# Homework Help: Acceleration of a block with static & kinetic friction

1. Mar 4, 2014

### ammcl30

A 10kg block is at rest on the floor, and then a force of 30 N pushes on the block horizontally. If the coefficient of static friction between the block and the floor is μs= 0.33 and the coefficient of kinetic friction between the block and the floor is μk= 0.20, what is the acceleration of the block, if it slides?
A. 0.23 m/s^2
B. 1.04 m/s^2
C. 3.00 m/s^2
D. 0.85 m/s^2
E. The block does not slide

The only equation I used was Fx=ma,x. Because the block is not moving in the y direction there is no need to calculate the force in that direction.

Fx=ma,x
μk-μs= (10kg)a
(.20)-(.33)=(10kg) a ======> a= -.13/10 ==> a= -0.13 or E. The block does not slide

Although I obtained an answer I'm not sure that my set up is right and it was more of a lucky guess. Any help is appreciated!

2. Mar 4, 2014

### ItsImpulse

It is true that the block does not slide. Since The maximum static friction is given by μs(mg), plugging the values in gives 0.33(10)(9.81)= 32.373N hence you would need a force greater than 32.373N to be able to move it in the first place. Only after movement will the kinetic friction be used.

3. Mar 4, 2014

### ammcl30

Thank you for answering but this leads me to a question. Why do we only account for the static friction and not the kinetic friction? Don't both of these factor into the overall movement of an object?

4. Mar 4, 2014

### jackarms

Both frictions do, but it's more like they act at different times. You first see if the force can overcome static friction -- in this case it doesn't, so you don't consider kinetic friction. At other times the applied force overwhelms static friction and so kinetic friction starts acting. So since static friction always works first, this is what you calculate first, and then move on if necessary.

A graph of the force of friction (both static and kinetic) versus applied force essentially looks like a linear increase in static friction (more friction as you push harder and harder for something to move), and then the friction suddenly drops when the force becomes great enough. So both frictions matter in the movement, but essentially they can be divided and analyzed separately and at different times.

5. Mar 5, 2014

### ammcl30

That makes so much more sense thank you! So theoretically if after I calculate the static friction and it was less than the applied force, I could solve the kinetic friction using newtons 2nd law and kinematics. Correct?