An object with a mass of $8 k g$ $8 kg$ is hanging from an axle with a radius of $27 c m$ $27 cm$ . If the wheel attached to the axle has a radius of $18 c m$ $18 cm$ , how much work would it take to turn the wheel a length equal to the circumference of the axle?

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Answer 1 · 2016-01-28T17:24:19

$W = 6.48 g π x N$ $W=6.48gpicolor(white)(x)"N"$

Here's the picture as I see it:

MFDocs

The circumference of the axle is given by:

$c_{1} = 2 π \times 0.27 = 0.54 π m$ $c_1=2pixx0.27=0.54pi"m"$

The circumference of the wheel is given by:

$c_{2} = 2 π \times 0.18 = 0.36 π m$ $c_2=2pixx0.18=0.36pi"m"$

If the wheel turns the circumference of the axle then it must turn through a distance of $0.54 π m$ $0.54pi"m"$ .

How many turns $n$ $n$ is this?

$n=(0.54cancel(pi))/(0.36cancel(pi))=3/2$

The no. of turns the axle completes must be the same so the total distance the axle rotates is:

$3/2xx0.54pi"m"$

$=0.81pi"m"$

The work done in lifting the 8kg mass is given by:

$W=mgh$

$:.W=8gxx0.81pi$

$W=6.48gpicolor(white)(x)"J"$

An object with a mass of 8 kg8kg8 kg is hanging from an axle with a radius of 27 cm27cm27 cm. If the wheel attached to the axle has a radius of 18 cm18cm18 cm, how much work would it take to turn the wheel a length equal to the circumference of the axle?