(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A 1350kg car is at rest on a plane surface.

The unit vector normal to the surface is: 0.231i+ 0.923j+ 0.308k.

The y axis points upwards.

Find the magnitude of the normal and friction forces the car's wheels exert on the plane.

2. Relevant equations

[tex]\sum[/tex] F = 0.

3. The attempt at a solution

--The weight has the vector W = 1350*9.81i

--The normal force has the vectorF= 0.231|F_{N}_{N}|i+ 0.923|F_{N}|j+ 0.308|F_{N}|k

I also need to express the frictional force as a vector. I know I can find an infinite number of vectors normal to the given vector, but I don't see how I am to choose which is the right one. Mentally, I imagine the car tending to slide "down" the slope relative to its incline, but I'm not sure how to turn this intuition into a vector involving the friction force. Moreover, wouldn't the slide direction depend on the relative strength of the gravitational vs. the normal force?

Even if I found that, I would still need to solve a system of three equations (resulting from setting the sum of components of the force vectors equal to zero). This makes me question my strategy since there are only two unknowns.

I feel like I am missing something obvious here, or that I'm over-complicating the problem. Can anyone clue me into where I am going wrong?

Thanks,

-Zac

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# Object on a plane (equilibrium problem)

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