An object is in equilibrium under the action of three forces.Two of these forces,A an B,are illustrated in the accompanying diagram.The third force,F,is not illustrated.
3.1What is meant by the resultant of A and B?
3.2Determine by means of accurate construction and measurement [scale:10mm=1N]the magnitude and direction of force F.
3.1 The resultant of forces A and B refers to the sum of these forces. It represents a single force that has the same effect as the combination of A and B. In other words, it is the vector that would be needed to replace A and B and still achieve the same net force and direction.
3.2 To determine the magnitude and direction of force F, we can use accurate construction and measurement based on the given scale (10mm = 1N). Here are the steps:
Step 1: Draw the vector representations of forces A and B on a piece of paper, using the given scale. Make sure the lengths of the lines accurately represent the magnitudes of A and B.
Step 2: Place the tail of vector A at the starting point of vector B (where the forces are in equilibrium). The head of vector A represents the direction and magnitude of A, and the head of vector B represents the direction and magnitude of B.
Step 3: Complete the triangle with vector F. Draw the third force starting from the head of A to the head of B. This represents the direction and magnitude of force F that would be needed to keep the object in equilibrium. Note that the triangle should be closed, meaning the tail of vector F should meet the tail of vector A.
Step 4: Measure the length of the vector F accurately using the given scale. Multiply the measured length by the scale factor to obtain the magnitude of force F in Newtons.
Step 5: Determine the direction of force F. Measure the angle between the positive x-axis (or any other reference direction) and the line representing force F using a protractor. This will give you the direction of F in degrees or radians.
By following these steps, you should be able to accurately measure the magnitude and direction of force F.