Answer:
(a) Vcm = 1.43m/s
(b) KEcm = 2.59J
Explanation:
Given
m = mass of the solid disk = 1.7kg
Radius R = 0.11m
F = 7N
Let the distance moved by the the center of mass be x = 0.15m
And the distance moved by in unwinding the rope be d = 0.22m
The total workdone on the disk is causing it to rotate and also move its center of mass is F×(d+x)
W = 7×(0.15+0.22)
= 7× 0.37 = 2.59J
By work-energy theorem,
W = ΔKE = 1/2mVcm² + 1/2×I×ω²....(1)
I = moment of inertia = 1/2MR² and
ω = angular speed = Vcm/R
So substituting these expressions into the equation above we have
W = 1/2MVcm² + 1/2×1/2MR²×(Vcm/R)²
W = 1/2MVcm² + 1/4MVcm²
W = 3/4MVcm²
Vcm² = 4/3×W/M
Vcm = √(4/3×W/M)
Vcm = √(4/3×2.59/1.7)
Vcm = 1.43m/s
KE = workdone = 2.59J.