How Does Friction Affect Particle Motion in Circular Dynamics?

[joemama69]

Homework Statement

A particle of mass m moves in a horizontal circle of radius R on a rough table. It is attached to a horizontal string fixed at the center of the circle. The speed of the particle is initially v0. After completing one full trip around the circle, the speed of the particle is v0/2.


a) Find the energy dissipated by friction during one revolution in terms of m, v0, and R.

b) What is the coefficient of kinetic friction?

c) How many revolutions will the particle make before coming to rest?

d) Suppose the experiment is repeated with one slight modification: the initial speed of the particle is doubled. How many revolutions does the particle make in this case?

Homework Equations

The Attempt at a Solution

I need some help withthe friction part

.5Iw_o² = .5Iw² - Friction energy

is the friction energy F = umg

.5Iw_o² = .5Iw² - umg

 

[ideasrule]

I need some help withthe friction part

.5Iw_o² = .5Iw² - Friction energy

is the friction energy F = umg

.5Iw_o² = .5Iw² - umg

umg would be the force. Work done is W=Fd.

 

[joemama69]

part a)

so the energy would be .5Iw_o² = 1/8Iw_o² + W_friction... at one rotation it is half the velocity

W_f = 3/8Iw_o²

is this the energy dissipated

 

[joemama69]

and for part b i use umgRQ. where Q is theta in radians as the Work of friction

and then i would solve it for u.

and part c i just solve for RQ

part d i would just double initial velocity and solve for RQ again

should i be solveing for RQ because of the distance it travels around the circle, or should the answer be in simply Q in radians