Equilibrium in Two Dimensions: What Force Does a Hanging Boy Exert on Each Tree?

In summary, a boy with a force of gravity of 400 N is hanging on to a rope stretched between two trees. The rope is sagging at an angle of 170 degrees at the boy's hands. The equation F=ma can be used to determine the force exerted by the rope on each tree, by creating unknowns and applying the equation to the problem.
  • #1
Leelo
1
0

Homework Statement


a boy on whom the force of gravity is 400 N hangs on to the middle of a rope stretched between two trees. The rope sags in such a way that it makes an angle of 170 degrees at the boys hands. what force does the rope exert on each tree?

Homework Equations


F=ma

The Attempt at a Solution


5 degree angle between horizontal and vertical components
 
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  • #2
Leelo said:
5 degree angle between horizontal and vertical components
That's not what you mean. The angle between those components is necessarily 90 degrees.
Anyway, you have an equation to use. Create unknowns as necessary and write out the equation as it applies to this problem. (I.e., show more of an attempt!)
 

1. What is equilibrium in two dimensions?

Equilibrium in two dimensions refers to a state in which the net force and net torque on an object are both equal to zero. This means that the object is not accelerating and is either at rest or moving at a constant velocity.

2. How is equilibrium achieved in two dimensions?

Equilibrium in two dimensions can be achieved by balancing the forces and torques acting on an object. This can be done by adjusting the magnitudes and directions of these forces and torques until the net force and net torque become zero.

3. What are the conditions for equilibrium in two dimensions?

In order for an object to be in equilibrium in two dimensions, the following conditions must be met:

  • The net force on the object must be equal to zero.
  • The net torque on the object must be equal to zero.
  • The object must be at rest or moving at a constant velocity.

4. What are some real-life examples of equilibrium in two dimensions?

Some common examples of equilibrium in two dimensions include a book resting on a table, a seesaw with two equally weighted individuals on either end, and a satellite orbiting the Earth at a constant speed.

5. How is equilibrium in two dimensions different from equilibrium in one dimension?

Equilibrium in two dimensions involves balancing both forces and torques, while equilibrium in one dimension only requires balancing forces. Additionally, equilibrium in two dimensions can involve motion in two perpendicular directions, whereas equilibrium in one dimension only involves motion in one direction.

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