# Homework Help: Friction incline with spring

1. Mar 31, 2015

### bnosam

1. The problem statement, all variables and given/known data
80kg box is on a 20 degree incline against a spring and is released from rest. Coefficient of static friction is .25. Determine max and in values of the intial compression force in the spring so that block will not slip on release.

Then calculate the magnitude and direction of friction acting on the block if the spring compression force is 200N

2. Relevant equations

FBD: http://i57.tinypic.com/2hs7orr.png

(80kg)*(9.81m/s^2) = 784.8N
Fnormal = (784.8 N) *(cos20) = 737.47 N
Fwparallel = 784.8sin20 = 268.42 N
Fwperpendicular = 784.8 * cos20 = 737.47 N

Ffriction = (268.42)*(.25) = 67.11N

3. The attempt at a solution
See 2

I'm not sure where to go with the spring. Don't we need a spring constant for this?

2. Apr 1, 2015

Say again?

3. Apr 1, 2015

### bnosam

Whoops.

Ffriction = (737.47)*(.25) = 184.37N.

4. Apr 1, 2015

### Svein

So, how much is left for the spring to do?

5. Apr 1, 2015

### bnosam

268.42 - 184.37 = 84.05N

6. Apr 1, 2015

### haruspex

No. You are only asked for the force, not the compression length.

7. Apr 1, 2015

### bnosam

I'm not understanding what it's asking for "min and max values of intial compression force for the spring" at all. I just can't turn the words into something meaningful to me.

8. Apr 1, 2015

### SammyS

Staff Emeritus
If the spring is compressed enough it may exert enough force to push the block up the incline. What is the maximum force the spring can exert, without pushing the block up the incline?

If the incline is steep enough, the block will need an external force applied so that it doesn't slide down the incline. In that case, what minimum force must the spring exert?

9. Apr 1, 2015

### bnosam

Wouldn't the maximum force it can exert be what I solved above since that is enough to stop the box from moving down further?

10. Apr 1, 2015

### haruspex

No, there are two different constraints. If the force is too small, the block will slide down. If too great, it will slide up. Think about which way friction acts in each case.

11. Apr 1, 2015

### bnosam

Friction will be opposite the direction of motion.

12. Apr 1, 2015

### haruspex

... or, for static friction, opposes the motion that would occur were there no friction.
So what equations do you get for the two extremes?

13. Apr 1, 2015

### bnosam

Ok, I'm still confused how to even go about this.

The only thing I'm familiar with in regards to springs is hooke's law.

14. Apr 1, 2015

### haruspex

The fact that it is a spring is irrelevant here. There is a block of known mass on a slope with known angle and known friction. A force is applied to it in the up slope direction. What is the minimum value of the force to prevent its slipping down the slope? What is the maximum to avoid pushing it up the slope?

15. Apr 1, 2015

### bnosam

So it's sliding down the slope with a force of 268.42 N, right?

Because of friction that force is reduced to 84.05 N so the spring would have to at least support that to prevent it from slipping down further.

But in that case wouldn't the minimum have to be the maximum be also equal to the minimum? :S

16. Apr 1, 2015

### haruspex

Think again about the direction of friction when the force from the spring is very large.

17. Apr 1, 2015

### bnosam

If the force is large the spring pushes it up so the friction will be moving down the slow while the block moves up.

18. Apr 1, 2015

### haruspex

Right, so what equation do you get for the forces in that case?

19. Apr 1, 2015

### bnosam

Fspring - Ffriction - Fwparallel

Fspring - 184.37 - 268.42
Fspring = 452.79 N

20. Apr 1, 2015

### haruspex

Good. All ok now?

21. Apr 1, 2015

### bnosam

So maximum is 452.79 and minimum is 84.05N, if I understand correctly

22. Apr 1, 2015

### haruspex

yes.

23. Apr 1, 2015

### bnosam

So if the spring compression force is 200N then. Assuming it pushes it up:

200N - Fwparallel - Ffriction ?
200 - 452.79 = -252.79N

24. Apr 1, 2015

### haruspex

Again, you need to decide which way friction acts. If there were no friction, with a spring force of 200N up the slope, which way would the block move?

25. Apr 1, 2015

### bnosam

200 - Fwparallel = -68.42 N

It would go down the slope