How can I calculate work done when raising a mass using W = 32r^2?

In summary, "work done" is the energy required to move an object against the force of gravity. It can be calculated by multiplying the force applied by the distance raised. The mass of the object affects the amount of work done, with larger masses requiring more energy. The work done can vary depending on the height the mass is raised and can be negative if the mass is lowered instead of raised.
  • #1
ElectronicTeaCup
23
1
Homework Statement
A cable weighing 2 pounds per foot of length (and so having a mass of 2 pounds per foot) is
suspended from the top of a well 200 feet deep and extends to the bottom. Find the work done in
raising the cable to the surface. Over the distance of 200 feet you may use 32m as the constant
weight of a mass m.
Relevant Equations
##\frac {dW} {dr} = F##
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I do not understand how to get ##W = 32r^2##
 

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  • #2
ElectronicTeaCup said:
I do not understand how to get ##W = 32r^2##
Integrate ##F## over ##r##.
 
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Likes ElectronicTeaCup
  • #3
Awesome, thank you!
 

1. How do I calculate work done when raising a mass using W = 32r^2?

To calculate work done when raising a mass using the formula W = 32r^2, you will need to know the value of r (the distance the mass is raised) and the mass of the object. You can then plug these values into the formula to find the work done.

2. What is the significance of the number 32 in the formula W = 32r^2?

The number 32 in the formula W = 32r^2 represents the acceleration due to gravity, which is approximately 9.8 m/s^2. This number is multiplied by 2 to account for the work done in both lifting the object and overcoming the force of gravity.

3. Can I use this formula for any mass and distance?

Yes, the formula W = 32r^2 can be used for any mass and distance as long as the units are consistent (e.g. mass in kilograms and distance in meters). This formula is commonly used in physics to calculate work done against gravity.

4. What are the units for work done in this formula?

The units for work done in this formula are joules (J). This is the standard unit of measurement for work and energy in the International System of Units (SI).

5. Can I use this formula to calculate work done in other scenarios?

No, this formula is specifically for calculating work done when raising a mass against gravity. There are other formulas and methods for calculating work done in different scenarios, such as pushing or pulling an object, or using a different type of force.

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