Question

On a construction site, a winch is used to wind cable onto the drum of the winch. For the first layer of cable, the line pull P of the winch is related to the diameter D of the drum by the formula P=K/Dwhere k is a constant. If P=4500 lb and D=4 in., find the value of the constant k in foot-pounds

Answer 1

Given:

On a construction​ site, a winch is used to wind cable onto the drum of the winch.

For the first layer of​ cable, the line pull P of the winch is related to the diameter D of the drum by the formula

$P=\frac{k}{D}$

where k is a constant.

Required:

To find the value of k if P=4500 lb and D=4 ​in.

Explanation:

Let

$P=\frac{k}{D}$

If

$\begin{gathered} P=4500lb \\ D=4in \end{gathered}$

Now we have to convert the given D inches into foot.

$\begin{gathered} D=4\text{ in} \\ =0.33333foot \end{gathered}$

Now

$\begin{gathered} 4500=\frac{k}{0,33333} \\ \\ k=1499.9985 \end{gathered}$

Final Answer:

The value of k is 1499.9985 foot-pounds.