An object with a mass of #4 kg# is hanging from an axle with a radius of #9 m#. If the wheel attached to the axle has a radius of #6 m#, how much force is needed to raise the object?

Question

An object with a mass of #4    kg# is hanging from an axle with a radius of #9   m#.  If the wheel attached to the axle has a radius of #6 m#, how much force is needed to raise the object?

Lily Adams · Accepted Answer

The force is #=58.8N#

The load #L=(4g)N#

Radius of axle #r=9m#

Radius of wheel #R=6m#

Taking moments about the center of the axle

#F*R=L*r#

#F*6=4*g*9#

#F=(4*g*9)/6=58.8N#

The force is #F=58.8N#

Lily Adams · Answer

undefined To calculate the force needed to raise the object, we can use the principle of torque. Torque (τ) is calculated as the product of force (F) and the distance (r) from the axis of rotation. The torque required to raise the object is equal to the torque exerted by the object's weight.

Torque exerted by the weight of the object = Force × radius of the wheel attached to the axle.

Torque = (mass × gravity) × radius of the wheel

Where:
- mass = 4 kg (given)
- gravity = 9.8 m/s² (acceleration due to gravity)
- radius of the wheel = 6 m (given)

Torque = (4 kg × 9.8 m/s²) × 6 m
       = 235.2 N·m

So, the force needed to raise the object is equal to the torque exerted divided by the radius of the axle.

Force = Torque ÷ radius of the axle

Force = 235.2 N·m ÷ 9 m
       ≈ 26.13 N

Therefore, approximately 26.13 Newtons of force is needed to raise the object.