A decorative piece consists of a 20cm long uniform brass rod weighing 4N and two ornaments, one weighing 6N and one weighing 10N, fixed to the ends. At what point should a supporting chain be attached so that the ornament balances?
At the center of mass (CM).
Measuring distance from the 6N ornament end,
4*10 + 10*20 = 20 X
X = 12 cm is the CM location
To determine the point at which the supporting chain should be attached for the ornament to balance, we need to consider the principle of moments, also known as the law of moments.
The principle of moments states that for an object to be in equilibrium (balanced), the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
In this case, we can assume the brass rod is weightless compared to the ornaments, so we only need to consider the moments of the ornaments themselves.
Let's label the distance between the fixed end of the rod and the point where the supporting chain is attached as "x".
Now, let's calculate the moments:
Clockwise moments = (6N) * (20cm - x)
Anticlockwise moments = (10N) * x + (4N) * (20cm)
To achieve balance, the clockwise moments should be equal to the anticlockwise moments:
(6N) * (20cm - x) = (10N) * x + (4N) * (20cm)
Let's solve this equation to find the value of x:
6N * 20cm - 6N * x = 10N * x + 4N * 20cm
120cmN - 6N * x - 10N * x = 80cmN
120cmN = 16N * x
x = (120cmN) / (16N)
Now we can calculate x:
x = 7.5cm
Therefore, the supporting chain should be attached 7.5cm from the fixed end of the brass rod in order to balance the ornaments.