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.
45 POINTS TO WHOEVER CAN ANSWER, THANK YOU VERY MUCH!

Answer 1

Answer:

The plank moves 0.2m from it's original position

Explanation:

we can do this question from the constraints that ,

• the wheel and the axle have the same angular speed or velocity
• the speed of the plank is equal to the speed of the axle at the topmost point .

thus ,

since the wheel is pure rolling or not slipping,

⇒$v=wr$

where

$v$ - speed of the wheel

$w$ - angular speed of the wheel

$r$ - radius of the wheel

since the wheel traverses 1 m let's say in time '$t$' ,

$v_{w}=\frac{distance}{time} =\frac{1}{t}$

∴

⇒$w=\frac{v_{w}}{r} = \frac{1}{t*0.25}$

the speed at the topmost point of the axle is :

⇒$v_{a}=w*r\\v_{a}=\frac{1}{t*0.25} *0.05\\v_{a}=\frac{1}{5t}$

this is the speed of the plank too.

thus the distance covered by plank in time '$t$' is ,

⇒$d=v_{a}*t\\d=\frac{1}{5t} *t\\d=\frac{1}{5} = 0.2m$