Question

A particle moves along the x axis from X=X 1 to under the influence a force given by F=2x find the work done in this process

Answer 1

Answer:

Ok.... You missed a "X2" in your question.....but still.... Here's the answer :)

Explanation:

We know....

W =$\int\limits^a_b {F} \, dx$

and here the a and b (i.e. the limits) are X1 and X2......

Therefore, the integration comes out to be

2[x2^2-x1^2/2]

which results in.......

x2^2-x1^2.......

That's it... Easy peasy.... Hope you get it.... It's simple integration.... Just learn some and you are good to go!!  Thank yoU!

Answer 2

Proper Question: A particle moves along the x axis from X= 0 to =X 1 to under the influence a force given by F=2x. Find the work done in this process.

Given: A particle moves along the x axis from X= 0 to =X 1 to under the influence a force given by F=2x.

To find: the work done in this process.

Solution: For a variable force, the work done is given by:

                       ∫dW = ∫F.ds

Putting the given values in the formula, we get:

                       ∫dW = ∫¹₀ (2x) dx

                               = 2(x²/2)¹₀

                               = 1 J

Hence, the work done in the process is 1 J.