A wheel rotates about a horizontal axis. It has an outer radius R 1 = 18.2 cm an

Question

A wheel rotates about a horizontal axis. It has an outer radius R1 = 18.2 cm and mass M1 = 4.59 kg. Attached to it concentrically is a hub (shown cross-hatched) of radius R2 = 4.77 cm and mass M2 = 1.18 kg. The axle has negligible radius and mass. Both the wheel and the hub are solid and have uniform density. Suspended from a massless string that is wound around the hub is a weight of mass m = 528 g.

b) When the weight has fallen a distance 75.1 cm, what is the kinetic energy of the rotating wheel?
2 J

Explanation / Answer

combined moment of inertia I = M1*R1^(2)/2 + M2^R2^(2)/2=0.07736

NOW TORQUE EQUATION FOR WHEEL-HUB SYSTEM T*R2= I*ALPHA WHERE T IS THE TENSION

IF THE STRING IS NOT SLIPPING SO ALPHA =a/R2 WHERE a IS THE ACCELERATION OH HANGING WEIGHT

SO T= 34a

NOW FORCE EQUATION FOR WEIGHT

Mg-T =Ma

a=Mg/(34+M)=0.1498 m/S^(2)

b)

CHANGE IN POTENTIAL ENERGY = KINETIC ENERGY OF ENTIRE SYSTEM=0.528 *9.8*0.751=3.885J

0.5*M*V^(2) + 0.5*I*W^(2) =3.885J

W=V/R2

SO V=0.4745m/s

W=9.949Rad/s

KINETIC ENERGY OF WHEEL = 0.5*M1*R1^(2)*W^(2)/2=3.762J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.