Question

A plank rests on top of the axles of two identical wheels. Each wheel's outer radius is 0.25 meters and each wheel's axle has radius 0.05 meters. If the wheels roll 1.00 meter from their original position, how much does the plank move from its original position?
Assume that there is no slipping anywhere, and that the plank does not tip.

Answer 1

Answer:

0·2 m

Explanation:

The distance by which the axle of the wheel is rotated must be the same as the distance travelled by the plank, as it is mentioned that there is no slipping anywhere because if the distance is not same then there will be slipping between them as friction will be acting

Let the angle by which the wheel is rotated when it rolls by 1 m be β

∴ 1 = (outer radius of the wheel) ×β

1 = 0·25 × β

∴ β = 4 radians

The angle by which the wheel's axle is rotated will  be the same as the angle rotated by the wheel as both are attached

∴ Wheel's axle will also be rotated by an angle β = 4 radians

Distance by which the axle of the wheel will get rotated = (radius of wheel's axle) × β

 = 0·05 × 4 =0·2 m

∴ Plank will move from original position by 0·2 m