Question

A 72N force accelerates an object with mass (m1) by 5.0 m/s2. The same force acts on another object with mass (m2) and accelerates (m2) by 20.0 m/s2. What acceleration will the same force impart to the two objects when they are joined together?

Answer 1

Let's first find the first mass from the Newton's Second Law of Motion:

$$m_1=\dfrac{F_1}{a_1}=\dfrac{72\ N}{5.0\ \dfrac{m}{s^2}}=14.4\ kg.$$

Similarly, we can find the second mass:

$$m_2=\dfrac{F_2}{a_2}=\dfrac{72\ N}{20.0\ \dfrac{m}{s^2}}=3.6\ kg.$$

Finally, we can find the acceleration that the same force will impart to the two objects when they are joined together:

$a=\dfrac{F}{m_1+m_2}=\dfrac{72\ N}{14.4\ kg+3.6\ kg}=4.0\ \dfrac{m}{s^2}.$

Answer:

$a=4.0\ \dfrac{m}{s^2}.$