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

Answered by Benjamin R. Physics tutor

1232 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

An electron is emitted from a cathode in an electron gun, with a potential difference of 150kV. Find the velocity of the electron after it is accelerated and find the De Broglie wavelength.


A circuit with a voltage source of 18V, has 3 resistors all connected on parallel, values at 2ohms, 6ohms and 7.5ohms. Find the total circuit resistance, and then subsequently, the total current supplied and power dissipated in the curcuit.


Asteroid of mass 10^16 kg is travelling in the equatorial plane of Earth. It hits the surface at 45°. After the impact the day shortens by 1% (15 mins). How fast was the asteroid - comment? Neglect effects of atmosphere. Consider only inelastic collision.


How can we explain the standing waves on a string?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences