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Physical quantities (Scalar and Vector quantities)
Addition of force vectors by triangle method (also known as head to tail method)
Step 1: Choose an appropriate scale. E.g. 1cm : 1N.
Step 2: Measure the angle between the two vectors you are adding.
Step 3: Move one of the vector to join up with the other vector in a head to tail fashion taking care the angle between the two vectors measured earlier is not changed (arrow head of one vector joins to the tail of another vector).
Step 4: Draw the resultant force from the tail to the arrow head of the two joined vectors forming a complete triangle.
Step 5: Measure length of this resultant vector and convert using the earlier scale to get the magnitude of this resultant force. (e.g. 7cm corresponds to 7N using the earlier scale of 1cm : 1N).
Step 6: Measure also the angle between this resultant force and any of the two vectors so that the resultant force can be described both in magnitude and direction to either of the two forces.
In this following video, addition of the two tension force vectors is used to find their resultant force, which is in turn used to find the weight acting downwards since the resultant force acting upwards caused by the two tension force vectors is equal to the weight acting downwards as all the initial three forces (two tension forces and weight) are in equilibrium (the weight is not moving at all).
Step 2: Measure the angle between the two vectors you are adding.
Step 3: Move one of the vector to join up with the other vector in a head to tail fashion taking care the angle between the two vectors measured earlier is not changed (arrow head of one vector joins to the tail of another vector).
Step 4: Draw the resultant force from the tail to the arrow head of the two joined vectors forming a complete triangle.
Step 5: Measure length of this resultant vector and convert using the earlier scale to get the magnitude of this resultant force. (e.g. 7cm corresponds to 7N using the earlier scale of 1cm : 1N).
Step 6: Measure also the angle between this resultant force and any of the two vectors so that the resultant force can be described both in magnitude and direction to either of the two forces.
In this following video, addition of the two tension force vectors is used to find their resultant force, which is in turn used to find the weight acting downwards since the resultant force acting upwards caused by the two tension force vectors is equal to the weight acting downwards as all the initial three forces (two tension forces and weight) are in equilibrium (the weight is not moving at all).
Addition of force vectors by parallelogram method
Step 1: Choose an appropriate scale (E.g. 1cm : 2N).
Step 2: Draw the two vectors according to chosen scale such that their tails are touching each other. Take care the angle between the vectors is not changed at all.
Step 3: Form a parallelogram by drawing two more dotted parallel lines to these two vectors.
Step 4: Draw the resultant force which is the diagonal of the parallelogram starting out from the meeting point of the tails of the two vectors.
Step 5: Measure the length of the diagonal and its angle from either one of the two vectors. Convert the length in cm to N according to chosen scale. Write down answer for resultant force in terms of N and angle from either of the two vectors. (e.g. Resultant force is 10 N at an angle of 64˚ from F1).
The following video is a simplified view of how the parallelogram is formed when adding two force vectors. The resultant force is the diagonal line of the parallelogram.
Step 2: Draw the two vectors according to chosen scale such that their tails are touching each other. Take care the angle between the vectors is not changed at all.
Step 3: Form a parallelogram by drawing two more dotted parallel lines to these two vectors.
Step 4: Draw the resultant force which is the diagonal of the parallelogram starting out from the meeting point of the tails of the two vectors.
Step 5: Measure the length of the diagonal and its angle from either one of the two vectors. Convert the length in cm to N according to chosen scale. Write down answer for resultant force in terms of N and angle from either of the two vectors. (e.g. Resultant force is 10 N at an angle of 64˚ from F1).
The following video is a simplified view of how the parallelogram is formed when adding two force vectors. The resultant force is the diagonal line of the parallelogram.
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Kindly ignore the uncertainty in readings of a mircometer screw gauge mentioned in this video. This is not in the O level syllabus.