A0.400kg particle slides around a horizontal track. the track has a smooth vertical outer wall forming a circle with a radius of 1.50m. the partical is given an initial speed of 8.0m/s. after one revolution, its speed has dropped to 6.0m/s because of friction whith the rough floor of the track. (a) find the energy transformation from mechanical to internal in the system owing to friction in one revolution. (b) calculate the coefficient of kinetic friction. (c) what is the total number of revolutions the partical makes before stopping?

We need first apply Kinetic energy law to find the distance done for the particles,

After that we can through the Work Formula find the Force, and with this force reach the coefficient of Kinetic friction.

A) We know that Kinetic Energy equation is given by,

B) We know that the Kinetic Frictional Force is given by,

Where is the coefficient of Kinetic friction and N the Normal (mg)

The work done by friction is equal to the Kinetic Energy, and the distance where this Work is applied is

m

and

Re-arrange for ,

Solving in the equation of Kinetic Frictional Force to find the coefficient we have,

c) The number of total revolutions is given by the initial KE, that is

, then