Chapter 10.1, Problem 9PP

a.

To determine

Work done by rider on the bike.

Answer to Problem 9PP

  $6.875\text{kJ}$

Explanation of Solution

Given:

Mass of bicycle is $m=13\text{kg}$

Length of road is $d=275\text{m}$

Inclination of hill is $\theta ={25}^o$

Force applied parallel to road is $F=25\text{N}$

Formula used:

As displacement is in the direction of force.

So, $W=Fd$ .... (1)

Calculation:

Putting the values in (1)

  $\begin{array}{l}W=25\times 275\\ =6.875\text{kJ}\end{array}$

b.

To determine

Work done by gravity on the bike.

Answer to Problem 9PP

  $W=-14.8\text{kJ}$

Explanation of Solution

Given:

Mass of bicycle is $m=13\text{kg}$

Length of road is $d=275\text{m}$

Inclination of hill is ${25}^o$

Formula used:

Work done is given as,

  $W=Fd\cos \theta$ .... (2)

Calculation:

As force is downward and inclination of hill is ${25}^o$

So, $\theta {\text{=90}}^o+{25}^o={115}^o$

Also $F=mg$

Putting the values in (1)

  $\begin{array}{l}W=mgd\cos \theta \\ =13\times 9.8\times 275\times \cos {115}^o\\ =-14.8\text{kJ}\end{array}$