Calculate the work done in Rectangle?

Click For Summary
SUMMARY

The discussion focuses on calculating the work done by a force F = 2y i + x² j on a particle moving from the origin to the coordinates (5,5) in the XY plane. The work is evaluated along three paths: OAC, OBC, and OC, using the integral W = ∫ F · dx. The user successfully integrates the force components along the specified paths, confirming the calculations with assistance from other forum members. The final answer and detailed solution can be found in the provided link.

PREREQUISITES
  • Understanding of vector calculus and line integrals
  • Familiarity with the concept of work in physics
  • Knowledge of conservative forces and their properties
  • Proficiency in evaluating definite integrals
NEXT STEPS
  • Study the properties of conservative forces in physics
  • Learn about line integrals in vector calculus
  • Explore the application of work-energy theorem in different contexts
  • Practice solving problems involving multiple paths in force fields
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of work done by forces in vector fields.

abrowaqas
Messages
113
Reaction score
0

Homework Statement



A force acting on a particle moving in XY plane is given by F= 2y i + x^2 j . particle moves from origin to a final position having coordinates (x,y)=(5,5). calculate the work done by force F along

B_____________C
| |
| |
O |____________| A

a) Path OAC
b) Path OBC
c) Path OC
d) is force F is conservative ?

Homework Equations


work. ∫ f. dx


The Attempt at a Solution



a)
Path OAC
W= ∫(O to A) + ∫(O to B)
= ∫ (O to A) F. dx + ∫ (O to B) F. dy
= ∫( 0 to 5 ) 2y dx + ∫(0 to 5 ) x^2 dy

how it goes in the intergration ..
kindly help i am not getting it cleary..
 
Physics news on Phys.org
hi abrowaqas! :wink:

yes that's fine :smile: …

in ∫ f(x) dy, x is a constant, so you can take it outside the ∫ …

f(x) ∫ dy :wink:​
 

Similar threads

Work Done in slowly pulling a thread
  • · Replies 28 ·
Replies
28
Views
2K
Forces involved in principle of virtual work
  • · Replies 2 ·
Replies
2
Views
886
How do I find the work done for a 100 N downward force?
  • · Replies 4 ·
Replies
4
Views
2K
Work done on crate moving on incline
  • · Replies 28 ·
Replies
28
Views
2K
Work done by non-conservative force while particle moves in circle
  • · Replies 25 ·
Replies
25
Views
2K
Integral for work done leading to potential energy sign confusion
  • · Replies 5 ·
Replies
5
Views
2K
Work done pushing a spring from the side
  • · Replies 9 ·
Replies
9
Views
2K
Work done on a pendulum by gravity
  • · Replies 7 ·
Replies
7
Views
3K
Solving a Motion Problem with Work-Energy Theorem
  • · Replies 23 ·
Replies
23
Views
2K
Work done in elevator problem — is it positive or negative?
  • · Replies 3 ·
Replies
3
Views
3K