Understanding Friction in Force and Motion: A Free Body Diagram Approach

[Seraph404]

Homework Statement

(I'm going to let the coefficient for friction be "u" since the actual greek letter that's generally used doesn't seem to be a a forum option; also, I'm going to use a dash since subscripts aren't an option)



A 40 kg slab rests on a frictionless floor. A 10 kg block rests on top of the slab. The coefficient of static friction (u-s) between the block and the slab is 0.60, whereas their kinematic friction coefficient (u-k) is 0.40. The 10 kg block is pulled by a horizantal force with a magnitude of 100N. What are the resulting accelerations of (a) the block and (b) the slab?

Homework Equations

mass of the block = 10kg
mass of the slab = 40kg

u-s = 0.60
u-k = 0.40

F = 100N

The diagram shown with the problem has the large rectangular slab resting on a frictionless surface, with the smaller cubed block on top of it. The force acting on the the block is going left.

The specific equations I use are dependent on how I set up my free body diagrams, which is what I'm sort of needing help with; but in general, friction is equal to the Normal force multiplied by the coefficient of friction; also, force equals mass multiplied by acceleration.

The Attempt at a Solution

All I need help with is setting up the equations; I'll know how to work it from there. Also, I already know what the answers to the problem are.

The forces acting on the block:

There's a leftward force of 100 Newtons; a frictional force going right; a normal force exerted by the slab going up; and mg going down

The forces acting on the slab:

So far, I have a normal force the the floor exerts on the slab, mg going down, and a normal force exerted by the box going downward.

Which way does friction go? I first tried it with the same frictional force going in the same direction as it did with the diagram for the block, using u-s when I calculated the slab's acceleration and u-k when I calculated the box's acceleration, but I didn't get the right answers. So, I'm thinking I set up my free body diagram for the slab wrong.

 

[Astronuc]

There are two ways to do superscipts and subscripts. In normal text <sup>a[/ sup] (without the space between / and sup) and <sub>a[/ sub], as in a and a.

Or one can use LateX which also allow Greek letters as in $$\mu_k\,,\,\mu_s$$. Just click on the LaTeX image and a box will open up to show the LaTeX code.


Now as for the physics of the problem, friction works opposite motion or against the applied force.

A useful reference for the future - http://hyperphysics.phy-astr.gsu.edu/hbase/N2st

To find out if the block moves with respect to the slab, one has to determine if 100 N exceeds the friction force between the block and slab for the static case first.

Then if the 100 N exceeds the static friction force, the block must be moving with respect to the slab.

Then one has to find the net force on the block which is just 100 N - (friction force) and divide by the mass of the block to get the acceleration.

The force on the slab is just the friction from the block.

If the 100 N is less than the static friction force, then the block and slab move together as a single mass.</sub></sup>

 

[Seraph404]

I appreciate your attempt to help, but I already know all that. I'm not trying to find out if the block moves - I know that it moves: the problem says that it moves. And I know that I need to find the net force; but in order to find the net force, I have to know what forces are acting on what bodies. I'm trying to figure out how friction is applied to the slab.

Are free body diagrams unique to my textbook and curriculum only? Nobody in this forum seems to understand what they are.