|Jul13-07, 10:27 AM||#1|
motion of particle on wedge on smooth surface
1. The problem statement, all variables and given/known data
a particle of mass m moves down the inclined face (angle A) of a wedge of mass M which is free to move on a smooth fixed horizontal table.
by determining the forces acting on i) the particle, ii)the wedge and iii) the system of wedge + particle, show that the acceleration f of the wedge = mgcosAsinA/(M+m(sinA)^2) and f' of the particle with respect to the wedge = (m+M)gsinA/(M+m(sinA)^2)
2. Relevant equations
3. The attempt at a solution
System as a whole I would assume the only force would be gravitational force acting downwards, which would be completely counteracted by the normal force of the table, leaving no net force, right?
particle: only forces acting on it are gravitational force, straight down, and the normal force of the wedge acting on it, which would be equal to mgcosA, leading to an overall force F1 of mgsinA parallel to the wedge right?
forces; gravitational force on the wedge, completely counteracted by normal force of table
force of particle on wedge, equal to mgcosA perpendicular to the surface of the wedge, downwards component would be counteracted by the reaction force of the table, resulting in a total force F2 in the direction of f of mgsinAcosA
this gives f as F2/M = mgsinAcosA/M
and f' as F1/m =gsinA
which is obviously not the solution I was expected to find.
I'm guessing I overlooked something obvious, probably to do with the reaction forces between the particle and the wedge, but can't work out what.
|Jul14-07, 06:43 AM||#2|
Consider the horizontal accelerations of the particle and wedge. What is their relationship? What horizontal forces act on each?
(You may find it helpful to view things from the accelerating frame of the wedge.)
|Jul14-07, 07:23 AM||#3|
the body on the wedge has a reaction perpendicular to the inclined surface, horizontal component of this force is the force which makes the system to change the state
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