An object with a mass of #8 kg# is hanging from an axle with a radius of #30 m#. If the wheel attached to the axle has a radius of #96 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 #30 m#.  If the wheel attached to the axle has a radius of #96 m#, how much force must be applied to the wheel to keep the object from falling?

Olivia Askew · Accepted Answer

The force is #F=24.5N#

The load is #L=8gN#

The radius of the axle is #r=30m#

The radius of the wheel is #R=96m#

The effort is #=FN#

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

Taking moments about the center of the axle

#F*96=8g*30#

#F=(8g*30)/96=24.5N#

The force is #F=24.5N#

Adam Arnold · 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:

$$ \text{Force} = \frac{m \cdot g \cdot r_2}{r_1} $$

Where:
- $ m $ = mass of the object (8 kg)
- $ g $ = acceleration due to gravity (approximately 9.8 m/s^2)
- $ r_2 $ = radius of the wheel (96 m)
- $ r_1 $ = radius of the axle (30 m)

Substituting the given values:

$$ \text{Force} = \frac{8 \times 9.8 \times 96}{30} $$

$$ \text{Force} = \frac{7526.4}{30} $$

$$ \text{Force} \approx 250.88 \, \text{N} $$

Therefore, approximately 250.88 Newtons of force must be applied to the wheel to keep the object from falling.