An object with a mass of #300 kg# is hanging from an axle with a radius of #3 cm#. If the wheel attached to the axle has a radius of #96 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 #300  kg# is hanging from an axle with a radius of #3 cm#.  If the wheel attached to the axle has a radius of #96 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

Lily Adams · Accepted Answer

The work is #=554.2J#

The load is #L=300gN#

The radius of the axle is #r=0.03m#

The radius of the wheel is #R=0.96m#

The effort is #=FN#

The acceleration due to gravity is #g=9.8ms^-2#

Taking moments about the center of the axle

#F*0.96=300g*0.03#

#F=(300g*0.03)/0.96=91.875N#

The force is #F=91.875N#

The distance is #d=2piR=2*pi*0.96m#

The work done is

#W=F*d=91.875*2*pi*0.96=554.2J#

Olivia Askew · Answer

undefined The work done to turn the wheel is 1,811,040 joules.

Xavier Adame · Answer

undefined To calculate the work required to turn the wheel a length equal to the circumference of the axle, we can use the formula for work:

Work = Force x Distance

First, we need to find the force applied to turn the wheel. This force is generated by the weight of the hanging object. The force (F) can be calculated using the formula:

F = m * g

Where:
m = mass of the object (300 kg)
g = acceleration due to gravity (approximately 9.8 m/s²)

Then, we need to find the distance the force is applied over. In this case, it's equal to the circumference of the axle, which is given by:

Circumference = 2 * π * radius

Now, we can plug in the values into the formulas to find the work:

Force = 300 kg * 9.8 m/s²
Distance = 2 * π * 0.03 m

Finally, we calculate the work:

Work = Force * Distance