Answer to Question #253291 in Classical Mechanics for lakhte

Question

A small collar is confined to travel along a horizontal circular rod of radius 0.35

0.35 m as shown. The coefficient of kinetic friction between the rod and collar is 0.36

At a particular instant the collar is moving at 2.45m/s.  At that instant ...

a) [3] ... what is its rate of change of speed? (Take g = 9.81 m/s².)    m/s² 

[Notes: you don't need the mass of the collar; it will cancel. Also, a reminder that the normal force has two components here: a normal/radial component and a binormal component. There is no calculus in this problem.]

b) [1] ... what angle does the normal force the rod exerts on the collar make above the horizontal?   degrees

Answer 1

a)

$a_1=\mu g=3.53~\frac{m}{s^2},$

$a_2=\frac{v^2}r=17.15~\frac m{s^2},$

$a=\sqrt{a_1^2+a_2^2}=17.51~\frac m{s^2},$

b)

$\alpha=\arctan \mu=19.8°.$