Question

Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless, stationary pulley. One of the blocks, with a mass of 1.0 kg accelerates downward at 34g. What is the mass of the other box?

Answer 1

1/7 kg

Step-by-step explanation:

Find the diagram attached for better understanding of the question.

Given the mass of one of the blocks to be 1.0kg and accelerates downward at 3/4g.

g = acceleration due to gravity.

Let the block accelerating downward be M, mass of the other body be 'm' and the acceleration of the body M be 'a'.

M = 1.0 kg and a = 3.4g

According to newton's second law;
`\sum fy = ma_y`

For body of mass m;

T - mg = ma ... (1)

For body of mass M;

Mg - T = Ma ... (2)

Adding equation 1 ad 2;

+Mg -mg = ma + Ma

Ma-Mg = -mg-ma

M(a-g) = -m(a+g)

Substituting M = 1.0 kg and a = 3/4g into the resulting equation;

3/4 g-g = -m(3/4 g+g)

3/4 g-g = -m(7/4 g)

-g/4 = -m(7/4 g)

1/4 = 7m/4

28m = 4

m = 1/7 kg

Therefore the mass of the other box is 1/7 kg