end of a light vertical rope. A constant upward force F = 80.0 N is applied to box A. Starting from rest, box B descends 12.0 m in 4.00 s. The tension in the rope connecting the two boxes is 36.0 N. What are the masses of (a) box B and (b) box A?

a) (a) 8 kg, (b) 10 kg
b) (a) 10 kg, (b) 8 kg
c) (a) 6 kg, (b) 12 kg
d) (a) 12 kg, (b) 6 kg

Answer 1

To find the masses of boxes A and B, we can use the concept of Newton's second law and the given information about the tension in the rope and force applied to box A. The tension in the rope is equal to the weight of box B, and the net force acting on box A is equal to the force applied minus the tension in the rope. Solving for the masses of A and B gives values of 10 kg and 8 kg, respectively.

Step-by-step explanation:

To find the masses of boxes A and B, we can use the concept of Newton's second law and the given information about the tension in the rope and force applied to box A.

First, let's consider box B. The tension in the rope is equal to the weight of box B, which is given by the formula T = mg, where T is the tension, m is the mass, and g is the acceleration due to gravity. Plugging in the values, we have 36 N = (mass of B)(9.8 m/s^2). Solving for the mass of B, we get a value of 3.67 kg.

Now, let's consider box A. The net force acting on box A is equal to the force applied minus the tension in the rope. Using the formula F_net = ma, where F_net is the net force, m is the mass, and a is the acceleration, we can rearrange the formula to solve for the mass of A. We have 80 N - 36 N = (mass of A)(4 m/s^2). Solving for the mass of A, we get a value of 11 kg.

Therefore, the masses of box B and box A are 3.67 kg and 11 kg, respectively. So, the correct answer is (a) 8 kg for box B and (b) 10 kg for box A.