Work Done using Calculus - Tank Problems
A series of free Calculus Video Lessons:
- How to Calculate the Work Required to Drain a Tank Using Calculus?
- How to Using integration to calculate the amount of work done pumping fluid?
- How to find the work required to lift a rope to the top of a building.
Related Pages
Integral Calculus
Calculus: Integration
Calculus: Derivatives
Calculus Lessons
How to calculate the work done in stretching a spring using Hooke’s Law and a definite integral?
The force required to maintain a spring stretched x units beyond its natural length is proportional to x (let k be the constant of proportionality) so we get F = kx.
Example:
A spring has a natural length of 20 cm. If a 25 Newton force is required to keep it stretched to 30 cm, how much work is required to stretch it from 20 cm to 25 cm.
How to use a definite integral to calculate the work done in raising a leaky bucket 20 feet?
Example:
A leaky 5 pound bucket is lifted 20 feet into the air at a constant speed. The rope weighs 0.3 lbs/ft. The bucket starts with 10 pounds of water and leaks at a constant rate. There are 5 pounds of water left as it reaches the top. How much work was done to raise the bucket?
Calculating the Work Required to Drain a Tank - Using Calculus
One complete example is shown along with a general procedure to follow.
Applications of Integrals - Pumping (Work)
Using integration to calculate the amount of work done pumping fluid.
Lifting a Leaky Bag of Sand
Demonstrates the use of integration to calculate the work done lifting a leaky bag of sand.
Finding Work using Calculus - The Cable/Rope Problem
This video shows how to find the work required to lift a rope to the top of a building.
Finding Work using Calculus - The Cable/Rope Problem - Part b
In this video, I find the work required to lift up only HALF of the rope to the top of the building.
Pump oil from inverted cone
Example:
An inverted conical tank with a height of 20 m and a base diameter of 25 m contains oil with density 800 kg/m3. The height of the oil is 10 m. How much work is involved in pumping all the oil out the top of the tank?
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