Question

Question #d8599

Answer 1

The relation between force (`F`) and acceleration (`a`) is given by Newton's second Law:

`F = ma`,

where `m` is the mass of the body under consideration.

Let us denote the following situations:
(1) 628 N applied to a crate of mass `m`, yielding an acceleration `a_1`;
(2) the same force applied to a crate of mass `3.8m`, yielding an acceleration `a_2`.

If we take the ration between the accelerations:

`a_2/a_1 = (F/m_2)/(F/m_1)`,

since the force is the same for both situations. Note that `m_2 = 3.8m_1`; then:

`a_2/a_1 = cancel(F)/(3.8cancel(m_1)) * cancel(m_1)/cancel(F)`;

`a_2/a_1 = 1/3.8`.

That is, the acceleration during situation (2) is smaller by a factor of 3.8 when compared to situation (1) (which is actually expected, since the force being applied is the same and the mass has increased).