Chapter 8.2, Problem 27PP

To determine

The force required to produce the same acceleration on the gear, as a force of $15\text{N}$ on the chain.

Answer to Problem 27PP

  $5.5\text{N}$

Explanation of Solution

Given:

The radius of the gear, $r_g=0.14\text{m}$

The radius of the tire, ${\text{r}}_t=0.38\text{m}$

Force on the chain, ${\text{f}}_c=15\text{N}$

Formula Used:

Torque is the product of the force applied and the perpendicular distance between the line of action and the axis of rotation.

  $\tau \text{=force}\times {\text{r}}_{\perp }$ .

Calculation:

  $\tau \text{=force}\times {\text{r}}_{\perp }$

Torque on the chain= torque on the gear

  ${\text{f}}_c\times {\text{r}}_g={\text{f}}_s\times {\text{r}}_t$

Substituting the values

  $15\text{N}\times 0.14\text{m}={\text{f}}_s\times 0.38\text{m}$

Solving for ${\text{f}}_s$

  ${\text{f}}_s=5.5\text{N}$

Conclusion:

The force required to produce the same acceleration on the gear is $5.5\text{N}$