Quick M2 Question

http://www.ocr.org.uk/Images/144604-question-paper-unit-4729-01-mechanics-2.pdf

Q8

Why do we assume friction acts downwards? Surely the friction would oppose the particle from slipping down the slope?

Friction is at the ground opposing motion, it would to the right at A

Reaction force is perpendicular to the surface, friction is perpendicular to reaction. So friction acts parallel to the surface. In the first bit of the question, the friction acts upwards because the natural tendency of the particle is to slip down the slope.

In the last part of the question, you want to maximise the angular speed with the constraint that the particle doesn't slip. That is, if you increase the speed beyond this maximum angular speed, the particle will spiral or 'slip' upwards. Friction opposes motion and acts down the slope instead.

Furthermore, you'll want to use the limiting value of friction in order to maximise centripetal acceleration and hence maximise angular velocity.

tl;dr:

Minimum angular speed occurs when the particle is going to slip downwards, because if it goes any slower it falls down the slope so friction acts upwards.

Maximum angular speed occurs when the particle is going to slip upwards, because if it goes any faster it flies up the slope, so friction acts downwards.

Friction opposes motion.

Friction opposes direction of motion so ya you're right

Sorry bro I didn't even open the question tbh, just thought because you said something was slipping down the plane that friction would act the oppose way 😁

Hahaha, yeah, I know that feel. Just try and make sure you read the question before answering next time, we don't want the OP walking away with a wrong understanding.

Will do lol