Question

Two boxes of masses 3M and 5M are attached by a massless rope. They are being pulled to the right with a constant force of P = 800 N, which allows them to just overcome static friction, with a μs= 0.70 between the floor and the boxes.

a. Find M.
b. Find the Tension in the rope between the two boxes.

Answer 1

a) about 14.577 kg

b) 300 N

Step-by-step explanation:

b) In order for the acceleration to be the same for each mass, the 800 N force must be divided between the boxes in proportion to their mass. That is, the net force on the 5M mass must be 5/8 of the total force, or 500 N. Then the tension in the rope is 800 N -500 N = 300 N, which is 3/8 of 800 N.

Tension: 300 N

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a) The total mass is 8M, and the total normal force on the floor is ...

F = ma = (8M)(9.8 m/s^2)

The friction force is 0.7 times this, and is equal to the 800 N force pulling on the boxes.

800 N = (8M)(9.8 m/s^2)(0.7)

M = 800/(8·9.8·0.7) kg ≈ 14.577 kg