A uniform meter stick of mass 40 g is used to suspend three objects: 15 g at 0.02 m, 40 g at 0.36 m and 35 g at 0.6 m. Where could you place your finger to balance the stick in the horizontal position?
To find the position where you can place your finger to balance the stick in the horizontal position, we need to consider the principle of moments. The principle of moments states that for a balanced system, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point.
In this case, the moments are calculated by multiplying the mass of each object by its distance from the balance point. Let's calculate the moments for each object first:
Object 1 (15 g at 0.02 m):
Moment = (mass) × (distance) = 0.015 kg × 0.02 m = 0.0003 kg·m (clockwise)
Object 2 (40 g at 0.36 m):
Moment = (mass) × (distance) = 0.04 kg × 0.36 m = 0.0144 kg·m (clockwise)
Object 3 (35 g at 0.6 m):
Moment = (mass) × (distance) = 0.035 kg × 0.6 m = 0.021 kg·m (clockwise)
Now, let's denote the distance from the balance point to your finger as "x". The moment due to the mass of the meter stick itself is the weight of the stick multiplied by the distance from the balance point to your finger, which is (0.04 kg × 9.8 m/s²) × x = 0.392x kg·m (anticlockwise), considering the acceleration due to gravity as 9.8 m/s².
According to the principle of moments, the sum of the clockwise moments must balance the sum of the anticlockwise moments. Therefore:
0.0003 kg·m + 0.0144 kg·m + 0.021 kg·m = 0.392x kg·m
Now, solve the equation to find the value of "x":
0.0357 kg·m = 0.392x kg·m
x = 0.0357 kg·m / 0.392 kg·m
x ≈ 0.0912 m
Therefore, you need to place your finger at approximately 0.0912 meters from one end of the meter stick to balance the stick in the horizontal position.