Home > Physics > Simple Machines

An object with a mass of #4 kg# is hanging from an axle with a radius of #8 cm#. If the wheel attached to the axle has a radius of #24 cm#, how much work would it take to turn the wheel #12 cm#?

Answer 1

Emily Abbate

The work done is #=1.57J#

The load #=(4g)N#

Radius of axle #r=0.08m#

Radius of wheel #R=0.24m#

Taking moments about the center of the axle

#F*0.24=4*g*0.08#

#F=(4*g*0.08)/0.24=13.07N#

The work done is

#W=F*d#

#=13.07*0.12#

#=1.57J#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Adam Arnold

To calculate the work done to turn the wheel by 12 cm, we can use the formula:

Work = Force × Distance

First, calculate the force required to lift the object attached to the axle:

Force = mass × gravity Force = 4 kg × 9.8 m/s^2

Next, calculate the distance the object is lifted using the axle's radius:

Distance_lifted = 2π × axle_radius

Now, use the principle of mechanical advantage to find the distance the wheel must be turned to lift the object:

Distance_wheel_turned = (axle_radius / wheel_radius) × Distance_lifted

Finally, plug in the values and calculate the work:

Work = Force × Distance_wheel_turned

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.