An object with a mass of #8 kg# is hanging from an axle with a radius of #27 m#. If the wheel attached to the axle has a radius of #21 m#, how much force must be applied to the wheel to keep the object from falling?

Question

An object with a mass of #8   kg# is hanging from an axle with a radius of #27  m#.  If the wheel attached to the axle has a radius of #21 m#, how much force must be applied to the wheel to keep the object from falling?

William Audy · Accepted Answer

The force is #=100.8N#

The load is #L=8gN#

The radius of the axle is #r=27m#

The radius of the wheel is #R=21m#

The effort is #=FN#

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

Taking moments about the center of the axle

#F*21=8g*27#

#F=8g*27/21=N#

The force is #F=100.8N#

Xavier Adame · Answer

undefined To calculate the force required to keep the object from falling, we can use the equation for torque:

Torque = Force × Distance

First, we need to find the torque exerted by the weight of the object:

Torque = (mass × gravity) × radius of axle

Then, we calculate the torque exerted by the wheel:

Torque = (Force × radius of wheel)

Since the wheel is preventing the object from falling, the torque exerted by the wheel must be equal and opposite to the torque exerted by the weight of the object:

Force × radius of wheel = mass × gravity × radius of axle

Now, we can solve for the force:

Force = (mass × gravity × radius of axle) / radius of wheel

Substituting the given values:

Force = (8 kg × 9.8 m/s² × 27 m) / 21 m