Question #d8599

1 Answer
Carlos S.
Jan 24, 2018

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).

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