A balanced lever has two weights on it, the first with mass $3 k g$ $3 kg$ and the second with mass $24 k g$ $24 kg$ . If the first weight is $9 m$ $9 m$ 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 $3 k g$ $3 kg$ and the second with mass $24 k g$ $24 kg$ . If the first weight is $9 m$ $9 m$ from the fulcrum, how far is the second weight from the fulcrum?

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Answer 1 · 2015-12-30T17:30:13

$r = 1.125 m$ $r=1.125m$

Explanation:

Let $m_{1} = 3 k g$ $m_1=3kg$ $m_{2}$ $m_2$ =24kg
Let $W_{1}$ $W_1$ and $W_{2}$ $W_2$ be the weights of $m_{1}$ $m_1$ and $m_{2}$ $m_2$ respectively.
$\Rightarrow W_{1} = m_{1} \cdot g = 3 \cdot 9.8 = 29.4 N$ $implies W_1=m_1*g=3*9.8=29.4N$
$\Rightarrow W_{2} = m_{2} \cdot g = 24 \cdot 9.8 = 235.2 N$ $implies W_2=m_2*g=24*9.8=235.2N$

Since the lever is balanced so both the torques produced by $W_{1}$ $W_1$ and $W_{2}$ $W_2$ should be equal.

Let the mass $m_{2}$ $m_2$ be at a distance from $r$ $r$ from the fulcrum.

Let $τ_{1}$ $tau_1$ and $τ_{2}$ $tau_2$ be the torques produced by $W_{1}$ $W_1$ and $W_{2}$ $W_2$ respectively.
$τ_{1} = τ_{2}$ $tau_1=tau_2$
$\Rightarrow W_{1} \cdot 9 = W_{2} \cdot r$ $implies W_1*9=W_2*r$
$\Rightarrow 29.4 \cdot 9 = 235.2 \cdot r$ $implies 29.4*9=235.2*r$
$\Rightarrow r = \frac{29.4 \cdot 9}{235.2} = 1.125 m$ $implies r=(29.4*9)/235.2=1.125m$
$\Rightarrow r = 1.125 m$ $implies r=1.125m$
Hence the second weight is at a distance of 1.125m from the fulcrum.

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A balanced lever has two weights on it, the first with mass $3 k g$ $3 kg$ and the second with mass $24 k g$ $24 kg$ . If the first weight is $9 m$ $9 m$ 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 3 kg 3kg3 kg and the second with mass 24 kg24kg24 kg. If the first weight is 9 m9m 9 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 $3 k g$ $3 kg$ and the second with mass $24 k g$ $24 kg$ . If the first weight is $9 m$ $9 m$ from the fulcrum, how far is the second weight from the fulcrum?