Two force of 5n and 12n respectively act on the same point.show how you would determine the magnitude of the resultant by using the tail- to head and tail to tail methods and Pythagoras theorem (13n)
They seem to have told you the answer...Pythagorean.
PS. Should have said they act at right angles.
Magnitude
Physics
To determine the magnitude of the resultant force using the tail-to-head method, follow these steps:
1. Draw a scale diagram: Represent the two forces as vectors with arrows. Choose a suitable scale, for example, let 1 cm represent 1 newton (1 cm = 1 N). Draw the first force of 5 N as a vector of 5 cm in a certain direction. Then, draw the second force of 12 N from the head of the first vector to the tail of the second vector.
2. Find the resultant vector: Draw a vector from the tail of the first vector to the head of the second vector. This vector represents the resultant force.
3. Measure the length of the resultant vector: Use a ruler to measure the length of the resultant vector in centimeters. Convert this length back to newtons based on the scale you initially chose. In this case, if 1 cm represents 1 N, and the length of the resultant vector is measured as 13 cm, then the magnitude of the resultant force is 13 N.
To determine the magnitude of the resultant force using the tail-to-tail method, follow similar steps:
1. Draw a scale diagram: Use the same scale as mentioned in the tail-to-head method. Draw the first force of 5 N as a vector of 5 cm in a certain direction. Then, draw the second force of 12 N as a vector of 12 cm in the opposite direction, starting from the tail of the first vector.
2. Find the resultant vector: Draw a vector from the tail of the first vector to the tail of the second vector. This vector represents the resultant force.
3. Measure the length of the resultant vector: Use a ruler to measure the length of the resultant vector in centimeters. Convert this length back to newtons based on the scale you initially chose. In this case, if 1 cm represents 1 N, and the length of the resultant vector is measured as 13 cm, then the magnitude of the resultant force is 13 N.
Alternatively, you can also determine the magnitude of the resultant force using Pythagoras's theorem. Given that the two forces are at right angles to each other:
1. Square the magnitudes of the two forces: Calculate 5^2 = 25 and 12^2 = 144.
2. Add the two squared magnitudes: 25 + 144 = 169.
3. Take the square root of the sum: √169 = 13.
Therefore, the magnitude of the resultant force is 13 N.