Chapter 8.2, Problem 15PP

To determine

The torque of the pedal in horizontal and vertical position.

Answer to Problem 15PP

The torque exerted on the pedal in horizontal position is $120\text{N}\cdot \text{m}$ and the torque exerted on the pedal in vertical position is $0\text{N}\cdot \text{m}$ .

Explanation of Solution

Given info:

Mass of the pedal, $m=65\text{kg}$

Distance of the pedal from the center of the ring, $r=18\text{cm}$

Angle for the horizontal position of the pedal, $\theta =90°$

Angle for the vertical position of the pedal, $\alpha =0°$

Formula Used:

The expression for torque exerted on the pedal in horizontal position is,

  $F_H=mgr\sin \theta$ …… (1)

The expression for torque exerted on the pedal in vertical position is,

  $F_V=mgr\sin \alpha$ …… (2)

Calculation:

Substitute the values in the above expression (1).

  $\begin{array}{c}{F}_H=\left(65\text{kg}\right)\left(9.8\text{m}/{\text{s}}^2\right)\left(18\text{cm}\times \frac{1\text{m}}{100\text{cm}}\right)\left(\sin 90°\right)\\ =120\text{N}\cdot \text{m}\end{array}$

Substitute the values in the above expression (2).

  $\begin{array}{c}{F}_V=\left(65\text{kg}\right)\left(9.8\text{m}/{\text{s}}^2\right)\left(18\text{cm}\times \frac{1\text{m}}{100\text{cm}}\right)\left(\sin 0°\right)\\ =0\text{N}\cdot \text{m}\end{array}$

Thus, the torque exerted on the pedal in horizontal position is $120\text{N}\cdot \text{m}$ and the torque exerted on the pedal in vertical position is $0\text{N}\cdot \text{m}$ .