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)
4 cm to the right of the fulcrum
8 cm to the right of the fulcrum
6 cm to the right of the fulcrum
3 cm to the right of the fulcrum

Explanation:

Step1: Recall the principle of moments

For a balanced plank, the product of mass and distance on one - side of the fulcrum is equal to the product of mass and distance on the other side. Let the distance of the 3 - gram mass from the fulcrum be \(d\). The 4 - gram mass is \(m_1 = 4\ g\) and its distance from the fulcrum is \(r_1=6\ cm\) (left of the fulcrum), and the second mass is \(m_2 = 3\ g\).

Step2: Set up the moment - balance equation

\(m_1r_1=m_2d\). Substitute \(m_1 = 4\ g\), \(r_1 = 6\ cm\), and \(m_2 = 3\ g\) into the equation: \(4\times6=3\times d\).

Step3: Solve for \(d\)

We have the equation \(24 = 3d\). Divide both sides by 3: \(d=\frac{24}{3}=8\ cm\). Since the 4 - gram mass is on the left of the fulcrum, the 3 - gram mass should be on the right of the fulcrum.

Answer:

8 cm to the right of the fulcrum