A barbell is loaded with two 20 kg plates on its right side and two 20 kg plates

Question

A barbell is loaded with two 20 kg plates on its right side and two 20 kg plates on its left side. The barbell is 2.2 m long, and its unloaded mass is 20 kg. The two 20 kg plates on the right side are locked in place at 35 cm and 40 cm from the right end of the bar. The two 20 kg plates on the left side have slipped. One is 30 cm from the left end of the bar, and the other is 20 cm from the left end of the bar.

1. Where is the center of gravity of this barbell with the four plates? (make sure you specify this distance relative to your axis of rotation – i.e. the left end of the bar, the right end of the bar, or the center of the bar)

2. Which direction would the center of gravity move if you added another 20 kg plate on the right end of the bar?

Explanation / Answer

1)

Center of gravity , Cg = (0.3*20 + 0.2*20 + (2.2 - 0.35 )*20 + (2.2 - 0.4)*20)/80

= 1.04 m from the left end (or 1.16 m from the right end)

2)

Now, new Center of graity, Cg' = (0.3*20 + 0.2*20 + (2.2 - 0.35 )*20 + (2.2 - 0.4)*20 + (2.2)*20)/100

= 1.27 m from the lleft end of the bar

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