Final answer:
By using the center of mass formula and incorporating the masses and positions of the plank and bowling balls, we calculated the horizontal distance to the center of mass of the plank-bowling balls system to be approximately 0.566 meters from the left end of the plank.
Step-by-step explanation:
To find the horizontal distance from the left end of the plank to the center of mass (COM) of the plank-bowling balls system, we will apply the concept of the center of mass for a system of objects. The center of mass is computed by finding the weighted average of the positions of the mass distribution.
We will use the formula for the center of mass of a system of particles, which is:
COM = (m1*x1 + m2*x2 + ... + mn*xn) / (m1 + m2 + ... + mn)
Where m represents the mass of each object and x represents the position of the center of mass of each object from the reference point (left end of the plank).
Given the following masses and positions:
- Mass of plank, mplank = 4.90 kg, position = 0.50 m (center of plank)
- Mass of ball A, mA = 3.65 kg, position = 0.280 m
- Mass of ball B, mB = 5.60 kg, position = 0.810 m
The calculation will be:
COM = (4.90 kg * 0.50 m + 3.65 kg * 0.280 m + 5.60 kg * 0.810 m) / (4.90 kg + 3.65 kg + 5.60 kg)
COM = (2.45 + 1.022 + 4.536) / 14.15
COM = 8.008 / 14.15
COM ≈ 0.566 m from the left end of the plank