Chapter 7, Problem 58A

When 56-kg Diane on rollerskates pushes against a wall with a force of 28 N, she accelerates away from the wall. Show that Diane’s recoil acceleration is $0.50{\text{ m/s}}^{\text{2}}$.

To determine

To show: Person D recoil acceleration is 0.5 m/s².

Explanation of Solution

Given:

Weight of person D, $F_g=56\text{kg}$

Force by person D on the wall, $F=28\text{N}$

Formula Used:

From Newton’s second law, the net force is

  $F=ma$

Where, $m$ is mass and $a$ is acceleration.

From Newton’s third law,

Action force = Reaction force

Calculation:

From Newton’s third law, the reaction force exerted by wall on person D is also $F=28\text{N}$ but in opposite direction.

So, for person D

  $\begin{array}{l}F=ma\\ 28=56\times a\\ \Rightarrow a=\frac{28}{56}=0.5{\text{m/s}}^2\end{array}$

Conclusion:

Therefore, it is proved that person D recoil acceleration is $0.5{\text{m/s}}^2$ .