Two forces of 5 N and 12 N respectivlely act on the same point. Show how to determine the magnitude of the resultant by using the tail to head and tail to tail methods and pythagoras theorem.
To determine the magnitude of the resultant force using the tail to head method, follow these steps:
1. Draw a sketch of the forces acting on the point. Label one force as 5 N and the other as 12 N.
2. Select one of the forces as the starting point (tail) and draw an arrow in the direction of the force. This arrow represents the first force.
3. Start from the head of the first force and draw another arrow representing the second force, maintaining the same length and direction.
4. Complete the parallelogram by drawing lines from the tail of the second force to the head of the first force, and from the head of the second force to the tail of the first force.
5. The diagonal of the parallelogram, drawn from the tail of the first force to the head of the second force, represents the resultant force.
6. Measure the length of the diagonal using a ruler. The length of the diagonal represents the magnitude of the resultant force.
7. In this case, measure the length of the diagonal in units of Newton (N) to determine the magnitude of the resultant force.
To determine the magnitude of the resultant force using the tail to tail method, follow these steps:
1. Draw a sketch of the forces acting on the point, and label them as 5 N and 12 N.
2. Start from the tail of the 12 N force and draw an arrow representing the 5 N force, maintaining its length and direction.
3. Draw a line from the tail of the 5 N force to the tail of the 12 N force. This line represents the resultant force.
4. Measure the length of this line using a ruler. The length of the line represents the magnitude of the resultant force.
5. Again, measure the length of the line in units of Newton (N) to determine the magnitude of the resultant force.
To determine the magnitude of the resultant force using Pythagoras' theorem, follow these steps:
1. Identify the horizontal and vertical components of each force. Break down each force into its x-axis and y-axis components. For example, for the 5 N force, assume it has a horizontal component of 5x and a vertical component of 5y.
2. Calculate the sum of the horizontal components of the forces, and represent it as Fx = 5x + 12x.
3. Calculate the sum of the vertical components of the forces, and represent it as Fy = 5y + 12y.
4. Apply Pythagoras' theorem using the magnitudes of the horizontal and vertical components: R^2 = Fx^2 + Fy^2.
5. Calculate the square root of R^2 to find the magnitude of the resultant force, R.
By following these methods, you can determine the magnitude of the resultant force acting on the point using different approaches.