Pulling mass on flat plane at an angle.

[TexasCow]

Homework Statement

A block of mass m is pulled along a rough horizontal surface by a constant applied force of magnitude F that acts at an angle theta to the horizontal. The acceleration is a. Express all algebraic answers in terms of m, F, theta, and a.
A. Derive an equation for the normal force
B. Derive an expression for the coefficient of friction between the block and surface.
Sketch the graphs of speed v and displacement x as teh functions of time if the block started at rest at x=0 and t=0

Homework Equations

Fy=(Applied force)(Sin(theta))
Fx=(Applied force)(Cos(theta))
Fnet=(mu)(Normal force)

The Attempt at a Solution

Well for part A, I figure that since it was being pulled at an angle that would provide for a lower normal force.

Normal Force=(Fg-Fy) *Fy is the y component of the force vector.
For the coefficient of friction, I don't know if I am supposed to derive an equation that soves for mu, or just the equation that factors in mu.

Here is what I have for part B:
Ff=u[Fg-Fy]

And for the graphs I am kind of lost. Thanks for any help!

 

[rootX]

=(Fg-Fy) *Fy is

Why you multiplied it by Fy?
It's kind of very rare(in dynamics) to multiply forces . . .

Ff=u[Fg-Fy]
here u is the coefficient of friction so, you do have it factored out.

Add all the horizontal forces(or analyze them), you will find an equivalent for Ff as net 'a' is provided.

For graphing, either use work-energy relationship or
simply use kinematicss,
you know 'a', and it is constant

 

[TexasCow]

the *Fy was sort of a side info comment. It isn't part of the equation. Are you saying that my friction equation is correct? I'm sorry but I'm still somewhat confused on the graphs as well.

 

[rootX]

as Ff = uFn
and so you know Fn is W-Fy
so yea, it is correct.

so acc. = a
and so how its related to x,v,t?
You don't need forces or dynamics for this question.

Ignore that Work-energy, I thought they are asking for v,x relationship

But, You cannot draw graph, as you are not given any numerical value.

 

[TexasCow]

Well...
A=v/t

This is an old AP question that asks for a graph. I would agree too but there is some type of solution out there.

Another question that is on the back that I didn't notice was:

-If the applied force is large enough, the block will lose contact with the surface. Derive an expression for the magnitude of the greatest acceleration Amax that the bllock can have and still maintain contact with the ground.

 

[rootX]

So, Fy = Fg

and F = Fy.sintheta


you may draw an approximation graph, like if it's linear draw a straight line...