5 - forces + friction

how do we simplify some mechanics problems

resolve diagonal forces into horizontal and vertical forces, using trigonometry

how might you find an unknown magnitude and direction of a resultant force, given two forces

make a triangle out of it all, using angle laws to label, then use trig rules to solve what u can!

when a question involves an inclined plane, how do we want to resolve the forces?

resolve so they are parallel/perpendicular to the PLANE

main force affected is weight, as it acts vertically downwards, so needs to be resolved to fit the plane

all the others (acceleration, friction, normal reaction) happen either parallel or perpendicular so its fine :)

how does friction work

it prevents motion up to a certain limiting value

beyond that, its a force of constant magnitude in the opposite direction to an object’s motion

general formula for friction

F ≤ μR

f = force of friction

mu = coefficient of friction

r = normal reaction btw surface + object

if friction is 0, then the coefficient of friction would be 0

how to write out the maximum value for friction

F_MAX = μR

what is happening with friction when an object is STILL

resultant of other forces parallel to the surface is less than/equal to F_MAX

F remains equal and opposite to the resultant forces, so its also less than/equal to F_MAX

when resultant forces are equal to F_MAX, what do we say about the object

its in limiting equilibrium

whats happening with friction when an object is in MOTION

resultant of other forces parallel to the surface is greater than F_MAX

f remains at F_MAX in the opposite direction to motion (thats its max value)

situations when u should remember to use the CoF

when calculating any resultant forces on a rough surface

what should u remember about friction

it acts parallel to a plane (context = inclined planes), so it won’t need resolving!

what can’t we assume when working with friction

if an object is in equilibrium, we don’t know if F = μR, because it might not be in limiting equilibrium

but when an object is in motion, then F = μR

whats something u have to be careful of regarding normal reaction forces

when you’ve resolved, the up must equal the down (if the object is at REST), so don’t assume R’s value beforehand

rather, put the letter R as a placeholder, resolve any more vertical up forces then set it equal to the weight to find R!!!

(relevant for questions with forces in the vertical direction of any sort)