# Static Equilibrium Problem (concept question)

• Sunwoo Bae
In summary, the OP was able to solve the problem and get the right answer. However, he solved it more with intuition, and he does not get how the force of the person pulling down on the rope makes the force to the left of the backpack equal to force to the right of the backpack.
Sunwoo Bae
Homework Statement
The two trees shown in the figure are 6.6 m apart. A back-packer is trying to lift his pack out of the reach of bears. Calculate the magnitude of the force F that he must exert downward to hold a 19-kg backpack so that the rope sags at its midpoint by (a) 1.5 m, (b) 0.15 m.
Relevant Equations
the sum of forces = 0 in static equilibrium

(figure)I was able to solve the problem and get the right answer. However, I solved it more with intuition, and I do not get how the force of the person pulling down on the rope makes the force to the left of the backpack equal to force to the right of the backpack.

Sunwoo Bae said:
force to the left of the backpack equal to force to the right
What would happen if this were not the case ?

Lnewqban
Sunwoo Bae said:
I was able to solve the problem and get the right answer. However, I solved it more with intuition, and I do not get how the force of the person pulling down on the rope makes the force to the left of the backpack equal to force to the right of the backpack.

View attachment 260882

There are a few assumptions that need to be made for both forces on the backpack to be of magnitude ##F##; The contact at the branch needs to be frictionless and the rope needs to be massless.

etotheipi said:
There are a few assumptions that need to be made for both forces on the backpack to be of magnitude ##F##; The contact at the branch needs to be frictionless and the rope needs to be massless.
But the OP's question is about the tensions in the rope either side of the backpack being equal. That does not require those assumptions, only that the pack is at the midpoint (which is not stated) and that the tree branches are at the same height.

etotheipi
haruspex said:
But the OP's question is about the tensions in the rope either side of the backpack being equal. That does not require those assumptions, only that the pack is at the midpoint (which is not stated) and that the tree branches are at the same height.

Right, it's just OP also mentioned the force pulling down on the rope. Indeed, the force on the left and right will be equal even if the two conditions I gave are not met. Sorry! If anything, it's decent pub quiz trivia... ish.

Last edited by a moderator:
Sunwoo Bae said:
... I do not get how the force of the person pulling down on the rope makes the force to the left of the backpack equal to force to the right of the backpack.
Consider these three cases and discuss with us what your intuition tells you about the forces within the rope:
1) Rather than a person pulling down, the left end of the rope is anchored to the branch, just like the right end is (backpack is located midway).

2) There is no backpack and the person still pulls down very strongly.

3) Rather than only one person pulling down, the right end of the rope goes around a branch and is pulled down by a second person with similar amount of force (backpack is located midway).

https://en.wikipedia.org/wiki/Tension_(physics)

haruspex said:
But the OP's question is about the tensions in the rope either side of the backpack being equal. That does not require those assumptions, only that the pack is at the midpoint (which is not stated) and that the tree branches are at the same height.
Technically, the tensions on either side of the backpack could be equal despite the pack not being at the midpoint -- if the tree branches are not at the same height.

If they are at the same height, the pack will tend to slide toward the midpoint -- if friction is ignored or if the rope is shaken until the bag settles into its equilibrium position.

## What is static equilibrium?

Static equilibrium is a state in which all forces acting on an object are balanced, resulting in a net force of zero and no movement or acceleration.

## How is static equilibrium different from dynamic equilibrium?

Static equilibrium refers to a stationary object with balanced forces, while dynamic equilibrium refers to a moving object with balanced forces. In dynamic equilibrium, the object may have a constant velocity, but its direction or speed can change.

## What are the conditions for static equilibrium?

The conditions for static equilibrium are that the net force acting on an object must be zero, and the net torque (or rotational force) must also be zero. This means that the object is either at rest or moving with a constant velocity.

## How do you calculate the net force and net torque for an object in static equilibrium?

The net force can be calculated by adding all the forces acting on an object in the same direction and subtracting any forces acting in the opposite direction. The net torque can be calculated by multiplying the force by the distance from the pivot point (or fulcrum) at which the force is applied.

## What are some real-life examples of static equilibrium?

Some examples of static equilibrium include a book resting on a table, a ladder leaning against a wall, and a person standing still on the ground. In each of these cases, the forces acting on the objects are balanced, resulting in no movement.

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