The Law of the Lever

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A beam balance is balanced when the net moment about its hinge point is zero. This is also called the law of the lever. The "product of the weight and its distance from the hinge point" should be equal to the "product of the other weight and its distance from the hinge point". This is a simple demo to explain this concept.

According to lever principle, a smaller force applied at a greater distance from the axis of rotation can lift a larger weight.

For a body to be in equilibrium, the net force and net torque should be zero. The setup consists of a scale hinged at its middle point. The scale has holes at regular interval to hang weights at different distances from the hinge point.

Procedure

1. Check that scale is almost balanced. If not, fix a suitable weight to balance it.
2. Attach a fixed weight at one end of the scale.
3. Attach another weight on other side of hinge point so that scale is balanced.
4. Repeat above step for different weights.
5. Verify that net force on the scale and net torque about the hinge point is zero in balanced condition.

Variant: Procedure

Balance the ruler across a pencil. Put 3-4 coins at any point on one side of the ruler. Balance it by placing same number of coins on the other side. Note the point where balance occurs. Are both points equidistant from the pencil?

Place one coin on one side of the ruler. Try balancing it by placing two coins at various points on other side of the ruler. Measure the distance of both points from the pencil. Repeat the above exercise with one coin on one side and three coins on other side. Do you find any relation between the number of coins and their distance from the pencil?

Discussion

Let $$W_1$$ be weight of the coins placed at distance $$x_1$$ from the pencil and $$W_2$$ be weight of the coins placed on the other side of pencil at a distance $$x_2$$ (see figure). The product of weight and distance on one side should be equal to the product of weight and distance on the other side i.e., $$W_1 x_1=W_2 x_2$$. The product of the force and arm length is called moment or torque.

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