An object with a mass of $7$ $7$ $k g$ $kg$ is hanging from an axle with a radius of $36$ $36$ $m$ $m$ . If the wheel attached to the axle has a radius of $9$ $9$ $m$ $m$ , how much force must be applied to the wheel to keep the object from falling?

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An object with a mass of $7$ $7$ $k g$ $kg$ is hanging from an axle with a radius of $36$ $36$ $m$ $m$ . If the wheel attached to the axle has a radius of $9$ $9$ $m$ $m$ , how much force must be applied to the wheel to keep the object from falling?

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Answer 1 · 2016-02-22T22:59:45

This is a similar case to a lever: the torque on both sides need to be the same for balance. $τ_{1} = r F = r m g = 36 \cdot 7 \cdot 9.8 = 2469.6$ $tau_1=rF=rmg=36*7*9.8=2469.6$ $N m$ $Nm$ . $τ_{2} = r F \to F = \frac{τ_{2}}{r}$ $tau_2=rF to F=tau_2/r$ but $τ_{1} = τ_{2}$ $tau_1=tau_2$ so $F = \frac{2469.6}{9} = 274.4$ $F=2469.6/9=274.4$ $N$ $N$ .

Explanation:

I think the explanation above is clear, but it's worth pointing out that the force acting one the $7$ $7$ $k g$ $kg$ mass is its weight force, $F = m g$ $F=mg$ where $g$ $g$ is the acceleration due to gravity, $9.8$ $9.8$ $m s^{- 2}$ $ms^-2$ .

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An object with a mass of $7$ $7$ $k g$ $kg$ is hanging from an axle with a radius of $36$ $36$ $m$ $m$ . If the wheel attached to the axle has a radius of $9$ $9$ $m$ $m$ , how much force must be applied to the wheel to keep the object from falling?

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An object with a mass of $7$ $7$ $k g$ $kg$ is hanging from an axle with a radius of $36$ $36$ $m$ $m$ . If the wheel attached to the axle has a radius of $9$ $9$ $m$ $m$ , how much force must be applied to the wheel to keep the object from falling?