- #1
MalachiK
- 137
- 4
Homework Statement
Two smooth planes are joined at one end so that they form a V shape. The join is such that a mass placed on one of the planes will slide smoothly down one side of the V and then move up the other side. Find the period of the motion (T) of such a mass in terms of x0 (the initial horizontal position) and θ (the angle between each of the planes and the horizontal.
Homework Equations
The potential energy in terms of horizontal position and hence the force and acceleration.
The Attempt at a Solution
The potential energy of the mass on the LHS of the well seems to go like...
V(x) = m.g.(x0-x).tan(θ) where x is the horizontal displacement from x0. I set things up like this to give V(x) = 0 when the mass is at the lowest point.
and by differentiating I get a horizontal force m.g.tan(θ) towards the centre and an acceleration of g.tan(θ).
Since the mass is uniformly accelerated through horizontal distance x0 in a time of T/4 I write
x0 = 1/2 . g.tan(θ) . (T/4)2 (assuming the initial speed is zero)
and find that
T = √[32x0/g.tan(θ)] = 4√[2x0 / g.tan(θ)]
I would like to know if this is correct. It seems like it should be the sort of thing you could just look up, but I don't seem to be able to describe the system well enough to Google to get results about anything other than harmonic oscillators.