Force and work Problem

[kimchixsushi]

I have two problems that I'm having trouble with. Please help.

The first question is
A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying horizontally on its side. (In other words, the tank is not standing vertically on one of its flat ends.) If the radius of the cylinder is 2.5 meters, its length is 7 meters, and its top is 1 meter under the ground, find the total amount of work needed to pump the gasoline out of the tank. (The density of gasoline is 673 kilograms per cubic meter; use g=9.8 m/s^2.)

From a free tutoring session I found out that for a cylindrical work problem there is a universal equation, which is W = pg integral of (l-x)A(x) dx from [a,b]. I've tried it where W = (673 kg/m^3)(9.8 m/s^2) integral of (7-x)(2pi(2.5)^2) dx from [1,5] I'm pretty sure I set up the formula correct, but I think I have the limits wrong. Can you help please?

the second problem is
A lobster tank in a restaurant is 1.25 m long by 1 m wide by 90 cm deep. Find the water forces
on the bottom of the tank: Force = ?
on each of the larger sides of the tank: Force = ?
on each of the smaller sides of the tank: Force = ?
(include units for each, and use g = 9.8 m/s^2)

for this problem i have no idea at all how to do.

Thank you!

 

[Deleted member 4993]

I have two problems that I'm having trouble with. Please help.

The first question is
A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying horizontally on its side. (In other words, the tank is not standing vertically on one of its flat ends.) If the radius of the cylinder is 2.5 meters, its length is 7 meters, and its top is 1 meter under the ground, find the total amount of work needed to pump the gasoline out of the tank. (The density of gasoline is 673 kilograms per cubic meter; use g=9.8 m/s^2.)

From a free tutoring session I found out that for a cylindrical work problem there is a universal equation, which is W = pg integral of (l-x)A(x) dx from [a,b]. I've tried it where W = (673 kg/m^3)(9.8 m/s^2) integral of (7-x)(2pi(2.5)^2) dx from [1,5] I'm pretty sure I set up the formula correct, but I think I have the limits wrong. Can you help please?

Did you understand - how those equations were derived?

the second problem is
A lobster tank in a restaurant is 1.25 m long by 1 m wide by 90 cm deep. Find the water forces
on the bottom of the tank: Force = ?
on each of the larger sides of the tank: Force = ?
on each of the smaller sides of the tank: Force = ?
(include units for each, and use g = 9.8 m/s^2)

What is the pressure applied by a fluid column - density r and depth h - acting on a point at the bottom of the column?

for this problem i have no idea at all how to do.

Thank you!

 

[galactus]

A lobster tank in a restaurant is 1.25 m long by 1 m wide by 90 cm deep. Find the water forces

on each of the larger sides of the tank: Force = ?

The smaller sides can be done analogously using those dimensions

Keep consistent units. Note the depth is 90 cm. So, that is .9 meters.

I am going to use fractions instead of decimals.

Water has a weight density of 1000 kg/m^3

\(\displaystyle h(y)=\frac{9}{10}-y\)

\(\displaystyle L(y)=\frac{5}{4}\)

\(\displaystyle 9810\cdot \frac{5}{4}\int_{0}^{\frac{9}{10}}\left(\frac{9}{10}-y\right)dy\)