Modern roller coasters use magnetic propulsion systems to ra

Modern roller coasters use magnetic propulsion systems to rapidly accelerate the trains from rest. Consider the track on the right with a large hill and an inverted circular loop. The height of the hill and the loop are both h = 30 m. The train of mass m = 3000 kg will safely make it to the end of the track. Find the minimum speed of the just train after the propulsion system. How much work must the propulsion system perform?

Solution

using law of conservation of energy

energy at the track = energy at the heightest point of the circular loop

0.5*m*v^2 = m*g*h

m cancels

0.5*v^2 = g*h

v = sqrt(2*g*h) = sqrt(2*9.81*30) = 24.3 m/sec

b) Work done by the propulsion system is W = m*g*h = 3000*9.81*30 = 8.82*10^5 J