# Forces and Motion - Sliding Box Up Inclined Plane w/ Friction

## Homework Statement

You are helping a friend move, and you need to load a 2.65x10^2 kg box of books. You slide the box up a ramp, which has an incline of 30 degrees and a coefficient of static friction of 0.45. You apply the force on the box at an angle of 39 degrees with respect to the ramp.

Calculate the minimum force needed to slide the box up the ramp.

Net force = ma

## The Attempt at a Solution

I'm not too sure how to draw the FBD for this situation since the static friction may be working in the same direction as the Fapp since the box would slide downwards if no Fapp was affecting it. But I don't really know.

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tiny-tim
Homework Helper
Hi Scimitar! Welcome to PF!
… the static friction may be working in the same direction as the Fapp since the box would slide downwards if no Fapp was affecting it. But I don't really know.
Ah, I see what you mean …

before anyone pushes, the static friction is pointing up, since it's stopping the box from sliding down.

You have to remember that static friction is not equal to µN, it is ≤ µN.

In fact, it's a "left-over" force that you have to calculate without using µ at all … it's the force that balances all the other forces.

So when you start to pull the box, the static friction gets less, and eventually it becomes 0.

Then it gets bigger, but down the ramp, until it equals µN.

After that point, it's dynamic friction, and so it is exactly µN (different µ of course ).

When you draw the FBD, you can forget about the history, of the static friction changing direction, and just apply the rule that the friction opposes the motion, which by definition (ie from what the question says) is that the box is about to move upwards

I was wondering how you solve the problem. And also what the answer is. (what equations to use and how to arrange them)

haruspex