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# A force applied to an object of mass $\text{m1}$ produces an acceleration of 3.00 ms$^{-2}$. The same force applied to a second object of mass $\text{m2}$ produces an acceleration of 1.00 ms$^{-2}$. If the two masses are combined into one object, what is the acceleration under the action of the force?

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• According to Newton's second law: When viewed from an inertial reference frame, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Answer:0.75 ms$^{-2}$
According to Newton's second law, $F = ma$
Given, $a1 = 3 m/s^2$ and $a2 = 1 m/s^2, \rightarrow F = m1 \times 3 = m2 \times 1 \rightarrow \large\frac{m1}{m2} $$= \large\frac{1}{3} \Rightarrow m2 = 3 m1 Now, if the masses are combined into one entity, F = (m1+m2) a \rightarrow F = (m1 + 3m1) a = 4m1 \times a This is equal to F = m1a1 \rightarrow m1a1 = 4m1a \rightarrow a = \large\frac{m1 \times 3}{4 \times m1}$$= 0.75 ms^{-2}$
edited Aug 19, 2014