Question

A simple plank balance has a mass of 4 grams placed 6 cm left of the fulcrum. Where should you place a 3-gram mass to balance the plank?(1 point)
Responses

3 cm to the right of the fulcrum
3 cm to the right of the fulcrum

8 cm to the right of the fulcrum
8 cm to the right of the fulcrum

4 cm to the right of the fulcrum
4 cm to the right of the fulcrum

6 cm to the right of the fulcrum

Answer 1

To balance the plank, we can use the principle of moments, which states that the moments (torque) around the fulcrum must be equal on both sides for the plank to be in equilibrium.

The moment is calculated as:

\[
\text{Moment} = \text{mass} \times \text{distance from the fulcrum}
\]

For the 4-gram mass placed 6 cm to the left of the fulcrum:

\[
\text{Moment}_{\text{left}} = 4\, \text{g} \times 6\, \text{cm} = 24\, \text{g cm}
\]

Let \( x \) be the distance (in cm) from the fulcrum to the right where the 3-gram mass should be placed. The moment for the 3-gram mass will be:

\[
\text{Moment}_{\text{right}} = 3\, \text{g} \times x\, \text{cm}
\]

For the plank to be balanced:

\[
\text{Moment}_{\text{left}} = \text{Moment}_{\text{right}}
\]

Thus,

\[
24\, \text{g cm} = 3\, \text{g} \times x\, \text{cm}
\]

Now, solving for \( x \):

\[
x = \frac{24\, \text{g cm}}{3\, \text{g}} = 8\, \text{cm}
\]

So, you should place the 3-gram mass **8 cm to the right of the fulcrum** to balance the plank.

The correct answer is:
**8 cm to the right of the fulcrum**.