Consider the situation at the right has a coefficent of static friction ?s bewte
ID: 2240357 • Letter: C
Question
Consider the situation at the right has a coefficent of static friction ?s bewteen all surfaces. If
the system is in equilibrium, find (a) the maximum value of M and (b) the minimum value of
M. (c) Find the ratio of the tension T2 from the case of minimum M over that of maximum M.
Consider the situation at the right has a coefficent of static friction ?s bewteen all surfaces. If the system is in equilibrium, find (a) the maximum value of M and (b) the minimum value of M. (c) Find the ratio of the tension T2 from the case of minimum M over that of maximum M.Explanation / Answer
a)For minimum value of M we must have a situation such that M just balances the force due to the 3m with friction acting up the incline.
So by Newton's law we have
3mgsin? = Mg + ?s*(3mgcos?)
=> M = 3m(sin? - ?scos?)
T2 in this case
T2 = 3mgsin? - 3?smgcos?
b)For maximum value of M we must have a situation such that M just balances the force due to both masses with friction acting down the incline.
So by Newton's law we have
3mgsin? + ?s*(3mgcos?) = Mg
=> M = 3m(sin? + ?scos?)
T2 in this case
T2 = 3mgsin? + 3?smgcos?
c) Ratio of tension in both caes
= (3mgsin? - 3?smgcos?)/(3mgsin? + 3?smgcos?)
= (sin? - ?scos?)/(sin? + ?scos?)