calculating mass

Question

A net force acts on mass m1 and creates an acceleration.A mass m2 is added to mass m1.The same net force acting on two mass together creates one-third the acceleration.Determine the ratio m2/m1

Answer 1

Let the forced be F. When it acts only on the mass m1, the acceleration is F/m1 = a

When it acts on the combined mass m1+m2, the acceleration is F/(m1+m2) = 1/3a.

Dividing the 2nd equation by the first, we have m1/(m1+m2) = 1/3, or m2/m1 = 2.