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Homework Statement
A wheel turns and moves in translation like a wheel of a bike on the road (cycloid). Inside the wheel there is the pressure P from a gas. Outside the wheel there is no pressure. Calculate the work of a point from pi/2 to pi/2+a. The radius of the wheel is 1. The pressure P is 1.
Given datas:
Radius of the wheel = 1
Difference of pressure = 1
Homework Equations
The work:
[tex]W=Fdcos(t)[/tex]
Equation of the cycloid:
[tex]x=r(t-sin(t))[/tex]
[tex]y=r(1-cos(t))[/tex]
The Attempt at a Solution
I integrate the distance by the cos(angle) of the force:[tex]\int_{\frac{\pi}{2}}^{\frac{ \pi}{2}+a}(t-sin(t)) cos(\pi/2-t) dt[/tex]
+
[tex]\int_{\frac{\pi}{2}}^{\frac{ \pi}{2}+a} (1-cos(t)) sin(\pi/2-t) dt[/tex]
The work is the sum of the result of the two last integrales ?
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