Two weights with masses m1 = 6 kg and m2 = 8 kg lying on a smooth horizontal table are connected by an inextensible thread.

Two weights with masses m1 = 6 kg and m2 = 8 kg lying on a smooth horizontal table are connected by an inextensible thread. With what force it is necessary to pull a load of mass m1 so that the thread tension is T = 60 N

Given:
m1 = 6 kilograms – the mass of the first body;
m2 = 8 kilograms – the mass of the second body;
T = 60 Newton – required thread tension.
It is required to determine F (Newton) – with what force it is necessary to pull the first body so that the tension force of the thread is equal to T.
Since the condition of the problem indicates that the table is smooth, the friction force will not be taken into account when solving the problem. Then, let the bodies move with some acceleration equal to a. Let’s compose a system of equations for these bodies:
F – T = m1 * a (1);
T = m2 * a (2).
From equation (2) we find that a = T / m2.
Substituting this value into equation (1), we get:
F – T = m1 * T / m2;
F = m1 * T / m2 + T;
F = (m1 * T + m2 * T) / m2 = T * (m1 + m2) / m2;
F = 60 * (6 + 8) / 8 = 60 * 14/8 = 105 Newton.
Answer: the load must be pulled with a force equal to 105 Newtons.