A meter stick is balanced at the 50-cm mark. You tie a 20-N weight at the 20-cm mark. At which mark should a 30-N weight be placed so that the meter stick will again be balanced?
Sum moments about the 50 cm mark.
20*30cm=30*X
x=20 cm from the fulcrum, or at the 70cm mark.
To balance the meter stick with a 30-N weight, we can use the principle of moments. The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.
In this case, the moments are determined by the weights and their distances from the fulcrum (fulcrum is the point where the meter stick is balanced). We'll use the equation:
Clockwise Moments = Counterclockwise Moments
First, let's determine the clockwise and counterclockwise moments.
For the 20-N weight at the 20-cm mark:
Clockwise Moment = 20 N * 30 cm
For the 30-N weight at an unknown mark (let's call it x):
Counterclockwise Moment = 30 N * (50 cm - x)
Since we want the meter stick to be in balance, the clockwise moment and counterclockwise moment must be equal.
20 N * 30 cm = 30 N * (50 cm - x)
Now we can solve for x:
20 N * 30 cm = 30 N * (50 cm - x)
600 cm*N = 1500 cm*N - 30 N * x
1500 cm*N - 600 cm*N = 30 N * x
900 cm*N = 30 N * x
x = (900 cm*N) / (30 N)
x = 30 cm
Therefore, the 30-N weight should be placed at the 30-cm mark so that the meter stick is balanced again.
To determine the position at which the 30-N weight should be placed in order to balance the meter stick, we can use the principle of moments. The principle of moments states that the moments on one side of a balanced lever are equal to the moments on the other side.
In this case, the moment of the 20-N weight on one side of the meter stick is equal to the moment of the 30-N weight on the other side. The formula for calculating the moment of an object is:
Moment = Force × Distance
Let's denote the position at which the 30-N weight should be placed as "x cm". The distance between the 50-cm mark (where the meter stick is balanced) and the position of the 20-N weight is 50 - 20 = 30 cm. Similarly, the distance between the 50-cm mark and the position of the 30-N weight is 30 - x cm.
Now we can set up the equation:
(20 N) × (30 cm) = (30 N) × (30 - x cm)
Simplifying the equation:
600 N·cm = 900 N·cm - 30 N·cm × x
Rearranging the equation:
30 N·cm × x = 900 N·cm - 600 N·cm
30 N·cm × x = 300 N·cm
Dividing both sides by 30 N·cm:
x = 300 N·cm / 30 N·cm
x = 10 cm
Therefore, the 30-N weight should be placed at the 10-cm mark for the meter stick to be balanced again.