Acceleration of a block on the floor

[iamkristing]

Homework Statement

The figure below shows an initially stationary block of mass m on a floor. A force of magnitude F=0.540mg is then applied at upward angle θ = 21°.



(a) What is the magnitude of the acceleration of the block across the floor if (a) s = 0.600 and k = 0.500?


(b) What is the magnitude of the acceleration of the block across the floor if s = 0.400 and k = 0.300?

Homework Equations

F=ma and F=s(N) or F=k(N)

The Attempt at a Solution

Well i drew a Free Body Diagram and found the forces in the x and y direction:

x: F(s)-Fcos(21)=0

y: mg-Fsin(21)-N=0

Then i solved for F(s)=Fcos(21)=0.54mg(cos(21))=4.94m

then i used F=s(N) to solve for N
N=8.233m

Then i set F=ma and F=s(N) equal and solved for a

a=8.233(.500)=4.11

I repeated the same steps for B...but the answers are not correct. Any help at all will be appreciated!

 

[Doc Al]

x: F(s)-Fcos(21)=0

This assumes equilibrium, that a = 0. Not good.

y: mg-Fsin(21)-N=0

Good. Use this to solve for N and thus compute the friction force.

The first thing to figure out is: Does it move? Compare the applied horizontal force with the maximum static friction.

If it accelerates, then use the kinetic friction to find the acceleration.

 

[Kurdt]

Why have you set up the initial equation to be zero? For it to accelerate there has to be some sort of force there.