(a) A 120-lb woman rides a 15-lb bicycle up a 3-percent slope at a constant speed of 5 ft/s. How much power must be developed by the woman? (b) A 180-lb man on an 18-lb bicycle starts down the same slope and maintains a constant speed of 20 ft/s by braking. How much power is dissipated by the

Question

(a)A 120-lb woman rides a 15-lb bicycle up a 3-percent slope at a constant speed of 5 ft/s. How much power must be developed by the woman? (b) A 180-lb man on an 18-lb bicycle starts down the same slope and maintains a constant speed of 20 ft/s by braking. How much power is dissipated by the brakes? Ignore air resistance and rolling resistance.

Accepted Answer

[latex]\begin{aligned} an heta & =\frac{3}{100} \quad heta=1.718^{\circ} \ ext{(a)} \quad \quad W & =W_B+W_W=15+120 \W & =135 \ ext{lb} \P_W & = \mathbf{W} \cdot \mathbf{v} =(W \sin heta)( u) \P_W & =(135)\left(\sin 1.718^{\circ} ight)(5) \P_W & =20.24 \ ext{ft} \cdot ext{lb} / s\end{aligned}[/latex]

[latex]P_W=20.2 ext{ft} \cdot ext{lb} / s \blacktriangleleft [/latex]

[latex]\begin{aligned} ext{(b)} \quad \quad& W=W_B+W_m=18+180 \& W=198 ext{lb}\end{aligned}[/latex]

[latex]P_B=118.7 \ ext{ft} \cdot ext{lb} / s \blacktriangleleft [/latex]

Brakes must dissipate the power generated by the bike and the man going down the slope at 20 ft/s

[latex]\begin{aligned}& P_B= \mathbf{W} \cdot \mathbf{v} =(W \sin heta)( u) \& P_B=(198)(\sin 1.718)(20)\end{aligned}[/latex]

[latex]P_B=118.7 \ ext{ft} \cdot ext{lb} / s \blacktriangleleft[/latex]

Question 13.49: (a) A 120-lb woman rides a 15-lb bicycle up a 3-percent slop...

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