A force (F) applied to an object of mass m1 produces an acceleration of 3.00 m/s^2.

The same force applied to a second object of mass m2 produces an acceleration of 1.00 m/s^2.

a) what is the value of the ratio m1/m2?

b) if m1 and m2 are combined into one object, what is its acceleration under the action of the force

A) For object with mass m1,

F = m1 * 3

m1 = F/3

For object with mass m2,

F = m2 * 1

m2 = F

Ratio of m1/m2

(F/3) / F = 1/3

A) using f=ma, F=m1 x 3.00 = 3m1

also F=m2 x 1.00 = m2

as the Fs are the same: 3m1=m2

this means that the ratio of m1 to m2 is 3 to 1 as there are 3 m1s for every m2.

b) again using f=ma, the combination of the masses is m1 + m2 or 4m1 as there are 3m1s in m2. so F=4m1 x a = 3m1 (as F is the same for all of them).

a = 3m1/4m1 = 3/4ms^-2