Two horse pull horizontally on ropes attached to a stump. The two forces f1 and f2 that they apply to the stump are such that the net(RESULTANT) force R has a magnitude equal to that of F and makes an angle of 90 with F1. Let F1=1300 N and R =1300 N also. Find the magnitude of F2 and its direction (relative to F1).
<<the net(RESULTANT) force R has a magnitude equal to that of F>>
You never say what F is. I assume you mean F1.
For the situation you describe, F1, F2 and the resultant F form an equilateral triangle.
F1 and F2 are aimed 120 degrees apart, and, strung end-to-end, form an equilateral triangle with the third side as the resultant.
Two horses pull horizontally on ropes attached to a stump. The two forces F1 and F2 that
they apply to the stump are such that the net (resultant) force R has a magnitude equal
to that of F1 and makes an angle of 90° with F1. Let F1 = 1300 N and R = 1300 N also. Find
the magnitude of F2 and its direction (relative to F1)
but what is the magnitude? Is it 120 degree and what direction?
Can u please break it down step by step the solution ?
To find the magnitude of F2 and its direction relative to F1, we can use vector addition and trigonometry.
1. Draw a vector diagram: Draw a horizontal line to represent the ground, and indicate the stump as a dot. Draw a vector F1 starting from the stump and pointing to the right (horizontal). Draw a vector R starting from the stump and pointing upwards (vertical). Finally, draw the unknown vector F2 starting from the stump.
R
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F1 | | F2
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2. Split vector R into two components relative to F1: Since the angle between F1 and R is 90 degrees, we can split R into two components: one parallel to F1 (horizontal) and one perpendicular to F1 (vertical).
3. Determine the magnitude of the horizontal component of R: Since the magnitude of F1 is equal to the magnitude of R, and the two components of R are perpendicular, the magnitude of the horizontal component of R is equal to the magnitude of F1, which is 1300 N.
4. Determine the magnitude of the vertical component of R: Since the magnitude of R is equal to the magnitude of F1, and the two components of R are perpendicular, the magnitude of the vertical component of R is also equal to the magnitude of F1, which is 1300 N.
5. Use trigonometry to find the magnitude of F2: Since F2 is the other force pulling on the stump, it should cancel out the horizontal component of R. Therefore, the magnitude of F2 is equal to the magnitude of the horizontal component of R, which is also 1300 N.
6. Determine the direction of F2 relative to F1: From the vector diagram, we can see that F2 is pulling at a 90-degree angle (perpendicular) to F1, in the opposite direction. This means that F2 is pointing directly to the left (opposite to the direction of F1).
Therefore, the magnitude of F2 is 1300 N and its direction relative to F1 is directly to the left.