What Is the Weight of a Block on an Inclined Plane?

[AnkhUNC]

[SOLVED] Weight/Normal Force of a block

Homework Statement

If P = 1.98, M = 1, Theta = 45 degrees what is the weight of m in Newtons?

http://img261.imageshack.us/img261/3339/fig450ph7.gif

Homework Equations

The Attempt at a Solution

I'm apparently doing this wrong. I was trying to solve for the normal force given that N = Mg/cos theta but this is just 9.8 so I'm doing something wrong. Any advice would be appreciated.

 

[Doc Al]

Any further description of the problem? Is the block sliding down the incline?

 

[AnkhUNC]

P (1.98) is such that the block is not moving.

Thats all I'm given :(

 

[Doc Al]

Start by identifying the forces acting on each mass. Draw a free body diagram for each.

What can you say about the net force on the block?

 

[Doc Al]

I was trying to solve for the normal force given that N = Mg/cos theta ...

How did you deduce this?

 

[AnkhUNC]

N cosθ – mg = ma(y). a(y) = 0 so N = Mg/cos theta?

Forces on triangle block are W (Mass pointed down), P (->), Normal force up mgcos(theta) opposite the angle of the block?

Small block is w pointed straight down and Normal force at an angle opposite (90d?)

 

[Doc Al]

N cosθ – mg = ma(y). a(y) = 0 so N = Mg/cos theta?

Good. But don't mix M and m: N = mg/cos(theta).

Forces on triangle block are W (Mass pointed down), P (->), Normal force up mgcos(theta) opposite the angle of the block?

Only worry about horizontal forces on the triangle.

Small block is w pointed straight down and Normal force at an angle opposite (90d?)

OK

Keep going. Apply Newton's 2nd law to the horizontal direction and see what you can deduce. Hint: What net horizontal force acts on the block? On both masses?

 

[AnkhUNC]

P = (M + m) g tanθ?

But this gives me m = .2020408163 so * 9.8 just = 1.98 again which is wrong.

N = Nx i + Ny j = N sinθ i + N cosθ j

–Nsinθ = –mgtanθ

P – mg tanθ = Max

N sinθ = mg tanθ = max

P = (M + m) g tanθ I guess I'm just having a hard time seeing what I need to get out of this.

F = Mgcos(45) - mgsin(45)? That doesn't even look right...

 

[Doc Al]

P = (M + m) g tanθ?

No. Just apply Newton's 2nd law to M + m. (Where did you get the g tanθ?)

After you do that, apply it to the block alone.

 

[AnkhUNC]

Ah its equal to 1! Sweet! I don't know if I did it right or not though. I did N = Mg/cos(45) to find N then N = mg/sin(45) so m = 1!

 

[Doc Al]

P = (M + m) g tanθ?

Actually, I take it back. This seems correct to me. (I just didn't see how you got. You gave your conclusion first. )

But your data doesn't seem OK.

But this gives me m = .2020408163 so * 9.8 just = 1.98 again which is wrong.

I don't see how you deduced this value for m.

 

[Doc Al]

Ah its equal to 1! Sweet! I don't know if I did it right or not though. I did N = Mg/cos(45) to find N then N = mg/sin(45) so m = 1!

Where did you get N = Mg/cos(45) = mg/sin(45)? I thought we had established that N = mg/cos(45).

 

[AnkhUNC]

I was just trying to find a value for N without having m. Like I said I got the right answer but I'm sure I did it wrong

 

[Doc Al]

What makes you think you got the right answer?

 

[tiny-tim]

N cosθ – mg = ma(y). a(y) = 0 so N = Mg/cos theta?

Hi AnkhUNC!

waaah … you've left out the y-component of the poor little friction force.

When you draw a diagram, you should always mark in all the forces

You need to take components in the normal direction, so that the friction component will be 0.

Then N = ?

 

[Doc Al]

..the poor little friction force.

Don't cry, tiny-tim! Now I'm starting to cry...

I would assume, lacking any statement to the contrary, that the surfaces are frictionless.

 

[AnkhUNC]

The answer checked as right but like I said I was sure I did it wrong. If its not moving then N is going to be equal to P?

Any websites you can recommend to help with these types of problems? :(

 

[Doc Al]

How about the site you're on right now?

Just attack it systematically, as I suggest in post #7. (I assume the surfaces are frictionless, correct?)

(I'd say that given the data you supplied, there is no correct answer. But you can solve for m symbolically in terms of P and M.)

 

[AnkhUNC]

Yeah there isn't a frictional force. I think the problem was just to get me thinking about the process and I spent way too much time on it :P

 

[Doc Al]

Just do it step by step. Analyze the forces and apply Newton's 2nd law:
(1) To the block (vertical direction)
(2) To the block (horizontal direction)
(3) To the entire system (horizontal direction)

 

[tiny-tim]

Don't cry, tiny-tim! Now I'm starting to cry...

I would assume, lacking any statement to the contrary, that the surfaces are frictionless.

Yes, looking at the diagram again, I think you're right!

Presumably the whole system is accelerating, but the little block is not moving relative to the big block, so resolving vertically was correct after all.

oh … I'm so much more cheerful now!

Thanks, Doc Al!