Re: [Phys-l] Ball on an inclined plane

["Josh Gates-fac" <Josh_Gates-fac@nobles.edu>]

here goes: 
What I'm getting from the problem description is that there's a vertical
wall (WLOG, put this on the left) and an inclined plane going from lower
left to upper right, theta above horizontal.  The forces on the ball are:
gravity - mg down
force of wall - directed horiz. to right
force of inclined plane - directed normal to plane, towards upper left of
diagram.

net force on ball vanishes in all directions.
In particular, choosing right and up as positive, 
Fnet, x = Fwall - Fplane sintheta = 0
Fnet, y = Fplane costheta - mg = 0

from this,

Fplane = mg/cos theta
and
Fwall = mg tantheta

dividing out mg gives Feynman's solution.
jg



Forum for Physics Educators <phys-l@carnot.physics.buffalo.edu> on
Wednesday, August 02, 2006 at 4:49 PM -0500 wrote:
> I have just finished reading "Feynman's Tips on Physics" and found it very
> enjoyable.  Then I got to the problems at the end of the book and the
> first one intrigued me.
>
> A Ball of Mass = 1 kg and radius of 3 cm is resting on an inclined plane
> against a wall, the incline is at an angle alpha.  The question is to find
> the force from the incline and the wall on the ball assuming negligable
> friction.
>
> Hubris is a terrible thing.  Thinking this was trivial, I plunged into the
> problem and got nowhere near the solution in the text:
>
> F(plane)= 1/cos(alpha)
> F(wall) = tan(alpha).
>
> I get (leaving mass unknown and g in the equations):
>
> F(plane) = Mg cos(alpha)
> F(wall) = 0.5Mg sin(2*alpha)
>
> Any help in where I went awry would be appreciated.
>
> Peter Schoch
> Sussex CC
>
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