# Just starting with friction, question

#### CollegeStudent

1. Homework Statement

Determine whether the block shown is in equilibrium and find the magnitude and direction of the friction force when θ = 25° and P = 750N

μs[\SUB] = .35
μk[\SUB] = .25

2. Homework Equations

Fs = μs * N
Fk = μk * N

3. The Attempt at a Solution

Attachment 1 up there is the drawing of the scenario.
Attachment 2 is my addition to it to solve this problem.

Using the axis shown, I have

ΣFy = Ncosθ - Fssinθ - 1.2kN = 0
and apparently
ΣFx = Nsinθ - Fscosθ - .750kN = 0

otherwise that similar triangle I drew there wouldn't make sense, just odd to think of the force of friction acting in the SAME direction as the force...regardless, continuing...

Solving Top equation for Fs[\SUB] I get

Fs[\SUB] = (Ncosθ - 1.2kN)/(sinθ)

And subbing that into the second equation for F I receive

Nsinθ - ((Ncosθ - 1.2kN)/(sinθ))cosθ - .750 = 0
Nsinθ - (Ncos^2 θ - 1.2kNcosθ) - .750 = 0
N(sinθ - cos^2θ) + 1.2kNcosθ - .750 = 0
N = (-1.2kNcosθ + .750)/(sinθ - cos^2 θ)
N = 0.8465kN

So Fs[\SUB] = .35*0.8465kN = .2963kN

Seeing as how this doesn't match up to the answer given, I'm not seeing where I went off...can anyone guide me in the right direction? Should I use a slanted axis?

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#### BiGyElLoWhAt

Gold Member
I don't think anyones gonna see where you went wrong.
1. Homework Statement

Determine whether the block shown is in equilibrium and find the magnitude and direction of the friction force when θ = 25° and P = 750N

μs[\SUB] = .35
μk[\SUB] = .25

2. Homework Equations

Fs = μs * N
Fk = μk * N

3. The Attempt at a Solution

Attachment 1 up there is the drawing of the scenario.
Attachment 2 is my addition to it to solve this problem.

Using the axis shown, I have

ΣFy = Ncosθ - Fssinθ - 1.2kN = 0
and apparently
ΣFx = Nsinθ - Fscosθ - .750kN = 0

otherwise that similar triangle I drew there wouldn't make sense, just odd to think of the force of friction acting in the SAME direction as the force...regardless, continuing...

Solving Top equation for Fs I get

Fs = (Ncosθ - 1.2kN)/(sinθ)

And subbing that into the second equation for F I receive

Nsinθ - ((Ncosθ - 1.2kN)/(sinθ))cosθ - .750 = 0
Nsinθ - (Ncos^2 θ - 1.2kNcosθ) - .750 = 0
N(sinθ - cos^2θ) + 1.2kNcosθ - .750 = 0
N = (-1.2kNcosθ + .750)/(sinθ - cos^2 θ)
N = 0.8465kN

So Fs = .35*0.8465kN = .2963kN

Seeing as how this doesn't match up to the answer given, I'm not seeing where I went off...can anyone guide me in the right direction? Should I use a slanted axis?
Sooooo many unnecessary "subs"

#### jbriggs444

Homework Helper
You can compute N much more easily by looking at the components of the 1.2 kN and the 0.75 kN normal to the surface. The the value of .8465 kN is not correct.

Yes, switching to a coordinate system aligned with the surface makes things easy.

#### BiGyElLoWhAt

Gold Member
[qoute]... And subbing that into the second equation for F I receive
$Nsin(\theta ) - \frac{Ncos(\theta ) - 1.2}{sin(\theta )}cos(\theta ) - .750 = 0$[/quote]
yes
$Nsin(\theta ) - Ncos^2(\theta ) - 1.2cos(\theta ) - .750 = 0$
try again.

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