Determining Acceleration Using Kinetic and Static Frictional Force Coefficients

[sb13]

Homework Statement

There is an initially stationary block of mass m on a floor. A force of magnitude 0.500mg is then applied at upward angle θ = 20°. What is the magnitude of the acceleration of the block across the floor if (a)μs = 0.630 and μk = 0.540 and (b)μs = 0.400 and μk = 0.330?

Homework Equations

F= ma
Fk= ukFN
Fs= usFN

The Attempt at a Solution

I know that first I must determine FN, but I don't know how when the mass is m. How do I use that if it is not even a specific value? What do I do when the force is not in Newtons?
I know that to the get mg or gravitational force I would multiply the mass by 9.8, but I am confused about that mass just simply being m.
Then the Fnet,y = may
FN- (applied force which is 0.5 mg in this case... 0.5sin20)- Fg=ma
I don't know where to go from there...

 

[Shootertrex]

Since there is no way to calculate the mass with the given numbers, the answer would be in terms of m. There is nothing really confusing about it. Some problems just want the answers in terms of a variable or multiple variables. This happens to be one of those problems.

 

[sb13]

So, I understand that I will just be using variables for the mass, but I don't understand how I use the fk and fs to find the acceleration. Once I get FN= ((9.8)mg)- (0.5(mgsin20)) and then times it by the coefficient of fs then what am I supposed to do with the value of fs?

 

[Shootertrex]

After looking at the problem more, I can see that the masses will cancel, so that is why the mass is given in terms of m.

Once I get FN= ((9.8)mg)- (0.5(mgsin20)) and then times it by the coefficient of fs then what am I supposed to do with the value of fs?

I do not know how you got to this. It looks like you multiplied by gravity twice in that one part.

The first thing you need to do is to see if the force being applied will move the object at all. This is when you use the coefficient of static friction. If the frictional force is greater than the force being applied, then the object does not move.

If the force being applied is greater, then you will now see how much it accelerates. This is when you use the coefficient of kinetic friction. You now make an equation for Fnet. Remember that the frictional force will be subtracted from the force being applied.

Fnet also equals ma. This will allow you to cancel out all of the masses, leaving you will with an equation for acceleration.

 

[sb13]

Oh. I did multiply by gravity twice. Ok. Thank you!