Forces put in equalibrium?

Question

Again I am asking a physics question and I would like some help. do NOT give me the answer...only clues in which to find it such as formulas.

Five forces act on an object:
1) 60N at 90
2) 40N at 0
3) 80 N at 270
4) 40N at 180
and 5) 50N at 60
what are the magnitude and direction of a sixth force that would produce equilibrium?
I understand that when you have three forces they can create a triangle, so can you do it with this problem yet have two triangles instead of one? I am going to keep trying to figure this out...and please no answers.
Thank you for your help.

Answer 1

The essence of statics is to draw a good free body diagram.

Forget about triangles and just resolve the force vectors into components.

Do it and put the force vectors on it and then resolve the forces in two orthogonal directions. Then what you need to balance these forces is a vector with the right components.

The first 4 forces are orthogonal: they add to

60-80 N in the 90 direction
and
40-40 N in the 0 direction.

Now you just need to resolve the force vector at 60 deg into its components:
50 N at 60 deg becomes 50(sin 60,cos 60) (note that angles are measured relative to 0 at the top)

You don't have to use my coordinates. You can call 0 deg the positive x axis and measure angles counter clockwise, as is more conventional..

Answer 2

It will be some what difficult to explain the steps. It will be easy to answer the problem.

Follow the steps and understand how to answer in similar questions.


40N at 0 is exactly opposite to 40n at 180. These two cancel each other.

The resultant of 80 at 270 is opposite to 60 at 90. The resultant is 20N at 270.

Thus,now ,there are only two forces 20N at 270 and 50N at 60.

The component of 50N along 0 degree is 50 cos 60 ( adjacent to 60 degree)

The component of 50N along 90 degree is 50 sin 60 ( opposite to 60 degree)

This 50 sin 60 is opposite to 20N at 270 .

Their resultant is (50 sin60 - 20) = 41.3 N at 90degree.

Now we have two forces 41.3 N at 90degree and 50 cos 60
= 25 N at 0 degree.

Since they are perpendicular to each other, Their resultant is determined using Pythagoras' theorem.

Sum of these two is 66.3 and difference is 16.3 and the product of 66.3 and 16.3 = 1081.

Square root of this is 32.9N.

To find the direction tan a = 41.3/ 25 = 1.652
a = 59 degree from the 25N ( from the one at the denominator)

Answer 3

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Answer 4

I wish I was smart enough to understand your questions.