Vectors - Practical example? "A buoy is being held stable by 3 swimmers...."

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mcarthyryan

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Vectors - Practical example? "A buoy is being held stable by 3 swimmers...."

I've just hit another questions I'm unsure of.

A buoy is being held stable by 3 swimmers.
Swimmer A is heading West
Swimmer B is heading South
Swimmer C is at an approx direction, which looks about North East

This is the question:
A. If the buoy is static, describe how the forces operating on the buoy relate to on another
B. Write this relationship mathematically using vector notation
C. Draw a vector diagram showing how these forces can be added together, and how the heads and tails of each vector relate to each other.



My thoughts:
A. The forces acting on the buoy from swimmer A, B and C are all equal as the buoy is not moving - Is that explained well enough?
B. I don't understand this at all?
C. I can draw this, it will just look like a triangle, with A going from right to left, B going down from the end of A, and then C joining up with the back end of A I think :)



Thank you for any pointers you can give me.
 
mcarthyryan said:
A buoy is being held stable by 3 swimmers.
Swimmer A is heading West
Swimmer B is heading South
Swimmer C is at an approx direction, which looks about North East

This is the question:
A. If the buoy is static, describe how the forces operating on the buoy relate to on another
B. Write this relationship mathematically using vector notation
C. Draw a vector diagram showing how these forces can be added together, and how the heads and tails of each vector relate to each other.

My thoughts:
A. The forces acting on the buoy from swimmer A, B and C are all equal as the buoy is not moving - Is that explained well enough?
B. I don't understand this at all?
C. I can draw this, it will just look like a triangle, with A going from right to left, B going down from the end of A, and then C joining up with the back end of A I think :)
Click to expand...

You might have been thinking correctly, for part (A), but your statement is not worded correctly. When the buoy is not moving, the net force acting on it is zero. In other words, vectors A, B, and C are not equal, but they combine to equal the zero vector (i.e., no force in any direction).

(We know that the vectors are not equal because a set of equal vectors all have the same length and all point in the same direction.)

Also for part (A), I would include a point diagram of the buoy, with the three vectors. (You get to choose the exact direction of vector C, and you get to choose the length of each vector.)

Part (B) is asking for a vector equation that shows the net force is zero. Use proper notation (whichever notation they taught you for vectors) to show that the vector sum of A, B, and C is the vector 0.

Your thoughts on part (C) are correct, but the diagram will be more than "just a triangle" because you will show the head of each vector with a little arrow. If you draw the relative vectors in each of your two diagrams carefully (i.e., corresponding vectors point in the same direction and have the same length), that will suffice to indicate how they can be re-arranged from one diagram to the other, and that the head-to-tail addition results in no net force (i.e., you end up where you started). :)
 
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