From what height, h, should a rail-cart fall to complete a loop-the-loop of radius r without falling off a the track? Assume the track on which the rail-cart travels is smooth and express h in terms of r.

This question combines the principles of energy conservation and circular motion. The insight is to realise the condition for which the rail-cart will fall off of the track - when there is no contact force between the cart and track at the apex of the loop.Energy of cart at top of track: mgh Energy of cart at apex of loop: mg(2r) + 0.5mv2Hence energy conservation implies that mgh = mg(2r)Newton's Second Law at apex of the loop: Fcentripetal = mv2/r = mg - FcontactSetting Fcontact = 0 and substituting v2 = g into energy conservation equation gives h = 2.5r

BR
Answered by Benjamin R. Physics tutor

1438 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

how do you calculate the charge of a neuclues compared to an ion?


Explain the findings from Rutherford's alpha particle scattering experiment.


If two cars are moving, labelled car A and car B. Car A moves at 15 m/s and B at 10 m/s but car B also accelerated at 2 m/s/s. If the two both travel for ten seconds, which car will travel further?


What is the Schwarzschild radius of a black hole?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning