A balanced lever has two weights on it, the first with mass $1 k g$ $1 kg$ and the second with mass $7 k g$ $7 kg$ . If the first weight is $8 m$ $8 m$ from the fulcrum, how far is the second weight from the fulcrum?

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A balanced lever has two weights on it, the first with mass $1 k g$ $1 kg$ and the second with mass $7 k g$ $7 kg$ . If the first weight is $8 m$ $8 m$ from the fulcrum, how far is the second weight from the fulcrum?

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Answer 1 · 2018-03-12T18:35:08

$~ 1.14$ $~1.14$ meters

Explanation:

When a lever is balanced, the torque exerted on either side of the fulcrum is equal, so the lever is held in equilibrium.

$τ = r F sin θ$ $tau = rFsintheta$ where $τ$ $tau$ is the torque on one side of the lever and $θ$ $theta$ is the angle that the side makes with the fulcrum.

$τ_{1} = (1 \cdot 9.8) \cdot 8 \cdot 1$ $tau_1 = (1*9.8) * 8 * 1$
$τ_{2} = (7 \cdot 9.8) \cdot r \cdot 1$ $tau_2 = (7*9.8) * r * 1$

Knowing that $τ_{1}$ $tau_1$ and $τ_{2}$ $tau_2$ are equal, we can combine the two equations to solve for $r$ $r$ .

$9.8 \cdot 8 = 68.6 r$ $9.8 * 8 = 68.6r$
$78.4 = 68.6 r$ $78.4 = 68.6r$
$r = 1.14$ $r = 1.14$

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A balanced lever has two weights on it, the first with mass $1 k g$ $1 kg$ and the second with mass $7 k g$ $7 kg$ . If the first weight is $8 m$ $8 m$ from the fulcrum, how far is the second weight from the fulcrum?

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Explanation:

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A balanced lever has two weights on it, the first with mass 1 kg 1kg1 kg and the second with mass 7 kg7kg7 kg. If the first weight is 8 m8m 8 m from the fulcrum, how far is the second weight from the fulcrum?

1 Answer

Explanation:

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A balanced lever has two weights on it, the first with mass $1 k g$ $1 kg$ and the second with mass $7 k g$ $7 kg$ . If the first weight is $8 m$ $8 m$ from the fulcrum, how far is the second weight from the fulcrum?