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

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Answer 1 · 2018-07-01T13:40:42

Force on wheel = 100.8N (in opposite direction)

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 :

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

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

$F (w h e e l) \cdot r (w h e e l) + F (o b j e c t) \cdot r (o b j e c t) = 0$ $F(wheel)*r(wheel) + F(object)*r(object) = 0$

$F (w h e e l) \cdot 0.28 + 28.224 = 0$ $F(wheel)*0.28 + 28.224 = 0$

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

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

An object with a mass of 18kg18 kg is hanging from an axle with a radius of 16cm16 cm. If the wheel attached to the axle has a radius of 28cm28 cm, how much force must be applied to the wheel to keep the object from falling?