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IMGOOD
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Homework Statement
What is the minimum work needed to push a car of mass [tex]m[/tex] kilograms, an absolute distance of [tex]d[/tex] meters (or a height of [tex]h[/tex] meters) up a [tex]\theta[/tex] degree incline plane. a) Ignore Friction. b) Assume that the effective coefficient of friction is [tex]\mu[/tex]
Homework Equations
[tex]W = F_{\parallel}d[/tex]
[tex]F_{fr} = \mu F_N[/tex]
The Attempt at a Solution
For part a), if you want to push the car up the inclined plane, then you would need to apply a vertical force with a magnitude equal to that of gravity, right? So you would want
[tex]F_y = F_g[/tex]
[tex]\Rightarrow F\sin(\theta) = F_g \Rightarrow F = \frac{F_g}{\sin(\theta)}[/tex]
where [tex]F[/tex] is a force in the direction of motion of the car. So the work needed to push the car would be
[tex] W = Fd = \frac{F_g}{\sin(\theta)} d[/tex]
and since [tex]h = d\sin(\theta)[/tex],
[tex] W = \frac{F_g h}{{\sin}^2(\theta)} = \frac{mgh}{{\sin}^2(\theta)}[/tex]
I think the answer should be [tex]mgh[/tex]? What did I do wrong?
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