Chapter 7, Problem 1P

To determine

The magnitude & direction of average force exerts on the wall.

Answer to Problem 1P

The correct answer is $\text{+69 N}$

Explanation of Solution

Given:

Mass is $46-\text{kg}$ .

Velocity is $-1.2 \text{ m}/\text{s}$ .

Time is $0.80s$ .

Formula:

Impulse-Momentum Theory

  $\overrightarrow{F_{avg}}=\frac{m{\overrightarrow{v}}_f-{\overrightarrow{v}}_i}{\Delta t}$

Where,

  $\begin{array}{l}{\text{F}}_{\text{avg}}\text{= Average}\text{force}\\ \text{m = mass}\\ {\overrightarrow{v}}_f\text{=velocity after the interaction }\\ \text{Δt= Change}\text{}\text{in}\text{time}\\ {\overrightarrow{v}}_i=\text{velocity before the interaction }\end{array}$

Calculation:

This average force is the force the wall is acting on the skater. According to newtons third law, so the force of the skater on the wall is the opposite of this.

Substituting the given values in above formula,

  $\begin{array}{c}{F}_{wall}=\frac{(46 kg)(-1.2 m/s)}{0.80 s}\\ =-\frac{55.2kgm/s}{0.80 s}\\ =-69 N\end{array}$

  $\begin{array}{c}{F}_{lady}=-F_{wall}\\ =-\left(-69\text{ N}\right)\\ =69\text{ N}\end{array}$

Conclusion:

The average force exerted on the wall is $\text{+69 N}$ .