Tension of rope between two trees

In summary, the conversation discusses the calculation of tension and weight in a physics problem involving two trees supporting a rope. The question asks whether the force balances out when projecting the weight onto tension or vice versa. It is noted that at the midpoint of the rope, only horizontal forces are acting and the trees provide a horizontal reaction force. The horizontal component of the tension is also mentioned.
  • #1
PhizKid
477
1

Homework Statement


XcVjm.png



Homework Equations


F = ma

The Attempt at a Solution


say I project the weight onto T
then I get the right answer
if theta = pi / 4 then Wcostheta = W / sqrt2
but if I project the tension onto the weight, i don't get the right thing
i get the opposite, Tcostheta = W
which makes no sense
i guess the question is
is Wcostheta - T = 0
or is Tcostheta - W = 0?
which forces actually balance out
im trying to see what balances out
i mean its really intuitively obvious that Tcostheta - W = 0 should be true
but that doesn't give the right answer
its not accelerating vertically so Tcostheta - W = 0 should be true
weird that it isnt
i don't think weight is just W there
 
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  • #2
Two trees are supporting the weight of the rope. What does that tell you about the vertical component of the tension at each end? What then is the tension?

At the midpoint of the rope only horizontal forces are acting in tension. The trees are providing the horizontal reaction force (equal and opposite, so nothing is moving). What's the horizontal component of the tension found above?
 
  • #3
Nvm, it's because I forgot to divide by 2
 

Related to Tension of rope between two trees

1. What is the tension of a rope between two trees?

The tension of a rope between two trees is the force exerted by the rope on the trees in opposite directions. It is the result of the weight of the rope and any additional forces acting on it, such as the weight of an object hanging from the rope.

2. How is the tension of a rope between two trees calculated?

The tension of a rope between two trees can be calculated using the formula T = (m x g) + F, where T is the tension, m is the mass of the rope, g is the acceleration due to gravity, and F is any additional forces acting on the rope.

3. Does the distance between the two trees affect the tension of the rope?

Yes, the distance between the two trees does affect the tension of the rope. The longer the distance, the greater the tension, as the weight of the rope has a longer distance to pull on the trees.

4. What factors can affect the tension of a rope between two trees?

Apart from the weight of the rope and the distance between the trees, other factors that can affect the tension of a rope include the type of rope, the strength and flexibility of the trees, and any external forces such as wind or additional weight on the rope.

5. Can the tension of a rope between two trees be greater than the weight of the objects hanging from it?

Yes, the tension of a rope between two trees can be greater than the weight of the objects hanging from it. This is because additional forces, such as the weight of the rope itself, can also contribute to the overall tension.

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