Two forces of 5n and12n respectively and act on the same point.show how you would determine the magnitude of the resultant by using tail to head method and tail to tail method and pythagoras of theorem
you should recognize the familiar 5-12-13 right triangle.
To determine the magnitude of the resultant of two forces by using the tail to head method, follow these steps:
1. Draw a vector to represent the first force (5N) with an arrow pointing in the desired direction.
2. From the tip of the first vector, draw a second vector to represent the second force (12N) with an arrow pointing in the desired direction.
3. Draw a vector from the tail of the first vector to the tip of the second vector. This represents the resultant force.
4. Measure the length of the resultant vector using a ruler.
5. The magnitude of the resultant force is equal to the length of the resultant vector.
To determine the magnitude of the resultant of two forces by using the tail to tail method, follow these steps:
1. Draw a vector to represent the first force (5N) with an arrow pointing in the desired direction.
2. From the tail of the first vector, draw a second vector to represent the second force (12N) with an arrow pointing in the opposite direction of the first vector.
3. Draw a vector from the tip of the first vector to the tail of the second vector. This represents the resultant force.
4. Measure the length of the resultant vector using a ruler.
5. The magnitude of the resultant force is equal to the length of the resultant vector.
To determine the magnitude of the resultant of two forces by using the Pythagorean theorem, follow these steps:
1. Square the magnitude of the first force (5N^2) and the magnitude of the second force (12N^2).
2. Add the two squared values together: (5N^2 + 12N^2).
3. Take the square root of the sum: √(5N^2 + 12N^2).
4. Calculate the square root using a calculator or by simplifying: √(25N^2 + 144N^2) = √(169N^2).
5. Simplify further: √(13 * 13 * N^2) = 13N.
6. The magnitude of the resultant force is 13N.
To determine the magnitude (or resultant) of the two forces using the tail to head method, follow these steps:
1. Draw a line segment representing the first force, 5N, starting from the chosen point.
2. Draw a second line segment representing the second force, 12N, with its tail starting from the head of the first force.
3. Complete the triangle by drawing a line from the starting point to the head of the second force.
4. Measure the length of this line, which represents the resultant force.
5. Use a ruler or a scale to measure the length accurately.
6. The measured length is the magnitude of the resultant force.
To determine the magnitude of the resultant using the tail to tail method, follow these steps:
1. Draw a line segment representing the first force, 5N, starting from the chosen point.
2. Draw a second line segment representing the second force, 12N, starting from a different point.
3. Complete the parallelogram by drawing two additional line segments: one from the tail of the first force to the head of the second force, and the other from the head of the first force to the tail of the second force.
4. The diagonal of the parallelogram that starts from the chosen point represents the resultant force.
5. Measure the length of this diagonal using a ruler or a scale.
6. The measured length is the magnitude of the resultant force.
To determine the magnitude of the resultant using the Pythagorean theorem, follow these steps:
1. Start by determining the horizontal and vertical components of the individual forces.
- For the 5N force, let the horizontal component be F1x and the vertical component be F1y.
- For the 12N force, let the horizontal component be F2x and the vertical component be F2y.
2. Use trigonometric functions (sine and cosine) to calculate the components:
- F1x = F1 * cos(theta1), where theta1 is the angle between the force and the horizontal axis of the coordinate system.
- F1y = F1 * sin(theta1)
- F2x = F2 * cos(theta2), where theta2 is the angle between the force and the horizontal axis.
- F2y = F2 * sin(theta2)
3. Add the horizontal components together: Fx = F1x + F2x.
4. Add the vertical components together: Fy = F1y + F2y.
5. Apply the Pythagorean theorem: Resultant magnitude = sqrt(Fx^2 + Fy^2).
By following these steps, you can determine the magnitude of the resultant using the tail to head method, tail to tail method, or the Pythagorean theorem, depending on the preferred approach or available information.