A cork is attached to a thread and whirled horizontally in a circle of radius 60cm of a rate of 30rpm. The cork has a mass of 15g
1) what is the period of the whirling cork?
2) hence calculate the linear speed of the cork
3) determine the magnitude of the tension in the thread
- oubaasLv 71 month ago
angular speed ω = n*2PI/60 = 2PI/60*30 = PI rad/sec
period T = 2PI/ω = 2PI/PI = 2.0 sec
Vt = r/T = 0.6/2 = 0.30 m/sec
T = m*ac = m*V^2/r = 15*10^-3*0.30^2/0.6 = 2.3 mN
- ArgentLv 71 month ago
1) 30 rpm = 1/2 rps, so the period T is 1/(1/2 sˉ¹) = 2 s.
2) The speed v is the circumference C divided by the period T.C = 2πr = 2π(0.60 m) = 1.2π m (≈ 3.8 m), so v = C/T = 0.6π m/s (≈ 1.9 m/s).
3) The tension force F = mv²/r = (0.015 kg)(0.6π m/s)²/(0.60 m) = 0.009π² N
(≈ 0.089 N).