Parallelogram of Forces

[mathxyz]

This question is found in chapter titled Parallelogram of Forces, Law of Sines & Law of Cosines.

Two forces of 50 and 68 pounds act on a body to produce a resultance force of 70 pounds. Find, to the nearest ten minutes or nearest tenth of a degree, the angle formed between the resultance force and the smallest force.

TEXTBOOK DEFINITION OF RESULTANT:

If two forces act at the same time on a body, the single force that has the same effect as these two, called resultant, is the diagonal of a parallelogram whose adjacent sides represent the two forces.

 

[tkhunny]

Two forces of 50 and 68 pounds act on a body to produce a resultance force of 70 pounds. Find, to the nearest ten minutes or nearest tenth of a degree, the angle formed between the resultance force and the smallest force.

If forces act in the same direction, simply adding them gives the resultant.

68 + 50 = 118

If forces act in opposite directions, simply subtracting them gives the resultant.

68 - 50 = 18
50 - 68 = -18

An important thing to note is that 70 is in the range just demonstrated [-18,118]. Otherwise, there is no solution.

It is also important to note that 70 > 68 > 50. This implies that the two forces will have to work together in somewhat the same direction. They don't get to cancel each other out.

1) Draw a line segment and label its measure 50. Label its endpoints A (starting point) and B (ending point).
2) From B, draw another line segment that doesn't go in quite the same direction as AB. Label its measure 68. Label its endpoint C.
3) Construct line segment AC. Label its measure 70. This should give you a triangle with all three sides known.
4) The law of cosines will give you the INTERNAL angle between 50 and 68 in your triangle. 70² = 68² + 50² - 2*50*68*cos(angle(ABC))
5) You have to figure out if that is the angle you want or if it is something related to it.

 

[mathxyz]

Great

Your explanation is simply great. I will review your notes and try a few forces questions.