Two forces of 60N and 80N act a point .sketch a tail to head diagram and determine their resultant
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To sketch a tail to head diagram for the two forces, follow these steps:
1. Draw a straight line to represent the first force with a length proportional to its magnitude. Label this line as Force A.
2. Starting from the end of Force A, draw another straight line to represent the second force with a length proportional to its magnitude. Label this line as Force B.
3. Label the starting point of Force A as the tail and the ending point of Force B as the head. This represents the tail to head diagram of the forces.
Next, to determine the resultant of the two forces, follow these steps:
1. Choose a scale for the diagram. For this example, assume 1 cm represents 10 N.
2. Measure the length of Force A and Force B on the diagram.
- Let's say Force A is 4 cm long, which represents 40 N.
- Force B is 6 cm long, representing 60 N.
3. Draw a straight line from the tail of Force A to the head of Force B. Label this line as the Resultant.
4. Measure the length of the resultant line.
- The length of the resultant line is approximately 10 cm.
5. Convert the length of the resultant line back to the actual force.
- Using the scale, 1 cm represents 10 N, so 10 cm represents 100 N.
6. Thus, the resultant of the two forces is 100 N in the direction shown by the resultant line in the diagram.
To sketch a tail-to-head diagram, we need to represent the two forces as vectors with their magnitudes and directions. The magnitude of the first force is 60N, and the magnitude of the second force is 80N. Let's say the first force is acting to the right, and the second force is acting to the left.
To start, draw a straight line and label it as the base line or reference line. Then, draw an arrow pointing to the right from the beginning of the reference line with a length of 60 units (representing 60N). Next, draw an arrow pointing to the left from the end of the reference line with a length of 80 units (representing 80N). The arrows should be parallel to each other.
The resultant force is determined by connecting the tail of the first vector to the head of the second vector. Draw a line from the tail of the 60N vector to the head of the 80N vector. This line represents the resultant force.
To determine the magnitude and direction of the resultant force, measure the length of the line representing the resultant force and label it accordingly. Then, draw an arrowhead on the line indicating the direction. The tail of the arrow should start from the tail of the 60N vector and the arrowhead should point towards the head of the 80N vector.
The magnitude of the resultant force can be calculated using the Pythagorean theorem. Given that the lengths of the vectors are 60 and 80, respectively, the resultant force, labeled R, can be calculated as:
R^2 = (60^2) + (80^2)
R^2 = 3600 + 6400
R^2 = 10000
R = √10000
R = 100N
Therefore, the magnitude of the resultant force is 100N.
To determine the direction of the resultant force, we need to find the angle between the reference line and the line representing the resultant force. This can be done using trigonometry. You can use the cosine rule or sine rule to find the angle, depending on the given information.