Given the force field F, find the work required to

kdgg0909gn

kdgg0909gn

Answered question

2021-11-20

Given the force field F, find the work required to move an object on the given oriented curve. F=y,x on the parabola y=2x2omPSK(0,0) to (2,8)

Answer & Explanation

Supoilign1964

Supoilign1964

Beginner2021-11-21Added 19 answers

F=y,x parabola y=2x2
(0,0) to (2,8)
parameterizing
r(t)=t,2t2,0t2
thereforer(t)=1,4t
the work is
w=022t2,t1,4tdt
simplify
w=02(2t2+4t2)dt=026t2dt
w=[2t3]{0}2=2(2)3=16
Forneadil

Forneadil

Beginner2021-11-22Added 18 answers

Step 1
The force field is
F(x,y)=(y,x).
The curve isr(t)=(t,2t2),t[0,2]r(t)=(1,4t).
Thus, the integral is
CFTds=02F(r(t))r(t)dt
=02(2t2,t)(1,4t)dt
026t2dt
=16.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?