Question

Winch A winch of radius 2ft is used to lift heavy loads. If the winch makes 8 revolutions every 15 s, find the speed at which the load is rising.

Short answer

$\mathbf{6}\mathbf{.7}\mathbf{\text{ft}}\mathbf{/}\mathbf{\text{sec}}$

Step-by-step solution

Step 1. Given information.

First, calculate the central angle in radian,.
Then evaluate angular speed by using$w=\frac{\theta }{t}$ and linear speed by using$v=rw$

The given values are:

Radius $r=2\text{ft}$, total revolution$=8$ and time$t=15\text{s}$

To find:

The linear speed to lift the load.

Step 2. Finding value of ω.

Value of central angle in radian for 8 revolutions.
Central angle $\theta =8\cdot 2\pi$

$$\begin{gathered} \theta =16\pi radians \\ \omega =\frac{\theta }{t} \end{gathered}$$

The angular speed at which load is rising is $\omega =\frac{16\pi }{15}$

$\omega =3.35\text{rad}/\text{sec}$

Step 3. Finding the value of v

The linear speed at which load is rising$v=rw$

$$\begin{gathered} v=2\cdot \left(3.35\right)\text{ft}/\text{sec} \\ v=6.7\text{ft}/\text{sec} \end{gathered}$$

Thus, this is the value of linear speed.