Lab Report of Vector Table PDF

Preview

Summary

This is the Lab report of Vector Table experminet...

Description

PHYSICS 023 – 02 LAB REPORT NAME: Prem Raj Oli ID: @02992540 Experiment Name: Vector Force Table

Vector Force Table Objective: The objective of this experiment is to study vectors and compare experimental results with graphical and analytical calculations by finding a resultant force that balances out the given force so that the system will be in equilibrium.

Apparatus: Force table, weight holders, sets of masses, rulers, protractors, spirit levels.

Theory: Vectors A and B can be added graphically by drawing them to scale and aligning them head to tail. The vector that connects the tail of A to the head of B is the resultant vector R. Vector addition is both associative and commutative. The components (Ax and Ay) of a vector A can be calculated by projecting the length of A onto the coordinate axes as shown in figure 1. The components can be obtained by using the following equations: Ax= |A| cos θA

Ay= |A| sin θA

(1)

The sign of a component gives its direction along the x or y axis. Conversely, from the components, the magnitude |A| and direction θ of the vector can be calculated using the following:

In order to add vectors analytically, they must be in component form. The components of a vector sum of two vectors A and B yields the components of a new vector, called a resultant vector and will be denoted by R. The components of R can be calculated by: Rx = Ax + Bx

Ry = Ay + By

In order to for the system to be in equilibrium, the following must hold:

(3)

A + B = ‐C

A+B+C=0

(4)

Procedure: At first, the force table was placed on a flat surface and leveled using spirit level. Three pieces of string of 21 inches long was cut and a loop was tied at the end of each pieces of string and the other end of the string was attached to the ring. The ring was placed in the circle of the force table encircling the pin and the string was placed over the pulley attached to the force table. The height of the pulleys around the table was fixed at the same height. Three mass holders were taken and for vector A, mass was added to one of the holders making the entire set up (mass holder and added mass) of 27g. Then it was placed at the end of the strings looped over a pulley and the pulley was set at an angle of 63. Similarly, for vector B, mass was added to the second holder making the entire setup of 41g. Then it was placed at the end of one of the available strings looped over a pulley and the pully was set at an angle of 154. For vector C, the last mass holder was attached to the end of the last string looped over the pulley. Mass was added to the system and the angle was adjusted until the system was in equilibrium. The system was determined to be in equilibrium after the ring with the attached strings paralleled to and suspended above the ring painted on the force table allowing the pin to be removed. The entire mass for the setup of vector C was determined once the system reached to equilibrium. The values for mass and angle for vectors A, B and C was recorded in Table 1. The value for the mass and angle of vectors A and B was recorded in table 2 and mass and x-component and y-component of vectors A and B using the formula given. Then, the mass, force component, and angle for vector C was calculated. The experimental results for mass and angle measure of vector C was compared with analytical calculations and the percentage error was determined.

Calculations and Results:

Sources of error: 1. The vector force table may not be on a flat surface. 2. The pulley on the vector force table may not be horizontal.

Conclusions: The vector force table could be compared to the graphical sketches drawn of vectors A, B, and C on one graph. In the experiment, the resultant force was found by adding weight on vector

setup C until equilibrium was reached. Similarly, the angle of vector C measured on the vector force table could be compared to the angle of vector C calculated analytically. The error percentage was only 0.51%, for mass and 0.26% for angle demonstrating how accurately the vector force table could depict the analytical calculations.

Data Sheet:...