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

In the figure, a 25 kg block is pulled by a 100 N force and slides across the floor of the elevator. The coefficient of friction is µ = 0.35. If the elevator is accelerating downward at 2.0 m/s^{2}, what is the resulting acceleration of the block?

See Figure 1

2. Relevant equations

F = u * F_{n}

where F = friction force, u = coefficient of friction force and F_{n}= normal force

F_{net}= ma

where m= mass and a = acceleration

3. The attempt at a solution

So I decided the three forces acting on the block are F_{n}(normal force), F_{g}(force due to gravity), and F (horizontal force). I can find F_{n}of the block relatively easily, but I'm not sure what to assign the force F_{g}as. I don't think that it's as simple as F_{g}= mg because the block is not in free fall. Can I say F_{g}is 2.0 m/s^{2}* 25 kg? Then I would theoretically have all of the forces acting on the block and would be able to solve the equation F_{net}= ma for a. I find this idea unsettling however, since I think that means the block would be slammed into the ceiling of elevator during this descent, since the downward force F_{g}is only 50 N and the upward force F_{n}is about 286 N.

Also, since the block is moving in two dimensions, this means I should solve for a_{x}and a_{y}separately, correct? So when I give my answer should I give it in Cartesian coordinates like a= 5 xhat + 8 xhat or should I convert it to magnitude angle notation? I didn't know if there was a standard preference.

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# Homework Help: Forces in an Elevator

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