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Pachacha [2.7K]

3 years ago

12

an 8 N weight is placed at one end of a meterstick. a 10N weight is placed at the other end. where should the fulcrum be placed

to have the meterstick balanced?

1 answer:

cluponka [151]3 years ago

3 0

<h3><u>The fulcrum should be placed 0.44 from the 12 N weight or 0.56 m from the 8 N weight.</u></h3>

Explanation:

<h2>Given:</h2>

$w_1$ = 8 N

$w_2$ = 10 N

Since the meter stick has a length of 1 m, and $d_1 \:+\:d_2\:=\:1\:m$

Let $d_1$ = x

Let $d_2$ = 1 - x

<h2>Question:</h2>

Where should the fulcrum be placed to have the meterstick balanced?

<h2>Equation:</h2>

For the system to be balanced, the product of the weight and distance of the objects on opposite sides should be equal. This is is shown by the equation:

$w_1 d_1 = w_2 d_2$

where: w - weight

d - distance from the fulcrum

<h2>Solution:</h2>

Substituting the value of $w_1, \:w_2, \:d_1 \:$ and $\: d_2$ in the formula,

(8 N)(x) = (10 N)(1 m - x)

x(8 N) = (10 N)m - x(10 N)

x(8 N) + x(10 N) = (10 N) m

x(18 N) = 10 N

x = $\frac{(10 \:N)m}{18 \:N}$

x = 0.56

<h3>Solve for $d_1$ </h3>

$d_1$ = x

$d_1$ = 0.56 m

<h3>Solve for $d_2$ </h3>

$d_2$ = 1 m - x

$d_2$ = 1 m - 0.56 m

$d_2$ = 0.44 m

<h2>Final Answer:</h2><h3><u>The fulcrum should be placed 0.44 from the 12 N weight or 0.56 m from the 8 N weight.</u></h3>

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