Calculate the work done in Rectangle?

In summary, the conversation discusses a particle moving in the XY plane with a force given by F=2y i + x^2 j. The particle travels from the origin to a final position at coordinates (x,y)=(5,5). The task is to calculate the work done by the force along different paths (OAC, OBC, and OC) and determine if the force is conservative. The solution involves using the equation for work, ∫ f. dx, and integrating the given force along the different paths. The complete solution can be found in the provided link.
  • #1
abrowaqas
114
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..
 
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  • #2
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:​
 
  • #3

Related to Calculate the work done in Rectangle?

What is the formula for calculating work done in a rectangle?

The formula for calculating work done in a rectangle is: Work = Force x Distance, where Force is measured in Newtons (N) and Distance is measured in meters (m).

How do I determine the force in a rectangle?

The force in a rectangle can be determined by multiplying the mass (m) by the acceleration (a). The formula for force is: Force = mass x acceleration, where mass is measured in kilograms (kg) and acceleration is measured in meters per second squared (m/s²).

What units are used to measure work in a rectangle?

The standard unit for measuring work in a rectangle is the joule (J). However, other units such as calories (cal) or kilowatt-hours (kWh) may also be used.

When is the work done in a rectangle considered positive or negative?

The work done in a rectangle is considered positive when the force and displacement are in the same direction. It is considered negative when the force and displacement are in opposite directions.

Can I use the same formula to calculate the work done in other shapes besides a rectangle?

No, the formula for calculating work done in a rectangle is specific to rectangles. Other shapes may require different formulas, depending on the forces and distances involved.

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