How much work is done lifting a 30 pound object from the ground to the top of a 60 foot building if the cable used weighs 1.5 pounds per foot ?

Question

asked Feb 17, 2023 102k views

1 Answer

Ava · Answer 1 · 2023-02-23T19:05:48+0000

Given:

1. Lifting a 30 pound object from the ground to the top of a 60 foot building.

2. The cable used weighs 1.5 pounds per foot.

To determine how much work is done, we first note that based on the given information, our continuous force would be:

$\begin{gathered} F(x)=30+((1.5)(60)-1.5x) \\ Simplify \\ F(x)=30+(90-1.5x) \\ F(x)=120-1.5x \end{gathered}$

Next, we apply the formula:

$\begin{gathered} W=\int_a^bF(x)dx \\ where: \\ W=work \\ a=0 \\ b=60 \end{gathered}$

We plug in what we know:

$\begin{gathered} W=\int_0^(60)(120-1.5x)dx \\ =\int_0^(60)(120)dx-\int_0^(60)(1.5x)dx \\ Simplify \\ W=7200-2700 \\ W=4500 \end{gathered}$

Therefore, the answer is: 4500 foot-pounds