Answer to Question #148351 in Physics for Erica

Question

72 N force accelerates mass m1 by 5.0 m/s ^ 2 The same force acts on another mass and imparts to it an acceleration of 20.0 m/s ^ 2 What acceleration will the same force impart to the two masses when they are joined together ?

Answer 1

Let's first find the mass $m_1$ from the Newton's Second Law of Motion:

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

Similarly, we can find the mass $m_2$:

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

Finally, we can calculate the acceleration that the same force impart to the two masses 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:

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