A block of mass (m) is placed on a rough slope inclined at an angle (a) to the horizontal, find an expression in terms of (a) for the smallest coefficient of friction (x), such that the block does not fall down the slope.

The first thing to do as with any mechanics question is draw a force diagram with the weight (mg), the friction (F) and the normal reaction (R). As we are finding the smallest coefficient of friction possible, the block must be in limiting equilibrium, so the friction (F) = the coefficient of friction (x) multiplied by the normal reaction (R), so F = xR. Now we can resolve forces parallel and perpendicular to the slope to obtain two simultaeneous equations. Resolving perpendicular, we find that R = mgcos(a), and resolving parallel we find that xR = mgsin(a). By substituting the first equation into the second, we get xmgcos(a) = mgsin(a). By cancelling out the "mg" term from both sides, and dividing through by cos(a), we end up with x = sin(a) / cos(a), which of course leads to our final answer that x = tan(a).

OW
Answered by Ollie W. Physics tutor

4099 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

What is EMF? How do we test for it?


A cup of tea contains 175 g of water at a temperature of 85.0 °C. Milk at a temperature of 4.5 °C is added to the tea and the temperature of the mixture becomes 74.0 °C. What is the internal energy lost by the water? What is the mass of the milk?


What is Olbers' Paradox?


Alex's rocket lands after 4.56s and Billy's lands after 5.21s. What was the initial (maximum) vertical velocity of both of their rockets as they left the launchpad to 3s.f.?


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