Heya
I have an easier way to solve this problem guys !!!!
just for fun ha i am doing this :D
okay so first draw the FBD for the collar, i hope you guys know how to do that because i don't have time to draw it for you sorry ><!
anyways we need to find the coefficient of kinetic friction to do so we need to consider stage one of the motion when T1 is zero and when the collar compresses the spring (Maximum deflection) because then also T2 = zero !
so our lovely equation will be
U total = T2 - T1
U total = 0 !
okay now U total consists of three things:
1. self weight
2. friction work
3. spring work
so our equation will be:
(mg sin (30) * 0.584) - ( mg cos(30) * Mk * 0.584) - (0.5 * 876* ( 0.127)^2) = 0
now solve this equation for Mk :D and thats your answer for part one :D i'll do now part two then i'll tell you how to do but i think u take the Mk for the first part apply the thing but without the spring part just before the collar hits the spring there the max.velocity i am sure 80 % this how you solve the next part.