Finding the coefficients of friction

  • #1

Homework Statement


A box with a mass of 22 kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficients of friction between the box and the ramp are uS = 0.78 and uK = 0.65.

a) Determine the magnitude of the largest force that can be applied upward, parallel to the ramp, if the box is to remain at rest.
b) Determine the magnitude of the smallest force that can be applied onto the top of the box, perpendicular to the ramp, if the box is to remain at rest.


Homework Equations



Fg = mg
Ff = ukFn
Ff = usFn




The Attempt at a Solution



I dont know where i should begin, i understand thati need to find the force of friction using static friction but I'm not sure how to start it.
 

Answers and Replies

  • #2
LowlyPion
Homework Helper
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Homework Statement


A box with a mass of 22 kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficients of friction between the box and the ramp are uS = 0.78 and uK = 0.65.

a) Determine the magnitude of the largest force that can be applied upward, parallel to the ramp, if the box is to remain at rest.
b) Determine the magnitude of the smallest force that can be applied onto the top of the box, perpendicular to the ramp, if the box is to remain at rest.

Fg = mg
Ff = ukFn
Ff = usFn

The Attempt at a Solution



I dont know where i should begin, i understand thati need to find the force of friction using static friction but I'm not sure how to start it.
You will need to draw a force diagram.
Friction is determined by the coefficient of friction times the weight that is normal (⊥ ) to the surface.

The force up the ramp then must offset both the component of weight (m*g) that points down the incline || to the surface and the force of friction determined by the coefficient of friction and the weight normal to the surface.
 
  • #3
alright well this is what i got for a)

Fg = mg sin45
= 22 kg (9.8 m/s^2) sin45
= 183.4 N

Ff = uSFn
= 0.78(183.4N)
= 143.1N
 
  • #4
LowlyPion
Homework Helper
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alright well this is what i got for a)

Fg = mg sin45
= 22 kg (9.8 m/s^2) sin45
= 183.4 N

Ff = uSFn
= 0.78(183.4N)
= 143.1N
I think you will want to check your math again for Fg.

I will trust that you know that Fn is not based on Sin45 but Cos45, which in this case does happen to be the same.
 
  • #5
ohhhh sorry, it is cos eh. so it equals 113.3 N not 183.4 N.

so that means Ff = 0.78(113.3 N)
= 88.4 N
 
  • #6
LowlyPion
Homework Helper
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ohhhh sorry, it is cos eh. so it equals 113.3 N not 183.4 N.

so that means Ff = 0.78(113.3 N)
= 88.4 N
No because 183.4 in not correct.

22*9.8*(.707) is not 183.4.
 
  • #7
yeah sorry, i didn't have my calculator in degrees that was the problem

and i thought you mean't that it was cos, and i was pretty sure it was sin anyways

but yeah so Fg = 152 N
and Ff = 118.6 N
 
  • #8
LowlyPion
Homework Helper
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yeah sorry, i didn't have my calculator in degrees that was the problem

and i thought you mean't that it was cos, and i was pretty sure it was sin anyways

but yeah so Fg = 152 N
and Ff = 118.6 N
Well you still have to construct the equations necessary to determine the answers to a) and b). I will presume that you have done that correctly.
 
  • #9
yeah so what i would do for a) is add the static frictional force and the gravitational force and then for b) i would do the same but use kinetic friction and subtract the 2 forces
 
  • #10
LowlyPion
Homework Helper
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yeah so what i would do for a) is add the static frictional force and the gravitational force and then for b) i would do the same but use kinetic friction and subtract the 2 forces
Careful. For a) and b) It says "to remain at rest". That suggests to me that kinetic frictional considerations are not relevant. So whatever excess of normal force that is needed (times the coefficient of static friction) to offset the force of gravity that is || along the incline.
 
  • #11
sorry its been awhile since i've replied, but i understand what you mean, and understand how to get normal force but do i have to sin or cos inorder to determine it? since its perpendicular
 
  • #12
LowlyPion
Homework Helper
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sorry its been awhile since i've replied, but i understand what you mean, and understand how to get normal force but do i have to sin or cos inorder to determine it? since its perpendicular
I suspect this link covers it in more detail than you want:
http://www.glenbrook.k12.il.us/gbssci/Phys/Class/vectors/u3l3e.html [Broken]
 
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  • #13
thanks, i figured it was that..
anyways this is what i got

Fn = mgcos45
= 22kg(9.8m/s^2)cos45
= 152.4 N

Ffs = FnuS
= 152.4 N(0.78)
= 118.9 N
 
  • #14
sorry i would also then subtract Fn - Ff

so it would be 152.4 N - 118.9 N
which would be 33.5 N
 
  • #15
LowlyPion
Homework Helper
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sorry i would also then subtract Fn - Ff

so it would be 152.4 N - 118.9 N
which would be 33.5 N
You have the force of friction, but you are apparently subtracting it from its weight.

What is the force of gravity down the incline?

Isn't that mg*sinθ ?

So for a) you have F up the incline = 118.9 + 154*sinθ won't you, because you have to overcome both gravity and friction in the up incline direction.
 
  • #16
LowlyPion
Homework Helper
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For b) consider how much additional force needs to act through the coefficient of static friction to keep it in position.

Remember that while the normal force acts perpendicular to the incline, its effect results in resistance along the incline.
 

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