# An object with a mass of 18 kg is hanging from an axle with a radius of 16 cm. If the wheel attached to the axle has a radius of 28 cm, how much force must be applied to the wheel to keep the object from falling?

Jul 1, 2018

Force on wheel = 100.8N (in opposite direction)

#### Explanation:

force due to gravity s 9.8N/kg (=176.4N for 18kg object)

turning moment is force*radius
remember to convert to standard units (metres, Newtons, etc.)

object's turning moment (a.k.a. torque) will be :

$M \left(o b j e c t\right) = 18 \cdot 9.8 \cdot 0.16 = 28.224$ Nm

to prevent the axle turning the sum of the moments must be zero

$F \left(w h e e l\right) \cdot r \left(w h e e l\right) + F \left(o b j e c t\right) \cdot r \left(o b j e c t\right) = 0$

$F \left(w h e e l\right) \cdot 0.28 + 28.224 = 0$

$F \left(w h e e l\right) = - \frac{28.224}{0.28} = - 100.8 N$

the negative value means the force is applied in the opposite direction to that due to the object