Question

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

Answer 1

(a) 1.08 m

(b) 1.06 m

Step-by-step explanation:

Step 1: calculate the center of gravity from 20kg mass

Let the center of gravity from 20kg mass = X

Applying the principle of moment; clockwise moment = ant-clockwise moment

20*X = 35*(1.7-X)

20X = 59.5 - 35X

55X = 59.5

X = 59.5/55

X = 1.08 m

Ignoring the weight of the bar, the center of gravity is 1.08m from left end of the barbell.

Step 2: calculate the center of gravity from 20kg mass, if the 8.0kg mass of the barbell in considered.

Applying the principle of moment

`(20*X)+(X)/(2)((8)/(1.7)) = 35(1.7-X) + ((1.7-X)/(2))((8)/(1.7))`

`20X + 2.353X = 59.5 -35X +2.353(1.7-X)`

20X +2.353X = 59.5 -35X + 4 - 2.353X

59.706X = 63.5

X = 63.5/59.706

X = 1.06 m

considering the weight of the bar, the center of gravity is 1.06m from left end of the barbell.