(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The first question asks:

Which (fictitious) force will cause the sledge to accelerate along the rails? Give the modulus and direction of the sledge at distance r<R from the centre.

The next question asks:

Obtain an expression for the displacement r(t) for r<R, starting from the acceleration, and the initial condition r(0) = [tex]r_0[/tex].

2. Relevant equations

3. The attempt at a solution

a) Centrifugal force is the fictious force that causes the sled to accelerate. The acceleration is given by [tex]\omega^2 * r[/tex].

b) Now this is where I get most stuck.

So far I have said that [tex]a = \frac{d^2r}{dt^2}[/tex], so I integrated twice and ended up with the basic kinematic equation [tex]r = ut + \frac{1}{2}at^2[/tex] (which I would have guessed, but integrated as I assumed thats what the question was hinting at).

From here I said that u = 0, and was left with [tex]r = \omega^2rt^2 + r_0[/tex], but I'm a little confused about this. Surely r cannot be on both sides of the equation at the same time. As I've been writing this I've also thought about using [tex]\frac{v^2}{r}[/tex] instead of [tex]\omega^2r[/tex], but on further thought I end up with the same problem of having r on both sides of the equation (it would now be multiplied by the constant term), as well as having the v term that is never mentioned in the question itself (I know I probably could use it, but further questions relate to omega so I have this gut feeling that I should stick with omega in this question).

Any thoughts about this?

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# Fictitious forces, and motion

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