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February 26th, 2018, 10:13 AM   #1
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Vectors / Magnitude

Hi All,

Having great difficulty in the following problem:

Magnitude of the 3 forces acing on a stable object

A = 800kN West
B = 650kN South
C = ?

What is the magnitude of force C?

Any help would be much appreciated.
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 February 26th, 2018, 11:01 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,098 Thanks: 1905 Are you required to use trigonometry rather than geometry? Thanks from topsquark and NAC54321
 February 26th, 2018, 11:27 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 895 I would write the vectors in "components", taking the positive x-axis to be "east" and the positive y-axis to be "north" A is "800 kN west" so A= <-800, 0>. B is "650 kN south" so B= <0, -650>. The sum of those is <-800, -650> so, in order that the object not move, C must be <800, 650>. The magnitude of C is $\displaystyle \sqrt{800^2+650^2}$. Thanks from topsquark and NAC54321
 February 27th, 2018, 02:08 AM #4 Member   Joined: Feb 2018 From: England Posts: 43 Thanks: 0 Thanks for the replies, much appreciated. Skipjack - With a limited question I am not sure however, if there are two ways I can answer the question I'll do both if you could shed any light? Country boy - Thanks for the detailed response. Makes sense now you've explained, so the magnitude of C = 1030.8kN? 1) How would I go about calculating the angles of each? 2) If the object has to be moved directly south. In order to achieve this what would have to happen to the resultant force acting on the object? (I assume I would have to calculate the resultant force first?) 3) State two ways the individual forces could be changed to achieve this resultant force? May change the magnitude and direction of any of the individual forces. Thanks for your time and support.
 February 27th, 2018, 03:52 AM #5 Global Moderator   Joined: Dec 2006 Posts: 20,098 Thanks: 1905 Forces.PNG The forces can be "chained", as in the above diagram. If the resultant force is non-zero, the corresponding diagram would show a fourth line (for the resultant). It should be obvious that trigonometry could have been used instead of Pythagoras. Use trigonometry to calculate the angles. It's usually convenient to start by using coordinate geometry. If you need to use trigonometry, a fully-annotated diagram is recommended.
 February 27th, 2018, 05:25 AM #6 Member   Joined: Feb 2018 From: England Posts: 43 Thanks: 0 Thanks again skipjack appreciate your help. Correct me if I'm wrong, with a resultant force of zero? What would happen to the resultant force once the object is moved directly South. Could this be easily achieved my changing the magnitude and direction of the other individual forces?
 February 28th, 2018, 01:26 AM #7 Member   Joined: Feb 2018 From: England Posts: 43 Thanks: 0 Any other feedback on this would be much appreciated. Correct me if I'm wrong, with a resultant force of zero? What would happen to the resultant force once the object is moved directly South. Could this be easily achieved my changing the magnitude and direction of the other individual forces? Thankyou All.
February 28th, 2018, 01:35 AM   #8
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Quote:
 Magnitude of the 3 forces acing on a stable object

A little tip. (useful theorem)

When a body is in equilibrium (your stable) under the action of three forces in the same plane, those three forces meet at a point.

 February 28th, 2018, 07:17 AM #9 Member   Joined: Feb 2018 From: England Posts: 43 Thanks: 0 Thanks studio. Is there a way to express the resultant force? My theory is (correct me if wrong please).... In order to move the object directly south: 1) The object is no longer in equilibrium, the resultant force would have to become dynamic? 2) Two individual forces that could achieve this: Force B Magnitude increased? Direction of Force A adjusted to that similar of Force B? Many thanks.
February 28th, 2018, 07:37 AM   #10
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Quote:
 Originally Posted by NAC54321 Thanks studio. Is there a way to express the resultant force? My theory is (correct me if wrong please).... In order to move the object directly south: 1) The object is no longer in equilibrium, the resultant force would have to become dynamic? 2) Two individual forces that could achieve this: Force B Magnitude increased? Direction of Force A adjusted to that similar of Force B? Many thanks.
If the object is in equilibrium there is no resultant.

That is the resultant = 0.

This allows us to write the equations of equilibrium, perhaps in component form as country boy suggests.

Alternatively you can note that the polygon ( a triangle in this case since there are 3 forces is closed.

If the three forces are not in equlibrium then the polygon is open.

Open means that when you place one vector after another, head to tail, in the manner showed by skipjack, you do not end up back where you started. The end point is not the same as the start point.

You need to choose one method, have you been taught one?

and did you understand my comment about 'stable' meaning that the object is in equilibrium?

Last edited by studiot; February 28th, 2018 at 07:40 AM. Reason: spelling

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