Question

Challenge Problem: Consider a bicycle wheel with rim of mass M and axle of mass m. The masses of the wheel's thin spokes are so m small that we will neglect them. Initially, the wheel is resting on a horizontal surface, and you hold its axle, a hand on each side of the wheel, so that it doesn't tip over. At time t = 0 s you exert a horizontal force of magnitude F on the axle so that the wheel begins to roll without slipping. Part 1. Determine the wheel's speed when you have pushed it forward a distance d. Part 2. Determine the magnitude of the friction force that the surface on which the wheel rolls exerts on the wheel while you are pushing it.

Answer 1

Step-by-step explanation:

Moment of inertial of wheel I = M R²

Work done by force

= F d

It will be converted into rotational + linear kinetic energy

= 1/2 I ω² + 1/2 M V²

= 1/2 M R²ω² + 1/2 MV²

=1/2 MV²+1/2 MV²

MV²

MV² = Fd

V =
`\sqrt{(Fd)/(M) }`

b )

acceleration of wheel

V² = 0 + 2 a d

a = V²/ 2d

= Fd / (M x 2d)

= F / 2M

if f be the force of friction

F - f = M a

= M x F / 2M

F - f = F /2

f = F /2

Friction force = F/2