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bcjochim07
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Homework Statement
A particle of mass m starts from xo= 0m with vo> 0 m/s. The particle experiences the variable force Fx= Fosin(cx) as it moves to right along the x-axis, where Fo and c are constants.
a)At what position xmax does the force first reach a maximum value?
b) What is the particle's velocity as it reaches xmax? Give your answer in terms of m, vo, Fo, & c.
Homework Equations
The Attempt at a Solution
Here is my idea for part a:
Take the derivative and set it equal to 0
Fx'=Fo*c*cos(cx)
0=Fo*c*cos(cx)
cos(cx)=0
cx= pi/2
xmax=pi/2c Is this correct?
Then for part b:
I took the integral of Fosin(cx):
(Fo/c) * (-cos(pi/2) + 1) = Fo/c This is the work done.
Then using the work-kinetic energy theorem:
.5mvo^2 + Fo/c = .5 mv1^2 where v1 is the velocity at x max
.5vo^2 +Fo/c*m = .5v1^2
vo^2 + 2Fo/c*m = v1^2
sqrt (vo^2 + 2Fo/c*m) = v1