The body M = 3 kg under the action of force acquires a. Determine the unknown body m if under

The body M = 3 kg under the action of force acquires a. Determine the unknown body m if under the action of the same force this body attached to the body m1 = 1 kg acquires the same acceleration in IFR.

Let F be the force under the action of which a body of mass M received acceleration a. According to the condition, a composite body of mass m1 + m under the action of the same force F also received an acceleration a. According to Newton’s second law

F = Ma and F = (m1 + m) a, whence

Ma = (m1 + m) a,

M = m1 + m,

m = M – m1 = 3 – 1 = 2 kg.

Answer: 2 kg.