An object with a mass of #6 kg# is hanging from an axle with a radius of #54 m#. If the wheel attached to the axle has a radius of #4 m#, how much force must be applied to the wheel to keep the object from falling?

Question

An object with a mass of #6  kg# is hanging from an axle with a radius of #54 m#.  If the wheel attached to the axle has a radius of #4 m#, how much force must be applied to the wheel to keep the object from falling?

Julia Aguilar · Accepted Answer

The force is #=793.8N#

The load #=6gN#

Radius of axle #r=54m#

Radius of wheel #R=4m#

Taking moments about the center of the axle

#F*4=6g*54#

#F=(6g*54)/4=81g=793.8N#

Benjamin Asiedu · Answer

undefined To keep the object from falling, the force applied to the wheel must counteract the force due to gravity acting on the object. The force required can be calculated using the formula:

$$ F = \frac{mgR_w}{R_a} $$

Where:
- $ F $ is the force applied to the wheel,
- $ m $ is the mass of the object (6 kg),
- $ g $ is the acceleration due to gravity (approximately $ 9.81 \, \text{m/s}^2 $),
- $ R_w $ is the radius of the wheel (4 m),
- $ R_a $ is the radius of the axle (54 m).

Substituting the given values:

$$ F = \frac{(6 \, \text{kg})(9.81 \, \text{m/s}^2)(4 \, \text{m})}{54 \, \text{m}} $$

$$ F = \frac{(58.86 \, \text{N})(4 \, \text{m})}{54 \, \text{m}} $$

$$ F ≈ \frac{235.44 \, \text{Nm}}{54 \, \text{m}} $$

$$ F ≈ 4.36 \, \text{N} $$

So, approximately 4.36 Newtons of force must be applied to the wheel to keep the object from falling.