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

Click For Summary
SUMMARY

The discussion centers on calculating work done using the formula W = 32r². The key insight provided is the integration of force (F) over the distance (r) to derive the work done in raising a mass. Participants emphasize the importance of understanding the relationship between force and distance in this context.

PREREQUISITES
  • Understanding of basic physics concepts, specifically work and energy.
  • Familiarity with integration techniques in calculus.
  • Knowledge of force and its relation to mass and acceleration.
  • Ability to manipulate algebraic expressions and equations.
NEXT STEPS
  • Study the principles of work and energy in physics.
  • Learn integration techniques in calculus, focusing on definite and indefinite integrals.
  • Explore the relationship between force, mass, and acceleration using Newton's laws.
  • Practice solving problems involving work done by varying forces.
USEFUL FOR

Students in physics, educators teaching mechanics, and anyone interested in understanding the mathematical foundations of work and energy calculations.

ElectronicTeaCup
Messages
23
Reaction score
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##
1591086794042.png

1591086826344.png
1591087613609.png

1591087650776.png

1591087693605.png
I do not understand how to get ##W = 32r^2##
 

Attachments

  • 1591087671816.png
    1591087671816.png
    18.3 KB · Views: 203
Physics news on Phys.org
ElectronicTeaCup said:
I do not understand how to get ##W = 32r^2##
Integrate ##F## over ##r##.
 
  • Like
Likes   Reactions: ElectronicTeaCup
Awesome, thank you!
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
936
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K
Replies
7
Views
2K
  • · Replies 94 ·
4
Replies
94
Views
5K
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
965
  • · Replies 16 ·
Replies
16
Views
1K
  • · Replies 15 ·
Replies
15
Views
2K
  • · Replies 7 ·
Replies
7
Views
8K