Static Equilibrium - trick question?

In summary: Now the person has five pieces, but no way of knowing which is the original square. This problem is analogous to the one given in the question. Since the person doesn't have the original, they can't solve the original problem.
  • #1
prettydumbguy
17
0

Homework Statement



A man stands on a board of negligible mass with a length of 10m is supported by 2 cables, one on the left on one on the right, with a tension of 300N and 200N respectively. How much does the man weigh in Newtons?

Homework Equations


F=ma
Torque= F*lever arm

The Attempt at a Solution


I'm tempted to just 500, but that's far to simple. I thought of setting up a torque equation, but I don't know how I would when I don't know his mass or where he stands. So, if I assume he's standing x meters from the left: 300(x)-200(10-x) + man(mans location) = 0.
So I set one of the cables as the axis of rotation: the left cable, giving me man(x)=200(10).
Multiply out to get man(x) = 2000.
Now I have two variables I can't get rid of.

But I still really want to just sum all the forces along the y-axis and set it equal to zero: 300 + 200 -man = 0, so I still get 500.
Am I just overthinking the hell out of this?
 
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  • #2
Assuming the cables are vertical, yes, you're overthinking it. It is as easy as it seems.
 
  • #3
haruspex said:
Assuming the cables are vertical, yes, you're overthinking it. It is as easy as it seems.
No angles were given, so I assume that they are vertical. The question comes after two much more in depth SE problems, hence my confusion. Thanks!
 
  • #4
prettydumbguy said:
No angles were given, so I assume that they are vertical. The question comes after two much more in depth SE problems, hence my confusion. Thanks!
Sounds like a classic way to catch people out, follow some tough questions by an easy one with redundant information.
There's an old geometry problem where you ask someone to cut an L shape, consisting of three squares, into four identical pieces. When they've solved it, you say ok, try this harder one: cut a square into five identical pieces.
 

1. What is static equilibrium?

Static equilibrium is a state where an object is at rest or in uniform motion with a constant velocity and there is no net force acting on it.

2. Can an object be in static equilibrium if it is moving?

Yes, an object can be in static equilibrium even if it is moving as long as its speed and direction remain constant and there is no net force acting on it.

3. Is static equilibrium the same as dynamic equilibrium?

No, static equilibrium refers to a state of no motion while dynamic equilibrium refers to a state of constant motion with no change in velocity. In static equilibrium, there is no net force acting on an object, while in dynamic equilibrium, there may be balanced forces acting on the object.

4. Can an object be in static equilibrium if there are multiple forces acting on it?

Yes, as long as the vector sum of all the forces acting on the object is equal to zero, it will be in static equilibrium. This means that all the forces are balanced and there is no net force acting on the object.

5. What is the difference between static and mechanical equilibrium?

Static equilibrium refers to the state of an object at rest or in uniform motion with a constant velocity, while mechanical equilibrium refers to the state where an object's potential and kinetic energies are balanced. In other words, in mechanical equilibrium, the object's energy remains constant, whereas in static equilibrium, the object's motion remains constant.

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