Thread: rollercoaster question about force & postion

Hi there,

A rollercoaster car has mass m and it has the postion vector given below when it moves along a certain section of track.

r(t) = cos(2t)i + sin(2t)j + (15t -3.5t^2)k where i,j & k are cartesian unit vectors and r is postion with respect to time, t (0 < t < 4π)

show that over the interval avobe that the magnitude of the force exerted on the car is constant.

Well, I would take two derivatives to obtain the acceleration vector, and then take the magnitude of that resulting vector. If , then , since, as Landau proved, mass must be positive. I think you'll find that the magnitude of the force is constant for all time, not just the interval specified.

Hope this helps.