How Is the Force of Friction Calculated for a Block Against a Wall?

[thaixicedxtea]

Homework Statement

As shown in the figure, a block is pushed up against the wall. Let the mass of the block be m=2.3 kg, the coefficient of kinetic friction between the block and the wall be µ= 0.53, and θ= 62. Suppose F = 68 N.
The acceleration of gravity is 9.8 m/s^2.
Find the force of friction. Answer in units of N.
http://img359.imageshack.us/my.php?image=71957582pz7.jpg
http://img359.imageshack.us/my.php?image=71957582pz7.jpg

Homework Equations

Fk= µ ( F sin θ - mg)
F=ma

The Attempt at a Solution

Well first I used F= µ(F sin θ), but I figured it was too simple, so I drew a free body diagram and saw mg going down on the block. I'm not sure how to go from there. Does the vertical component of force equal mg?

 

[Hootenanny]

Yes, the sum of the vertical components must be equal to the weight of the block.

 

[thomate1]

I would approach this problem by first defining the variables and equations that will be used to solve for the force of friction. The force of friction can be calculated using the formula Ff = µN, where µ is the coefficient of friction and N is the normal force. In this case, the normal force is equal to the weight of the block, which can be calculated using the formula N = mg.

Next, I would use the given information to solve for the normal force, which is equal to the weight of the block. Using the mass of the block (m=2.3 kg) and the acceleration of gravity (g=9.8 m/s^2), we can calculate the weight of the block to be approximately 22.54 N.

Then, I would use the given force (F=68 N) and the angle (θ=62) to calculate the horizontal component of the force, which is equal to F sin θ. Plugging this value into the formula for force of friction, we get Ff = (0.53)(F sin θ - mg).

Solving for the force of friction, we get Ff = 6.06 N. This means that the force of friction acting on the block is approximately 6.06 N.

I would also consider the limitations and assumptions of this solution. For example, the coefficient of friction may vary depending on the materials of the block and the wall, and there may be other forces acting on the block that could affect the accuracy of this calculation. Further experimentation and analysis may be needed to confirm this result.