Question #253291

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/s

[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



1
Expert's answer
2021-10-19T15:13:14-0400

a)

a1=μg=3.53 ms2,a_1=\mu g=3.53~\frac{m}{s^2},

a2=v2r=17.15 ms2,a_2=\frac{v^2}r=17.15~\frac m{s^2},

a=a12+a22=17.51 ms2,a=\sqrt{a_1^2+a_2^2}=17.51~\frac m{s^2},

b)

α=arctanμ=19.8°.\alpha=\arctan \mu=19.8°.


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