Tensions in a swing problems using variables

In summary, we are asked to determine the tension in a rope and the horizontal force exerted by an adult on a swing, as well as the tension in the rope after the swing is released. To solve these problems, we need to draw a free body diagram and use Newton's second law of motion. Part a) and b) can share the same diagram, while part c) requires a new diagram. Part d) may be skipped for now.
  • #1
Confusingmeh
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Homework Statement


An adult exerts a horizontal force on a swing that is suspended by a rope of length L, holding it at an angle [tex]\Theta[/tex] with the vertical. The child in the swing has a weight W and dimensions that are negligible compared to L. The wights of the rope and of the seat are negligible.
In terms of W and [tex]\Theta[/tex] , determine:

a) the tension in the rope

b) the horizontal force exerted by the adult

The adult releases the swing from rest. In terms of W and [tex]\Theta[/tex] determine:

c) the tension in the rope just after the release (the swing is instantaneously at rest)

d) the tension in the rope as the swing passes through its lowest point


Homework Equations





The Attempt at a Solution



ok so I am trying to check if I'm right for these problems...

a) T = W + W(tan[tex]\Theta[/tex])

b) F = W(tan[tex]\Theta[/tex])

c) T = W + W(tan[tex]\Theta[/tex])

d) less sure about this one teacher emailed and said we didnt have do it because we havnt learned this yet but i got:
T = W + m(19.8{tan[tex]\Theta[/tex]}{([tex]\Theta[/tex] 2 [tex]\pi[/tex])/(360)})
 
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  • #2
A few things to remember,

Draw your free body diagram (FBD). Parts a) and b) can share the same FBD for this problem since all the forces are identical, but you'll need to draw a new one for part c).

Remember Newton's second law of motion.
  • For a given direction (x- or y-component), ma = sum of all forces in that direction (for the acceleration component a in the same direction).
  • For parts a) and b), nothing is accelerating (static equilibrium), so the sum of all forces [in any given direction] equals zero.
  • For part c) things are accelerating, so the sum of all forces do not add up to zero in both directions. There is a "resultant" net force.
Also, when looking at your FBD, always remember the following:

[tex] \sin \theta = \frac{\mathrm{opposite}}{\mathrm{hypotenuse}} [/tex]

[tex] \cos \theta = \frac{\mathrm{adjacent}}{\mathrm{hypotenuse}} [/tex]

[tex] \tan \theta = \frac{\mathrm{opposite}}{\mathrm{adjacent}} = \frac{\sin \theta}{\cos \theta}[/tex]

Confusingmeh said:
ok so I am trying to check if I'm right for these problems...

a) T = W + W(tan[tex]\Theta[/tex])
You'll need to redo part a). Take a look at your FBD again.
b) F = W(tan[tex]\Theta[/tex])
Part b) looks good to me! :approve:
c) T = W + W(tan[tex]\Theta[/tex])
Remember, you need to draw a new FBD, because the adult's horizontal force is no longer there. You'll have to redo part c)
d) less sure about this one teacher emailed and said we didnt have do it because we havnt learned this yet but i got:
T = W + m(19.8{tan[tex]\Theta[/tex]}{([tex]\Theta[/tex] 2 [tex]\pi[/tex])/(360)})
I think you might be on the right idea, generally speaking, for part d), but I got something quite a bit different. You seem to be converting units (radians to degrees or some-such). But that's not necessary. Θ is Θ, whatever units that might be. And I think you're using the wrong trigonometric function. But if your instructor says that part d) is not necessary, perhaps we can skip part d) for now.
 
Last edited:

1. What are tensions in a swing?

Tensions in a swing refer to the forces acting on the swing, including the force of gravity, tension in the ropes or chains, and the force applied by the person on the swing.

2. How do variables affect tensions in a swing?

Variables such as the length of the ropes or chains, the weight of the person on the swing, and the angle at which the swing is released can all affect the tensions in a swing.

3. Why is it important to consider tensions in a swing?

Understanding tensions in a swing is important for safety and efficiency. Too much tension can cause the swing to break or become unstable, while too little tension can prevent the swing from moving properly.

4. How can we calculate tensions in a swing?

Tensions in a swing can be calculated using the equations of motion and principles of physics. Variables such as mass, acceleration, and distance can be used to determine the tensions in the swing.

5. What are some common problems involving tensions in a swing?

Common problems involving tensions in a swing include determining the optimal length of ropes or chains for a specific weight, calculating the tension needed for a desired swing height, and understanding the effects of varying angles on tensions in the swing.

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