An object with a mass of #3 kg# is hanging from an axle with a radius of #2 cm#. If the wheel attached to the axle has a radius of #16 cm#, how much work would it take to turn the wheel a length equal to the circumference of the axle?

To find the work required to turn the wheel a length equal to the circumference of the axle, we need to calculate the force required and then use the formula for work, which is work = force × distance.

First, let's find the circumference of the axle: Circumference = 2 × π × radius Circumference = 2 × π × 0.02 m Circumference ≈ 0.1257 m

Next, let's find the force required to turn the wheel: The torque required to turn the wheel is equal to the torque exerted by the hanging object on the axle. Torque = force × radius

The torque exerted by the hanging object is given by the formula: Torque = mass × gravity × radius Torque = 3 kg × 9.8 m/s^2 × 0.02 m Torque = 0.588 Nm

Now, we need to find the force required to turn the wheel, which is given by: Force = Torque / radius of the wheel Force = 0.588 Nm / 0.16 m Force ≈ 3.675 N

Finally, we can find the work required using the formula: Work = Force × distance Work = 3.675 N × 0.1257 m Work ≈ 0.461 J

Therefore, it would take approximately 0.461 joules of work to turn the wheel a length equal to the circumference of the axle.