Two forces of 60n and 80n respectively act simultaneously at a point . Sketch and determine their resultant by using the following methods. Tail to head
To determine the resultant of two forces using the tail-to-head method, we start by drawing a vector representing one of the forces. Let's start with the 60N force.
1. Draw a line segment to represent the 60N force. Label it as F1 and draw an arrow at the end to indicate the direction of the force.
---------------------> F1 (60N)
2. Now, draw a line segment beginning from the arrow head of F1 towards the tail of the next force, which is 80N. Label it as F2 and draw an arrow at the end to indicate the direction of the force.
---------------------> F1 (60N)
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V F2 (80N)
3. Finally, draw the resultant vector beginning from the tail of F1 and ending at the arrow head of F2. Label it as R and draw an arrow at the end to indicate the direction of the resultant.
---------------------> F1 (60N)
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V F2 (80N)
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---> R (Resultant)
To determine the magnitude of the resultant, we can use the Pythagorean theorem. The magnitude of the resultant force (R) is given by:
R = √(60² + 80²) = √(3600 + 6400) = √10000 = 100N
So, the magnitude of the resultant force is 100N.
To determine the direction of the resultant force, we can use trigonometry. The angle between the resultant vector and the horizontal axis can be found by:
θ = tan^(-1)(opposite/adjacent) = tan^(-1)(80/60) = 53.13°
Therefore, the direction of the resultant force is 53.13° above the horizontal axis.