Experiment Number One: The Law Of Levers Updated 2/5/07 In M

Experiment Number One The Law Of Levers Updated 2 5 07in Man

EXPERIMENT NUMBER ONE --- The Law of Levers updated 2-5-07 In many situations, an applied force can be multiplied by use of a lever. The “law” governing this phenomenon was first written by Archimedes in about 250 BC. In words, the law states that the product of a force times its “moment arm” on one side of a fulcrum equals the product of a second force and its “moment arm” on the other side of the fulcrum. On a see-saw, a lighter child has to sit further back (longer “moment arm”) from the pivot than his heavier friend (shorter moment arm). But the product of their respective weights and their distances from the fulcrum is equal when the see-saw is balanced.

In equation form, the law is written: F1 ( L1 ) = F2 ( L2), where F’s are forces and numbers are subscripts. Since forces are proportional to masses, the equation can also be expressed as: M1 ( L1 ) = M2 ( L2 ). In this experiment, the validity of these equations will be demonstrated by balancing a meter stick horizontally with various weight/distance combinations placed upon it. We will predict where masses should be placed to balance the stick using the “mass” equation, then verify experimentally and calculate the percentage error between the predicted and actual values.

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The purpose of this experiment is to verify the law of the lever as formulated by Archimedes, which states that the torque produced by a force about a fulcrum is balanced when the product of the force and its lever arm on one side equals that on the other side. This fundamental principle of physics not only explains simple systems like see-saws but also underpins complex mechanical devices, emphasizing the importance of the relationship between force, distance, and equilibrium.

To begin, the experiment involves balancing a meter stick on a fulcrum to find its center of gravity, a task essential as it determines the point about which torques are calculated. Once identified, various weights—namely a quarter, a nickel, and a penny—are placed at specific points along the stick. The goal is to find where these weights balance each other, either by experimental placement or by calculation, illustrating the law in action.

The first step involves locating the center of gravity of the meter stick. This is achieved by balancing the stick on a pencil placed under its midpoint. The balance point, marking the center of gravity, is recorded with high precision. This step establishes the reference point for subsequent measurements, ensuring accurate calculation of lever arms.

Next, a quarter is placed on the stick at the 32 cm mark, and the lever arm is calculated as the distance from the center of gravity to this point. Using the law of levers, the distance required for a penny to balance the quarter is determined both mathematically and through physical repositioning. The experimental position of the penny is then measured, and the percentage error between this and the calculated value is computed, demonstrating the law’s predictive power and identifying experimental uncertainties.

This process is repeated with the quarter positioned at different points (28 cm and 8 cm) and with different weights (such as a nickel), illustrating how the law holds true across various configurations. Each iteration reinforces the concept that the product of mass and distance remains constant at equilibrium, affirming the law's validity.

In a more complex setup, two and then three quarters are stacked and placed at the 2 cm mark, and the point of balance is recorded. From these measurements, the mass of the meter stick itself can be calculated by setting the moments of the stationary weights against the stick’s own weight. The average mass is derived from repeated measurements, and if a scale is available, it provides an external validation of these findings. If no scale is accessible, percentage differences between calculated values reflect the experiment’s internal consistency.

Throughout, care is taken to measure lengths to the nearest tenth of a centimeter and to record all data meticulously, acknowledging that small errors can cascade in experimental physics. The experiment demonstrates how simple tools and careful measurement can verify foundational principles like the law of levers, underscoring the practical nature of physics.

In conclusion, this experiment not only validates the mathematical formulation of the law of levers but also emphasizes the importance of precision and repeated trials in scientific inquiry. It shows that with simple apparatus, one can observe and quantify universal physical laws, connecting theoretical physics to tangible, real-world applications.

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