# The inclined plane: Movement & Coefficients of Friction

1. Oct 15, 2015

### raindrop264

1. The problem statement, all variables and given/known data
A block is projected up a 30° slope at 4m/s. When it is moving the coefficient of friction is 0.3. When the block is stationary the maximum coefficient of friction is 0.5.
a. Calculate how far up the block will go.
b. Show that the block will not remain there.
c. Calculate the velocity of the block when it reaches the bottom

2. Relevant equations
ΣF=mg
μ=Friction / Perpendicular Contact force

3. The attempt at a solution
I just joined a class in the middle of a topic, and so I am completely stuck at this one.
I know that when the block is stationary ΣF=0 in the x-direction (x-Axis is parallel to the inclined plane)
so when the object stops, the coefficient of friction is far greater.
I am not sure how to do the question, as we are not supplied a Mass (m), and I have no idea how to
use the angle θ to solve this. Any help would be appreciated!

2. Oct 15, 2015

### paisiello2

Maybe you can start by drawing yourself a free body diagram of each condition. You should then be able to apply your kinematic formulae to solve.

3. Oct 15, 2015

### Staff: Mentor

Apply Newton's 2nd law to find the acceleration. Then use kinematics. (That's one way to go.)

4. Oct 15, 2015

### raindrop264

I have already done that. I am focusing on part a.) of the question right now.
so There are 2 forces slowing the object down, the weight (gravity) and the friction.
But I don't understand how to use these equations. Could you perhaps give me an example,
or help me a bit more?
Thanks!

5. Oct 15, 2015

### Staff: Mentor

Good. What are they equal? (Symbolically, not numbers.) Then find ΣFx and set it equal to ma.

6. Oct 15, 2015

### raindrop264

They are equal to the total downward (negative) force of Fx?
So we got something moving that is being deccelerated by two forces and we need to work out the distance it will travel, so we need to calculate the decceleration first as I understand it but I'm at a total loss here as to "how to find ΣFx and set it equal to ma." :/

7. Oct 15, 2015

### Staff: Mentor

Give me an expression for each force: one for the weight and one for the friction force.

8. Oct 15, 2015

### haruspex

There are three forces altogether: gravity, normal force and friction.
While the block is sliding, there is a simple relationship between the magnitudes of the normal force and friction.
So to find the friction force you must first find the normal force.
The normal force from a surface is the force of least magnitude that will stop the object from penetrating the surface. Necessarily, that means it is at right angles to the surface. If you do a force balance in that direction you can find the normal force.
Do you know how to take the components of forces in a given direction and obtain a $\Sigma F$ force balance equation?

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