Q 50 - Calculus

Question

Find the work described in each of Exercises 49–60.

The work required to lift a bathtub full of water 30 feet into the air, given that the bathtub itself weighs 150 pounds and it holds a rectangular volume of water measuring 5 feet by 2 feet by 2 feet.

Step-by-Step Solution

Answer

Work required is 41,940 foot pounds .

Step 1: Given Information

The work required to lift a bathtub full of water 30 feet into the air, given that the bathtub itself weighs 150 pounds and it holds a rectangular volume of water measuring

5 feet by 2 feet by 2 feet.

Step 2: Volume and Weight formula

Volume of bathtub= length times width times height 

a rectangular volume of water measuring 5 feet by 2 feet by 2 feet.

$V=5*2*2=20 fee{t}^3$

Step 3: Find Force

Force exerted by weight density and Volume V is 

$$\begin{gathered} F=V\omega \\ weight density of soda \omega =62.4 \\ V=20 \\ F=20(62.4) \\ F=1248 \\ Force exerted 1248 pounds \end{gathered}$$

Bathtub weighs 150 pounds

Combined weight of bathtub and water is 

1248 + 150=1398

Step 4: Work

Work formula is 

$$\begin{gathered} W=Fd \\ a bathtub full ofwater 30 feet into the air, \\ d=30 \\ F=1398 \\ W=1398\left(30\right) \\ W=41940 \end{gathered}$$

Work required is 41,940 foot pounds