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

μ_{s[\SUB] = .35
μk[\SUB] = .25}

2. Homework Equations

F_s = μ_s * N
F_k = μ_k * 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

ΣF_y = Ncosθ - F_ssinθ - 1.2kN = 0
and apparently
ΣF_x = Nsinθ - F_scosθ - .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 F<sub>s[\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?</sub>

 

[BiGyElLoWhAt]

I don't think anyones going to 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

μ<sub>s[\SUB] = .35
μk[\SUB] = .25

View attachment 76183 View attachment 76184
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?</sub>

Sooooo many unnecessary "subs"

 

[jbriggs444]

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]

[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.

 

[HalfLostAndSearching]

Your solution seems correct, but it is always a good idea to double check your calculations and make sure you are using the correct values for the given variables. Also, it may be helpful to draw a free body diagram of the block and label all the forces acting on it. This will help you visualize the problem and make sure you have accounted for all the forces correctly.

Additionally, it is important to note that the direction of the friction force always opposes the direction of motion or attempted motion. In this case, the block is not moving, so the friction force will act in the opposite direction of the applied force P. This means that your equation for ΣFx should be Nsinθ + Fscosθ - .750kN = 0. This will give you a different value for N, and subsequently a different value for Fs. Make sure to re-check your calculations using this equation.

Overall, it seems like you are on the right track and just need to double check your calculations and make sure you are using the correct values and equations. Keep up the good work!