# Homework Help: FRICTIONLESS INCLINED PLANE. . . (some guidance please)

1. Jan 19, 2005

### Utsav

I have this problem that i'm not too sure about...
it states....

you have an inclined plane with a mass of (capital) M. The angle of the incline of the plane is alpha. there is also a mass on the plane that has a mass of (lower case) m.

All of the surfaces (the inclined plane, the surface the plane lies on and the mass *ARE ALL FRICTIONLESS*.

Fast must the inclined plane be moving in order for the mass to stay exactly where it is.

(Answer in terms of the variables. Consider gravity to be -10 m/s2 [taking down to be negative]).

I'd appreciate any help!
THANKS

Last edited: Jan 20, 2005
2. Jan 19, 2005

### newcool

Do you know how to start the problem? What have you done?

3. Jan 19, 2005

### Staff: Mentor

Welcome to PF!

Realize that the inclined plane must be accelerating in order to prevent the mass from sliding down. Start by identifying the forces acting on the mass (there are only two). Then apply Newton's 2nd law for the vertical and horizontal components. Hint: The mass must have a horizontal acceleration (which is what you need to find), but set the vertical acceleration to zero.

4. Jan 19, 2005

### futb0l

Welcome to PF! Try and draw a Free Body Diagram.

5. Jan 20, 2005

### Utsav

Thanks

i'll try it and ask again if i need help

6. Jan 20, 2005

### Utsav

Still not getting it!?!???

I know that much....i just don't know how i'm supposed to fiugure out the needed applied force on the inclined plane..............

7. Jan 20, 2005

### MathStudent

show what youve got so far:
list the forces acting on the mass.... set up a coordinate system
I reccommend a coordinate system where the x axis lies along the inclined plane.

8. Jan 20, 2005

### Utsav

i added an attachment of the diagram i made showing the forces

the inclination is alpha and the areas are all frictionless (*just a reminder)

9. Jan 20, 2005

### Staff: Mentor

For the moment, forget about any force applied to the inclined plane. Concentrate on the mass resting on the plane. Your attachment did not appear, but a free body diagram should show the two forces acting on the mass. Consider vertical and horizontal components. You'll get two equations, which will allow you to solve for the acceleration.

In your original post it's not clear what exactly you are asked to find. But if you need to find the force on the plane, first find the acceleration as I outline above and in my earlier post.

10. Jan 20, 2005

### Utsav

What i have to solve is 'hpw much force is required to keep the mass on the plane eactly where it is.'

Thanks for helpin' me out... ; )

11. Jan 20, 2005

### Utsav

*attachment Of Diagram*

#### Attached Files:

• ###### fictionless plane diagram 2.bmp
File size:
49.3 KB
Views:
188
12. Jan 20, 2005

### Utsav

ok so i did a little analysis n here's what i've got.

the force of gravity on the mass is '10*m.' derived into their x and y compontents, Fg in the x is -10 * sin(alpha); Fg in the y is 10 * cos(alpha). i don't think there is any y force to worry about, since the second law gives it the opposite = force (normal force).
The main force to focus on is the Fg in the x. we need to figure out how much force is required to overcome that force using the inclined plane. t h a t 's w h e r e i 'm s t u c k. Is the force needed to overcome the gravitational force of the mass 10 * sin(alpha) * 'M' (<-the mass of the inlined plane.)

thats what i've got.....please give some feedback!

13. Jan 21, 2005

### Staff: Mentor

Hint: There are two forces acting on the mass. The weight acting down (which is just mg) and the normal force of the plane. Call the normal force "N" (it's an unknown). (What are the vertical and horizontal components of the normal force?) Now go back to my earlier posts and write down the equations for Newton's 2nd law for vertical and horizontal components. (Do not use components parallel and perpendicular to the plane! That will just make it harder.)

14. Jan 21, 2005

### Utsav

i know that in order to find the vert. and horiz. force, you have to make a reference triangle. but i'm not sure what the angles of the triangle are (i am guessing that one of the angles is alpha and the other is 90 - alpha).

15. Jan 21, 2005

### Staff: Mentor

Figure out the angle that the normal force makes with the horizontal axis by drawing a careful diagram. Then you can find its components (I presume).

16. Jan 24, 2005

### Utsav

tried that.....i used the trig functions..... wether or not alpha is an angle in the normal force, i'm still un sure....

and i'm also worried about what my answer will look like (with alphas and cos and sin etc.)

17. Jan 24, 2005

### Staff: Mentor

I don't know what you mean when you say you "tried that". Did you find the angle that the normal force makes with the horizontal (or vertical)? What is it? (Of course, it will be in terms of alpha.) Draw a picture of the normal force and label the angles.

You are thinking way too hard on this one. Just do it. (It's much easier than you think.)

18. Jan 25, 2005

### Utsav

i think i got it. here's what i think the answer is (try not to lose me in my explination; drawing what i say might help.)

you have the object with mas 'm'. it rests on an inclined plane with mass 'M' and inclination alpha. (all surfaces are fictionless)

OBJECT
the force to gavity on the object is 10m. the normal force is 10m * cos (alpha). the acceleration of the object is 10m * sin(alpha).

Keeping the object in place.
now that we know the force on the object, we need to keep it in place. the acceleration of the object is 10m * sin(alpha); the mass of the inclined plane is 10M; i think that the force applied must be greater than 10m * sin(alpha) + 10M.

Fapp > 10m * sin(alpha) + 10M

(i hope thats it)

19. Jan 25, 2005

### Staff: Mentor

Right: the weight of the object is mg acting downward.
No. This would be the normal force if the plane were stationary. But it's not: it is accelerating.

No. This doesn't even have the units of acceleration.

Call the normal force "N" and the acceleration "a". Then do what I suggested in posts 3, 9, and 13. (Do it!)

Find the acceleration, then we'll worry about the force needed to produce that acceleration.

20. Jan 25, 2005

### plusaf

i may be all wet, but how about this approach....

1) if the incline mass, M, were at rest, how fast would the block, m, on it, accelerate down the slope? i.e., what is the acceleration of mass m down the ramp of mass M with slope = alpha.
2) in order to keep the mass m in place on the incline of mass M, assuming all surfaces are frictionless, mass M must be accelerating at a rate which would cancel the acceleration of gravity on mass m, right? looks to me if mass M were accelerating at the same rate in the same direction as mass m was "trying" to accelerate down the ramp, all would be in balance.... no?
3) here's the gotcha nobody's mentioned yet.... what force, F, is needed to accelerate mass M to get it up to that needed rate of acceleration, is the wrong answer. the force is determined by F=ma, but here, we got the "a" above, but F=(M+m)a! ya gotta accelerate the combination of the two masses at that rate of acceleration. don't miss that part!

+af