1. A block with mass 1.0 Kg slides on the inside of a circular hoop (a slice of
ID: 1772629 • Letter: 1
Question
1. A block with mass 1.0 Kg slides on the inside of a circular hoop (a slice of a cylindrical pipe) with radius R = 2.0 m, as shown in the figure. The coefficient of sliding friction is 0.30. (a) If the block is pushed tangentially around the hoop with a constant force F of 3.0 N, what will be its terminal angular frequency? Give the frequency in radians per second (w), and also in cycles per second (f). Ignore gravity. (b) If the force is suddenly turned off, the block coasts to a stop. How much heat must be dissipated by friction to bring it to a stop? R.Explanation / Answer
1. given, mass m = 1kg
radius of loop, R = 2 m
coefficient of sliding friction, k = 0.3
a. Applied tangential force F = 3 N
at terminal linear velocity acceleration = 0
hence F = kN ( where N is normal reaction force)
but N = mv^2/R [ where m is mass of opbject]
hence
3 = 0.3*1*v^2/2
v = 4.472 m/s
hence terminal angular frequency, w = v/R = 2.236 rad/s
now, 2*pi rad/s = 1 rps
so, f = w/2*pi = 0.355 rounds per second
b. when the force is turned off suddenly, the block coasts to stop due to friction
so net heat dissipated = KE lost by the block
KE of the block = 0.5mv^2 = 0.5*1*4.472^2
Heat dissipated = 10 J
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.