An object with a mass of 7 kg7kg is hanging from an axle with a radius of 8 cm8cm. If the wheel attached to the axle has a radius of 56 cm56cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?

1 Answer
May 14, 2016

34.496J

Explanation:

The mass of the object lifted = (m)=7kg(m)=7kg

The radius of the axle (r)=8cm=0.08m(r)=8cm=0.08m

The radius of the Wheel attached with the axle

R=56cm=0.56mR=56cm=0.56m

We are to find out the work done to turn the wheel a length

equal to the circumference of the axle. When turning of axle

equal to its circumference(2pir)(2πr) occurs ,the weight is lifted

to the same height (h= "circumference of axle")(h=circumference of axle) against the gravity .

Hence the work done W=mgh=mxxgxx2pir=7xx9.8xx2xx22/7xx0.08=34.496JW=mgh=m×g×2πr=7×9.8×2×227×0.08=34.496J