Chapter 11, Problem 1CP

Which bicyclist is more likely to go faster: one who keeps his head and his body in the most upright position or one who leans down and brings his body closer to his knees? Why?

To determine

Whether bicyclist who keeps his head and his body in the most upright position is faster than the one who leans down and brings his body closer to his knees.

Explanation of Solution

Write the expression for the drag force.

  $D=C_D\frac{1}{2}\rho U^{2}A$........ (I)

Here, the coefficient of the drag is $C_L$, the density is $\rho$, the flight speed is $U$ and the frontal area is $A$.

The frontal area of the body is directly proportional to the drag force on the body. If the head of the bicyclist and his body is in the most upright position then the frontal area will also increase. Due to increase in the frontal area, the drag force will also increase. The increase in the drag force results in an increase in the resistance to the free movement of the bicyclist. The increase in the resistance will decrease the velocity of the body.

But, if the bicyclist leans down and brings his body closer to his knees, then the frontal area will decrease. Due to a decrease in the frontal area, the drag force will also decrease. The decrease in the drag force results in the decrease in the resistance to the free movement of the bicyclist. The decrease in the resistance will increase the velocity of the body.

Therefore, the bicyclist one who leans down and brings his body closer to his knees goes faster.