2 identical trolleys of mass M(one is loaded with 2 blocks of mass m) are on a ramp inclined at 35° and are connected by a wire that passes around a pulley at the top of the ramp. They are released and accelerate accordingly. Show that a=(mgsin35°)/(M+m).

Construction of Free Body Diagrams of the Trolleys and resolving the forces (Weight and Tension) components acting parallel to the ramp (assuming friction and air resistance are negligible) show that for Trolley A: F=ma--> (M+2m)a=(M+2m)gsin35-T and for Trolley B: F=ma-->Ma=T-Mg. Note that the magnitude of acceleration a is identical for both trolleys but acceleration acts in opposite directions (assuming pulley is massless and frictionless) Rearranging the equations in terms of T gives T(Trolley A)=(M+2m)gsin35-(M+2m)a and T(Trolley B)=Ma+Mgsin35. Tension is the same throughout the whole wire (assuming light inextinsible wire) so combining the T equations gives (M+2m)gsin35-Mgsin35=Ma+(M+2m)a. Factorising both sides with (gsin35) and (a) accordingly and simplifying results in gsin35(M+2m-M)=a(M+M+2m) --> 2mgsin35=2a(M+m). Finally rearranging for a gives the solution which is a=(mgsin35)/(M+m)

Answered by Neophytos V. Physics tutor

3191 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

A 0.20 kg mass is whirled round in a vertical circle on the end of a light string of length 0.90 m. At the top point of the circle the speed of the mass is 8.2 m/s. What is the tension in the string at this point?


When 0.81 m of a wire with cross-sectional area of 3.1*10^-11 m^2 is connected across a 2 V battery a current of 1.6 A flows in the wire. Find the resistivity of the material of the wire.


From the 2016 OCR B paper A ball is thrown at an angle of 30 Degrees to the horizontal. The initial kinetic energy of the ball is K. Air resistance is negligible. What is the kinetic energy of the ball at the maximum height.


How should I structure my experiment report?


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