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

1 Answer
Jan 28, 2016

Answer:

#W=6.48gpicolor(white)(x)"N"#

Explanation:

Here's the picture as I see it:

MFDocs

The circumference of the axle is given by:

#c_1=2pixx0.27=0.54pi"m"#

The circumference of the wheel is given by:

#c_2=2pixx0.18=0.36pi"m"#

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

How many turns #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"#