Finding the Center of Mass: Balancing a Plank with an 800-N Person

  • Thread starter gcombina
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    Equilibrium
In summary, the problem involves a horizontal plank with a weight of 100 N and two supports placed 1.0 m from each end. An 800-N person wants to stand on the plank without causing it to tip. The equations used for static equilibrium are ΣF = 0 and Στ = 0, where torque is equal to force multiplied by the level arm. The fact that the body is in static equilibrium means that the sum of torques is equal to 0.
  • #1
gcombina
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1. A horizontal, 10-m plank weighs 100 N. It rests on two supports that are placed 1.o m from each end. How close to one end can an 800-N person stand without causing the plank to tip?
 

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  • #2
Hi gcombina :smile:

so far how you have attempted the problem?
 
  • #3
I know is a torque
that is all I know and I don't know where to start
 
  • #4
Your diagram is not the most useful since it shows the person right at one of the supports. Redraw it with a bit more overhang for the person to stand on. Draw in the relevant forces. No need to draw a stick figure, just indicate the force of the weight of the person. What equations do you know for static equilibrium?
 
  • #5
for static equilibrium? I know ΣF = 0
 
  • #6
plank exercise.png
 
  • #7
1. SO, I got 4 forces
F1 - W + F2 - W = 0
F1 - 100N + F2 - 800N = 0

i DONT EVEN KNOW WHY AM I DOING WHAT I AM DOING
I AM TRYING TO FIND THE DISTANCE OF THE PERSON

IM SO LOST, SORRY
 
  • #8
what does the fact that the body is in static equilibrium indicate to you?
 
  • #9
that there are no external forces??
 
  • #10
mmm no.
what do you know about torques in static equilibrium ?
 
  • #11
I know torque = force x level arm

when a rigid body is in equilibrium then it means that the sum of torques = 0
 
  • #12
try to write both
1)∑F=0
2)∑τ=0
for your system
 
  • #13
I got it, thank you!
 

1. What is a rigid object?

A rigid object is a solid body that maintains its shape and size even when subjected to external forces. This means that the distance between any two points on the object remains constant.

2. What does it mean for a rigid object to be in equilibrium?

A rigid object is in equilibrium when it is at rest or moving at a constant velocity, with no unbalanced forces acting on it. This means that the forces acting on the object are balanced, resulting in a net force of zero.

3. How do you determine if a rigid object is in equilibrium?

To determine if a rigid object is in equilibrium, you must first identify all the external forces acting on the object. Then, you can use the principle of equilibrium, which states that the sum of all forces in any direction must equal zero and the sum of all torques (rotational forces) must also equal zero. If these conditions are met, the object is in equilibrium.

4. What is the difference between static and dynamic equilibrium for a rigid object?

Static equilibrium refers to an object that is at rest, while dynamic equilibrium refers to an object that is moving at a constant velocity. In both cases, the object is in equilibrium because the forces acting on it are balanced, but the difference lies in the object's state.

5. What factors can disrupt the equilibrium of a rigid object?

The equilibrium of a rigid object can be disrupted by the introduction of an unbalanced external force or torque. Additionally, changes in the object's mass or shape can also affect its equilibrium. Friction, air resistance, and other external factors can also disrupt the equilibrium of a rigid object.

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