Question

Open Box. Consider a hollow box with the top missing. The sides have negligible thickness and each has length L and mass m. (a) Find the x-coordinate of the center of mass.

Answer 1

x_{cm} = L / 2

Step-by-step explanation:

The center of mass is defined by

`x_(cm)` = 1 / M ∑ m_{i} x_{i}

where M is the total mass of the system

in this case the system is continuous so, for which we use the density

ρ = dm / dx

dm = ρ dx

substituting

x_{cm} = 1 / M ∫ x ρ dx

x_{cm} = ρ / M ∫ x dx

we integrate and evaluate from x = 0 to x = L

x_{cm} = ρ / M (L² /2 -0)

we introduce the density which is constant

ρ = M / L

x_{cm} = 1 /M (M/L) L² / 2

x_{cm} = L / 2