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**1. 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]

**2. Homework Equations**

[tex]W = F_{\parallel}d[/tex]

[tex]F_{fr} = \mu F_N[/tex]

**3. 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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