Calculating Work Done by a Variable Applied Force

  • Thread starter Thread starter MissPenguins
  • Start date Start date
  • Tags Tags
    Integration Work
AI Thread Summary
The discussion centers on calculating the work done by a variable force defined by the equation F = k1xn - k2, with specific values for k1 and k2. The correct formula for work is confirmed to be W = k1 x^4/4 - k2x, evaluated from the initial to the final position. Participants share their initial calculations, with one user initially obtaining incorrect results before realizing the need for precision in their calculations. The final correct answer is around 97.904 kJ, emphasizing the importance of using sufficient significant digits. The thread concludes with one user expressing gratitude for resolving their calculation error.
MissPenguins
Messages
58
Reaction score
0

Homework Statement


An applied force varies with position according to F = k1xn - k2, where n = 3, k1 = 8.3 N/m3, and k2 = 87 N. How much work is done by this force on an object that moves from xi = 6.47 m to xf = 14.9 m? Answer in units of kJ.

Homework Equations



W = k1 x4/4 ]from the integral of x1 to x2
- k2x]from x1to x2

The Attempt at a Solution


I plugged in everything, and I got 96.778 at first, then I thought I should use x33/3, then I got 6.543478 kJ.
I got both them wrong, did I do the calculation wrong? Please help, thanks. :D
SOLVED
 
Last edited:
Physics news on Phys.org
Agree with W = k1 x^4/4 - k2x from x1 to x2.
I got about -15000.
 
Delphi51 said:
Agree with W = k1 x^4/4 - k2x from x1 to x2.
I got about -15000.

I still didn't get that answer. :(
 
It is really W = k1 x^4/4 - k2 x , and I got 97904, similar to your result. Use enough digits during the calculations. ehild
 
ehild said:
It is really W = k1 x^4/4 - k2 x , and I got 97904, similar to your result. Use enough digits during the calculations.


ehild

I found my mistake, thank you very much.
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

Identifying Multiple Oscillations in a Graph
Replies
19
Views
3K
An applied force varies with position
Replies
6
Views
6K
How do I find the work done for a 100 N downward force?
Replies
4
Views
2K
Work done in elevator problem — is it positive or negative?
Replies
3
Views
2K
Calculating Work Done by Gas at Constant Pressure
Replies
2
Views
2K
My Mistake? Understanding Friction Force & Work Done on Snowy & Icy Surfaces
Replies
29
Views
2K
Finding displacement using net work?
Replies
9
Views
2K
Work done for round trip when force is function of velocity
Replies
17
Views
1K
Work done on a pendulum by gravity
Replies
7
Views
3K
Finding Friction Force & Work with No Applied Force
Replies
8
Views
1K

Hot Threads

Recent Insights

Back
Top