Solve 10 Kg Mass on Plank Angle Problem | Coefficient of Friction

[pol1313]

A 10 Kg mass rests on a plank. The coefficient of static friction between the mass and the plank is 0,2. If the angle is of inclination is slowly increased, at what angle will the mass begin to slip?
Thank you i have tried but i can't solve it...

 

[Drakkith]

Is this homework? If so please post in the appropriate homework section to ensure you get the best help for your question!

 

[Fewmet]

A 10 Kg mass rests on a plank. The coefficient of static friction between the mass and the plank is 0,2. If the angle is of inclination is slowly increased, at what angle will the mass begin to slip?
Thank you i have tried but i can't solve it...

The force down an incline is mgsin(theta), where theta is the angle to the horizontal. Does that let you see how to set up the sum of the forces and see when slipping starts?

(Drakkith is right: I should have caught that).

 

[pol1313]

I know that the mass is going to start to slip when the gravitational component exceeds the static friction
but i don't know where to go from there

 

[mikelepore]

The way I do it is sum forces perpendicular to the incline = 0, solve for (mg), substitute that into the equation for sum forces parallel to the incline = 0. Notice which variables will cancel out. Then you get a relationship between the coefficient of static friction and the maximum angle.

 

[Doc Al]

I know that the mass is going to start to slip when the gravitational component exceeds the static friction
but i don't know where to go from there

That's all you need, if you can express it mathematically.

 

[pol1313]

the problem is i don't

 

[Doc Al]

the problem is i don't

Give it try. What's the component of gravity parallel to the plank? What's the normal force? What the maximum static friction?

 

[pol1313]

Ms=0.2
Fsmax=98X0.2= 19.6?
FN=98 because 9.8N x 10kg
So if this is right how do i get the angle?

 

[Doc Al]

Ms=0.2
Fsmax=98X0.2= 19.6?
FN=98 because 9.8N x 10kg
So if this is right how do i get the angle?

Not quite right. The normal force depends on the angle. (The normal force would equal mg if the plank were horizontal, but not when it's tilted.)

Read about inclined planes here: http://www.physicsclassroom.com/Class/vectors/u3l3e.cfm"

 

[pol1313]

So i do the Ms=(sinq/cosq)
Ms=0.2
0.2=tanq
-tan0.2=q
q=11.3 degrees??

 

[Doc Al]

So i do the Ms=(sinq/cosq)
Ms=0.2
0.2=tanq
-tan0.2=q
q=11.3 degrees??

That's it. (As long as you know how to get that first line: μ = sinθ/cosθ.)

 

[pol1313]

lol thanks
but what do you mean with that?

 

[Doc Al]

lol thanks
but what do you mean with that?

Just making sure you were able to figure out that first line. (As opposed to finding it in some book.) You didn't show your steps, perhaps because that part was clear to you. If so, great!

 

[Fewmet]

pll1313: sorry to have deserted you after my first post. My students graduated today, and that drew all of my attention.

Thanks to all who picked up the ball I dropped.

 

[pol1313]

np i could solve the problem thank you very much anyways