An object with a mass of #7 kg# is hanging from an axle with a radius of #15 cm#. If the wheel attached to the axle has a radius of #65 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Question

An object with a mass of #7  kg# is hanging from an axle with a radius of #15 cm#.  If the wheel attached to the axle has a radius of #65 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Leo Abeyta · Accepted Answer

The work is #=14.9J#

The load L=(7g)N#

Radius of axle #r=0.15m#

Radius of wheel #R=0.65m#

Taking moments about the center of the axle

#F*R=L*r#

#F*0.65=7*g*0.15#

#F=(7*g*0.15)/0.65=15.83N#

The force is #=15.83N#

The distance is #=2pir=2*0.15*pi=0.3pi#

The work is

#W=F*d=15.83*0.3pi=14.9J#

Sebastian Acosta · Answer

undefined The work done to turn the wheel a length equal to the circumference of the axle can be calculated using the formula:

Work = Force × Distance

The force required to turn the wheel is equal to the force exerted by the hanging object due to gravity, which can be calculated as:

Force = mass × gravitational acceleration

The distance the wheel is turned is equal to the circumference of the axle. Given the radius of the axle, you can find the circumference using the formula:

Circumference = 2 × π × radius

Substituting the given values into the formulas, you can calculate the work required.