Two bowling balls are at rest on top of a uniform wooden plank with their centers of mass located as in the figure below. The plank has a mass of 5.10 kg and is 1.00 m long. Find the horizontal distance (in m) from the left end of the plank to the center of mass of the plank-bowling balls system.

To solve this problem, we need to calculate the center of mass of a system consisting of the plank and two bowling balls. The formula for the center of mass of a system is given by:

\[
x_{cm} = \frac{\sum m_i x_i}{\sum m_i}
\]

Where:
- \( x_{cm} \) is the horizontal position of the center of mass of the system.
- \( m_i \) is the mass of each object (plank and bowling balls).
- \( x_i \) is the horizontal position of the center of mass of each object.

### Step 1: Identify known quantities
- Let \( m_p = 5.10 \, \text{kg} \) be the mass of the plank.
- The length of the plank is 1.00 m, so its center of mass is located at the midpoint, i.e., \( x_p = 0.50 \, \text{m} \) from the left end.
- We will denote the mass of the first bowling ball as \( m_1 \) and the second as \( m_2 \), with their corresponding positions \( x_1 \) and \( x_2 \), but we don't have their specific values yet.

### Step 2: Center of mass calculation
We can now calculate the center of mass of the system using the formula provided, once we have the mass and positions of the bowling balls. Could you share the details from the figure or tell me their masses and positions?



Learn how to calculate the center of mass of a system consisting of a uniform plank and two bowling balls. This example covers key physics mechanics concepts such as the center of mass formula and weighted averages. The plank has a mass of 5.10 kg and is 1.00 m long. Suitable for high school students in Grades 10-12.

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