| Aim | To understand the concept of weight and the parallelogram law of vectors To determine the weight of a given body using the parallelogram law of vectors To verify the result using a spring balance |
| Apparatus Required | Given body Spring balance Protractor Meter scale Paper Pen Calculator |
| Theory | The weight of a body is the force with which the body is attracted towards the center of the earth. The magnitude and direction of the weight of a body can be determined using the parallelogram law of vectors. In this experiment, we will use the parallelogram law of vectors to determine the weight of a given body. The parallelogram law of vectors states that when two vectors acting simultaneously on a point are represented in magnitude and direction by the adjacent sides of a parallelogram, then the resultant vector is represented in magnitude and direction by the diagonal passing through that point. This principle can be used to find the weight of a given body. If the body is suspended from two points using two strings, the tension in each string can be considered as a vector. By drawing the parallelogram of these two vectors, the diagonal represents the weight of the body. If an unknown weight body S is suspended from the middle of the hanger, and P and Q are the two balance weights from the other two ends of the hanger, then the unknown weight can be calculated using the equation: S = (P + Q)/2 This equation is based on the principle of moments. When the system is in equilibrium, the sum of the clockwise moments about any point must be equal to the sum of the anticlockwise moments about the same point. If we take moments about the point where the unknown weight is suspended, then we have: P (distance from the point to P) = S (distance from the point to S) and Q (distance from the point to Q) = S (distance from the point to S) Rearranging these two equations, we get: S = (P x distance from S to P + Q x distance from S to Q) / (distance from S to P + distance from S to Q) Since the distance from S to P and the distance from S to Q are equal (since the body is suspended from the middle of the hanger), we can simplify this equation to: S = (P + Q)/2 This equation allows us to find the weight of the unknown body S by measuring the balance weights P and Q.  |
| Procedure | Place the given body on a sheet of paper and trace its outline. Using the meter scale, draw a straight line from the base of the outline of the body to a point outside the outline. Using the protractor, measure the angle between the drawn line and the vertical line passing through the base of the outline. Draw another line from the top of the outline of the body to the point where the first line was drawn. Using the protractor, measure the angle between the second line and the vertical line passing through the top of the outline. Using the parallelogram law of vectors, draw a vector diagram with the two lines as the adjacent sides of a parallelogram. The diagonal of the parallelogram represents the weight of the body. Measure the length of the diagonal using the meter scale and record it. Using the spring balance, measure the weight of the body and record it. Compare the results obtained from the parallelogram law of vectors and the spring balance. |
| Observation and Result | Results: Record the measured angles and the length of the diagonal in a table. Record the weight measured using the spring balance. Calculate the weight of the body using the parallelogram law of vectors. Discussion: Discuss the accuracy and precision of the results obtained from the parallelogram law of vectors and the spring balance. Comment on the sources of error in the experiment and suggest ways to minimize them. Discuss the practical applications of the parallelogram law of vectors in determining the weight of objects. Conclusion: The weight of a body can be determined using the parallelogram law of vectors, which provides a graphical method of finding the weight of an object. The experiment successfully determined the weight of a given body using the parallelogram law of vectors and verified the result using a spring balance. The results indicate that the parallelogram law of vectors is a reliable method for determining the weight of objects. |
