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Mechanics Question -- Ball bearing on top of an accelerating car

1. The problem statement, all variables and given/known data
  1. A ball bearing rests on a ramp fixed to the top of a car which is accelerating horizontally. The position of the ball bearing relative to the ramp is used as a measure of the acceleration of the car. Show that if the acceleration is to be proportional to the horizontal distance moved by the ball (measured relative to the ramp), then the ramp must be curved upwards in the shape of a parabola.

2. Relevant equations


3. The attempt at a solution
I sort of found out that the gradient at point of equilibrium is acceleration/ g but don't know if it's useful.
 

DEvens

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Can you start by showing what angle will correspond to a given acceleration? Can you write this in terms of a slope?

Can you write down the equation for a parabola in terms of a slope?
 
Can you start by showing what angle will correspond to a given acceleration? Can you write this in terms of a slope?

Can you write down the equation for a parabola in terms of a slope?
Please bear with me but......I think tan( angle) =a / g so angle = tan^1( a / g ) is probably what you want. I don't know what do you mean by writing it in terms of a slope......
 

haruspex

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Please bear with me but......I think tan( angle) =a / g so angle = tan^1( a / g ) is probably what you want. I don't know what do you mean by writing it in terms of a slope......
You need to get the slope and the bit about acceleration being proportional to position expressed in terms of x and y coordinates.
 

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