Question

A 1.7-m-long barbell has a 20 kg weight on its right end and a 35 kg weight on its left end. If you ignore the weight of the bar itself, how far from the left end of the barbell is the center of gravity? Where is the center of gravity if the 8.0 kg mass of the barbell itself is taken into account?

Answer 1

Answer:

0.61818 m from the left.

0.64761 m from the left.

Explanation:

$m_2$ = Left weight = 35 kg

$m_1$ = Right weight = 20 kg

x denotes the distance

The center of mass is given by

$X_{cm}={\frac {1}{M}}\sum _{i=1}^{n}m_{i}{r} _{i}$

For first case (left side taken as reference)

$X_{cm}=\dfrac{m_1x_1+m_2x_2}{m_1+m_2}\\\Rightarrow X_{cm}=\dfrac{20\times 1.7+35\times 0}{35+20}\\\Rightarrow X_{cm}=0.61818\ m$

The center of gravity of the barbell ignoring the mass of the bar is 0.61818 m from the left.

For second case (left side taken as reference)

$X_{cm}=\dfrac{m_1x_1+m_2x_2+m_3x_3}{m_1+m_2+m_3}\\\Rightarrow X_{cm}=\dfrac{20\times 1.7+35\times 0+8\times \dfrac{1.7}{2}}{35+20+8}\\\Rightarrow X_{cm}=0.64761\ m$

The center of gravity of the entire barbell is 0.64761 m from the left.