An object with a mass of #5 kg# is hanging from an axle with a radius of #18 cm#. If the wheel attached to the axle has a radius of #42 cm#, how much work would it take to turn the wheel #12 cm#?

Question

An object with a mass of #5  kg# is hanging from an axle with a radius of #18 cm#.  If the wheel attached to the axle has a radius of #42 cm#, how much work would it take to turn the wheel #12 cm#?

Nathan Ashcroft · Accepted Answer

The work is #=2.52J#

The load #L=(5g)N#

Radius of axle #r=0.18m#

Radius of wheel #R=0.42m#

Taking moments about the center of the axle

#F*R=L*r#

#F*0.42=5*g*0.18#

#F=(5*g*0.18)/0.42=21N#

The force is #F=21N#

The distance is #d=0.12m#

The work is

#W=Fd=21*0.12=2.52J#

Olivia Askew · Answer

undefined To calculate the work required to turn the wheel 12 cm, you can use the formula for work done by a force, which is equal to the force applied multiplied by the distance over which the force is applied.

Work = Force × Distance

The force exerted by the hanging mass can be calculated using the formula:

Force = Mass × Gravity

Where:
- Mass = 5 kg (given)
- Gravity = 9.8 m/s² (standard acceleration due to gravity)

The distance over which the force is applied is the circumference of the wheel, which can be calculated as:

Circumference = 2 × π × radius of the wheel

The radius of the wheel is given as 42 cm.

Once you have the force exerted by the hanging mass and the distance over which it acts, you can calculate the work done to turn the wheel 12 cm.