Finding the Coefficient of Friction: Wrong Answer and Need to Fix

[Port]

ok i worked out the problem but i got the wrong answer. the values i got are: for normal force=69.62N. for ap=12.19. for af=6.19. for Ff=24.8N final answer=.356 and i need .816 what did i do wrong?

here is the problem again:
A 4kg block is pushed alomng the ceiling with a constant apllied force of 85N that acts at an angle of 55 degrees with the horizontal. The block accelerates to the right at 6m/s^2. detremine the coefficient of kinetic friction between the block and the ceiling.

 

[learningphysics]

I get 0.814 (close enough I hope).

Port your normal force is wrong. There are 3 forces along the vertical... gravity, the vertical component of the 85N, and the normal force. All 3 add to zero.

 

[Curious3141]

Sorry, I deleted my last post after realising my mistake. I forgot to take weight of the mass into account

The correct answer is $\mu = 0.814$.

The expression is $$\mu = \frac{F\cos\theta - ma}{F\sin\theta - mg}$$

 

[Port]

wait could u explain how u got that please??

 

[learningphysics]

wait could u explain how u got that please??

Ok. Sum of forces in y direction;

85sin55 - mg - Fn =0

Solve for Fn

You'll get 30.4N

The your coefficient of friction is 24.8/30.4= 0.816

 

[Port]

omg i love u thanks so much! (its a gratitute type love ok!)

 

[Yapper]

Yeah, port we forgot to take into account gravity originally so take the normal force you had subtract(i think) gravity, and then use that as the normal force, it should work

 

[Curious3141]

wait could u explain how u got that please??

Consider the forces acting on the mass. There is a 85 N force angled at 55 degrees to the horizontal pushing the mass to the right and there is a gravitational force acting vertically downwards. There is also a frictional force acting to the left impeding the motion of the mass. Finally, as a result of the mass being pushed against the ceiling there is a normal force of the ceiling on the mass, which acts vertically downwards.

Can you see that the block is in equilibrium in a vertical direction and in disequilibrium in a horizontal direction ? This is why the block doesn't move up or down, only to the right.

Resolve the 85 N pushing force into horizontal and vertical components. Now come up with equations that relate all the forces we discussed above. You should have one equation for the horizontal forces and one for the vertical. Finally, from your knowledge of the relationship between the frictional force and the normal force, you can derive an expression for $\mu$

Sometimes it's harder to explain how to do stuff than just give away the solution.

 

[Curious3141]

Yeah, port we forgot to take into account gravity originally so take the normal force you had subtract(i think) gravity, and then use that as the normal force, it should work

Strange that we ALL forgot gravity initially. Must be something bad in the ether.