An object with a mass of 5 kg5kg is hanging from an axle with a radius of 24 cm24cm. If the wheel attached to the axle has a radius of 38 cm38cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

1 Answer
Jul 2, 2016

~~73.85J73.85J

Explanation:

Given

  • "The radius of the axle " (r) =24cm0.24mThe radius of the axle (r)=24cm0.24m

  • "The mass of the object " (m) =5kgThe mass of the object (m)=5kg

We are to calculate the work done to lift the object by turning the wheel a length equal to the circumference of the axle.

"Now circumference of the axle" (l)=2pir=2xxpixx0.24mNow circumference of the axle(l)=2πr=2×π×0.24m

Actually the work done occurs due to the lifting of the object against the gravitational pull by length l=2pirl=2πr

So "Work done"(W)=mxxgxx2pirWork done(W)=m×g×2πr

=5xx9.8xx2xx3.14xx0.24J~~73.85J=5×9.8×2×3.14×0.24J73.85J