Q55E - University Physics with Modern Physics

Question

A tandem (two-person) bicycle team must overcome a force of 165 N to maintain a speed of 9.0m/s. Find the power required per rider, assuming that each contributes equally. Express your answer in watts and in horsepower

Step-by-Step Solution

Answer

The power required per rider is 742.5 W or 0.99 HP 

Step 1: Identification of given data

The given data can be listed below,

• The force on tandem is, $F=165 \mathrm{N}$  
• The velocity of tandem is, $v=9.0 \mathrm{m}/\mathrm{s}$  

Step 2: Concept/Significance of power

Power may alternatively be defined as the result of the force used to move an item multiplied by the speed of the object moving in the direction of the force.

Step 3: Determination of the power required per rider in watts and in horsepower

The power of the two rider is given by,

$$\begin{gathered} P=\overrightarrow{F}·\overrightarrow{v} \\ =Fv\cos \theta \end{gathered}$$ 

Here, $F$ is the magnitude of the force on the tandem and  $v$ is the magnitude of the velocity of the rider.

Substitute all the values in the above,

$$\begin{gathered} P=\left(165 \mathrm{N}\right)\left(9 \mathrm{m}/\mathrm{s}\right)\cos 0° \\ =1485 \mathrm{W} \end{gathered}$$ 

Power of each rider is given by,

$$\begin{gathered} P_{each}=\frac{1485 \mathrm{W}}{2} \\ =742.5 \mathrm{W} \\ =\left(742.5 \mathrm{W}\right)\left(\frac{1\mathrm{HP}}{746 \mathrm{W}}\right) \\ =0.99 \mathrm{HP} \end{gathered}$$  

Thus, the power required per rider is $742.5 \mathrm{W}$ or 0.99 HP