Two metal disks are taped to a meterstick. The mass of the
meterstick is 460 grams. Disk 1 has a mass of 300 grams
and is located at the 28 cm mark. Disk 2 has a mass of
500 grams and is located at the 64 cm mark. At what posi-
tion along the meterstick should you place a fulcrum so that
the entire system (meterstick plus the 2 masses) is balanced?
totalmass*cg=mass1*position1 + mass2*position2 + massstick*50cm
solve for cg.
Thanks for your guidance
To determine the position along the meterstick where you should place the fulcrum so that the entire system is balanced, you need to consider the principle of moments. The principle of moments states that the sum of the clockwise moments about a fulcrum is equal to the sum of the anticlockwise moments about the same fulcrum.
In this case, we can calculate the moments of each mass relative to the fulcrum using the equation:
(Mass x Distance) = Moment
Let's assign the unknown position of the fulcrum as "x".
The moment of the meterstick is calculated as the product of its mass and its distance from the fulcrum, which is (460 grams) * (x cm).
The moment of disk 1 is calculated as the product of its mass and its distance from the fulcrum, which is (300 grams) * (28 cm - x cm) since it is located at the 28 cm mark.
The moment of disk 2 is calculated as the product of its mass and its distance from the fulcrum, which is (500 grams) * (x cm - 64 cm) since it is located at the 64 cm mark.
Now, according to the principle of moments, the sum of the clockwise moments should be equal to the sum of the anticlockwise moments:
(300 grams) * (28 cm - x cm) + (500 grams) * (x cm - 64 cm) = (460 grams) * (x cm)
We can now solve this equation to find the value of "x" which represents the position of the fulcrum. By simplifying the equation:
(8400 grams cm - 300 grams x cm) + (500 grams x cm - 32000 grams cm) = 460 grams x cm
Simplifying further:
5200 grams cm - 300 grams x cm = 460 grams x cm
5200 grams cm = 760 grams x cm
5200 grams / 760 grams = x cm
x cm ≈ 6.84 cm
Therefore, you should place the fulcrum at approximately the 6.84 cm mark along the meterstick to balance the entire system.