Question

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?

Answer 1

The fulcrum should be placed 0.44 from the 12 N weight or 0.56 m from the 8 N weight.

Step-by-step explanation:

Given:

`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

Question:

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

Equation:

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

Solution:

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 =
`((10 \:N)m)/(18 \:N)`

x = 0.56

Solve for
`d_1`

`d_1` = x

`d_1` = 0.56 m

Solve for
`d_2`

`d_2` = 1 m - x

`d_2` = 1 m - 0.56 m

`d_2` = 0.44 m

Final Answer:

The fulcrum should be placed 0.44 from the 12 N weight or 0.56 m from the 8 N weight.