A wheel rotates about a horizontal axis, as shown in the figure. It has an outer

ID: 1288200 • Letter: A

Question

A wheel rotates about a horizontal axis, as shown in the figure. It has an outer radius R1 = 21.5 cm and mass M1 = 4.57 kg. Attached to it concentrically is a hub (shown cross-hatched) of radius R2 = 5.11 cm and mass M2 = 1.19 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 = 545 g.

a)What is the acceleration of the hanging weight after it is released?

b)When the weight has fallen a distance60.9cm, what is the kinetic energy of the rotating wheel?

Explanation / Answer

I = 0.5*M1*R1^2 + 0.5*M2*R2^2

= 0.5*4.57*0.215^2 + 0.5*1.19*0.0511^2

= 0.107 kg.m^2

let T is tension in the thread and a is the acceleration of
the hanging block.

m = 0.545kg

net force acting on hanging block,

Fnet = m*g - T

m*a = m*g - T

T = m*g - m*a ---(2)

net Torqe acting on hub,

Torque = m*g*R1*sin(90)

I*alfa = T*R1

I*a/R1 = T*R1

==> T = I*a/R1^2 --(2)

fromequations 1 and 2 we get

m*g - m*a = I*a/R1^2

a*(m + I/R1^2) = m*g

a = m*g/(m + I/R1^2)

= 0.545*9.8/(0.545 + 0.107/0.0511^2)

= 0.129 m/s^2 <<<<<------------Answer

s = 0.5*a*t^2

t = sqrt(2*s/a)

= sqrt(2*0.609/0.129)

= 3.07 s

alfa = a/r

= 0.129/0.215

= 0.6 rad/s^2

w = wo + alfa*t

= 0 + 0.6*3.07

= 1.842 rad/s

KE = 0.5*I*w^2

= 0.5*0.5*M1*R1^2*w^2

= 0.25*4.57*0.215^2*1.842^2

= 1.3 J <<<<<<<<<<------------Answer

Navigate

A wheel on a game show is given an initialangular speed of 1.25 rad/s. It comes

A wheel rotates about a horizontal axis, as shown in the figure. It has an outer

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

A wheel rotates about a horizontal axis, as shown in the figure. It has an outer

Question

Explanation / Answer

Related Questions

Navigate