Problem 6: Shown in the figure below is a 1.5 kg thin ring with a radius of 15 c

Question

Problem 6: Shown in the figure below is a 1.5 kg thin ring with a radius of 15 cm rolling up a 15 degree ramp without slipping and with an initial COM velocity of 5 m/s a) Calculate the magnitude of the COM acceleration while going up the ramp. b) Calculate the initial rotational kinetic energy of the ring. c) Calculate the initial translational kinetic energy of the ring. d) Calculate the change in height the COM undergoes from it initial position to the turnaround point e) Calculate the distance d, from a to b, the ring travels up the ramp before turning around. This can be done with energy or kinematics. 12

Explanation / Answer

a) a = - gsin15 = - 2.54 m/s^2

b) initial rotational KE = Iw^2 /2

= (M R^2 ) (v/R)^2 /2 = mv^2 /2 = 1.5 x 5^2 /2 = 18.75 J

c) translational KE = mv^2 /2 = 18.75 J

d) using energy conservation,

Gain in PE = loss in KE

mgh = (rot KE + trans KE)

1.5 x 9.81 x h = (18.75 + 18.75)

h = 2.55m

e) d sin15 = h

d = 2.55 / sin15 = 9.85 m

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