1) Consider two non-parallel forces, each with a specified magnitude and directi
ID: 582163 • Letter: 1
Question
1) Consider two non-parallel forces, each with a specified magnitude and direction, acting on an object. We wish to add a third force such that the sum of all three forces is zero. Does this third force need to act at a specific angle and have a specific magnitude or are there multiple angles and magnitudes that will work? (All forces are acting in a plane.) Explain your reasoning.
2) The three forces listed below, and only these three forces, are acting on an object that remains at rest. Determine the magnitudes of the two unspecified forces. Show your work. F1 = 80 N at 0.0 F2 = ? N at 60.0 F3 = ? N at 210.0
3) If you were to actually set up this situation how close to your calculated values, e.g. within half a Newton, or within a Newton, do you think the forces would need to be for the object to remain at rest? Explain
Explanation / Answer
1)
The sum of all the X components and also the sum of all the Y components must be zero.
so, there could be multiple angles and magnitudes that will work.
2)
80 cos 0 + F2 cos 60 + F3 cos 210 =0
80 sin 0+ F2 sin 60 + F3 sin 210 =0
on solving,
80+0.5F2-0.866F3 =0 ---eq1
0.866F2-0.5F3 =0 so, F3 = 1.732 F2
Substitute in eq 1
80+0.5 F2-(0.866*1.732F2) =0
80-F2 =0
F2 = 80 N
F3 = 1.732*80
F3 = 138.56 N
3)
With the obtained values, the object would remain at rest
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