Question

A barbell is loaded with one 20 kg plate and one 15 kg plate on its right side and left side. The barbell is 2.2 m long, and its unloaded mass is 20 kg. On the left side the plates are locked in place with the 15kg plate at 35 cm and the 20 kg plate 40 cm from the left end of the bar. The two plates on the right side have slipped. The 15kg plate is 5 cm from the right end of the bar, and the 20kg plate is 10 cm from the right end of the bar. Where is the center of gravity of this barbell with the four plates?

.32 from the left end of the bar
1.22m from the left end of the bar
.98m from the left end of the bar
1.15m from the right end of the bar

@Pompeii00

Answer 1

So the center of gravity is another way of saying the "center of mass". This is where we can assume all the mass of the object to be and calculate how gravity will affect it.

The way we do this is by weighting the masses given with their coordinates.

\[CM=\frac{\sum_{i} m_{i}x_{i}}{\sum_{i} m_{i}}\]

Answer 2

Okay, so let's start with the easiest part. The denominator. That is just the total mass present and summed up.

Can you calculate the total mass this system has?

Answer 3

the total weight would be (20+20+15+15)= 70?

Answer 4

Close. Don't forget the bar unloaded!

Answer 5

(20+20+20+15+15) =90

Answer 6

Yes! That's the total mass. 90 kg.

Here's a pic.