On a thread thrown over a fixed block, weights of m and 2m are suspended.

On a thread thrown over a fixed block, weights of m and 2m are suspended. With what acceleration the loads move and what is the tension force of the thread.

Given:

m1 = m is the mass of the first load thrown over the block;

m2 = 2 * m is the mass of the second weight thrown over the block;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine the acceleration of the weight system a and the thread tension T.

According to Newton’s second law:

For the second load:

F gravity – T = m2 * a

m2 * g – T = m2 * a (1);

For the first load:

T – F gravity = m1 * a;

T – m1 * g = m1 * a. (2)

Substitute the value of T from equation (2) into equation (1):

m2 * g – (m1 * g + m1 * a) = m2 * a;

m2 * g – m1 * g – m1 * a = m2 * a;

m2 * g – m1 * g = m2 * a + m1 * a;

g * (m2 – m1) = a * (m2 + m1);

a = g * (m2 – m1) / (m2 + m1) = g * (2 * m – m) / (2 * m + m) = g * m / (3 * m) = g / 3 = 10 / 3 = 3.3 m / s ^ 2.

Then the tension force of the thread is equal to:

T = m1 * a + m1 * g = m * a + m * g = m * (a + g) = m * (3.3 + 10) = 13.3 * m Newton.

Answer: the bodies move with an acceleration of 3.3 m / s ^ 2, the tension force of the thread is 13.3 * m Newton.