"400N Child in Swing: Calc Potential Energy

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In summary, the 400N child on swing has a potential energy of 400J. The child is at the bottom of a circular arc, so the height is zero. The gravitational potential energy of the child Earth system relative to the child's lowest position when the ropes are horizontal is 200J. The attempt at a solution is to find the Wnet of the system and thus the change in potential energy of the system. First, for this question in general, would I be finding the Wnet of the system and thus the change in potential energy of the system? Is that what they want when they say "find the gravitational potential energy of the child Earth system? No. When they say a "400N child" does that mean I
  • #1
~christina~
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[SOLVED] 400N child on swing

Homework Statement


A 400N child is in a swing attatched to ropes 2.0m long

Find the gravitational potential energy of the child Earth system relative to the child's lowest position when

a) the ropes are horizontal

b) rope makes angle 30 deg with vertical

c) child is at bottom of circular arc


Homework Equations


[tex] U_g= mgy[/tex]


The Attempt at a Solution



First of all for this question in general would I be finding the Wnet of the system and thus the change in potential energy of the system? Is that what they want when they say "find the gravitational potential energy of the child Earth system?

When they say a "400N child"
does that mean I can consider that the force of the mass and the gravity already multiplied and thus I can just use that in place of mg


a) I think that the distance y for a would be 2m b/c the ropes are horizontal and thus since the length of the ropes are 2m then it would be logical that the distance traveled would be 2m.

Would I assume that the child is a distance 0.5m above the ground?
I think I would.. assuming they want the net force

Wnet= [tex]\Delta U_g[/tex]

Ui= mgyi = 400N (0.5m)= 200J ====> does that seem sort of large??

I would like to see if my thinking is correct before I go further..

Could someone Please help me ?

Thanks :smile:
 
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  • #2
Where did the 0.5 come from?
 
  • #3
well the book assumed heights on another question so...
but seriously the child wouldn't be sitting on the floor right?
 
  • #4
Ah. Well, you don't need to assume anything for this. It asks for everything relative to the child, right? This means it doesn't matter how high off the ground the child is, only how high he/she gets from his/her lowest point.

You know how high that is, so just use the Energy = Force * Height equation.
 
  • #5
but how would I find the height for part b?

b) gives the angle that it has with the vertical but I don't know how I'd find the height traveled by it.

c) child=> at bottom of arc so I think that means it doesn't move and thus the height would be 0?
wouldn't that give potential E= 0? I know that that can't be though...


Help?
 
  • #6
My interpretation is that the "child's lowest position" is when the "child is at bottom of circular arc" so I'd take that as datum and measure all other heights above it.

This leads to the GPE in part c being trivially easy.

For part b the rope is straight, at 30 degress to vertical and the child at the end of it. How much higher is the child compared to when the rope is vertical?
 
  • #7
catkin said:
My interpretation is that the "child's lowest position" is when the "child is at bottom of circular arc" so I'd take that as datum and measure all other heights above it.

This leads to the GPE in part c being trivially easy.

For part b the rope is straight, at 30 degress to vertical and the child at the end of it. How much higher is the child compared to when the rope is vertical?

first..what is "datum"??

c) isn't it...0m ? since the child doesn't move...

this gets me confused since I know that the equation is

Ug= mgy

but if y= 0...that would make the rest of the equation = 0 too...

b) I seriously don't know how I'll get the difference in height of the child compared with before with a 0 deg angle...

Thanks.
 
  • #8
Datum is Latin for "given" (and you thought this was the Physics forum!) and is used here in the sense it is used when mapmaking and surveying to indicate level zero. See http://en.wikipedia.org/wiki/Datum for more than you ever wanted to know.

c)

"but if y= 0...that would make the rest of the equation = 0 too...". Exactly. That's what I meant by trivially easy; it doesn't get much easier!

b)

It's so easy I don't know how to explain. I guess you are somehow making it harder than it really is. Have to go now. Will need a diagram if you don't figure it out before tomorrow.
 
  • #9
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  • #10
Thanks for the diagram. Yes you have to use the angle.

Draw a horizontal from the mid point of the grey seat. Now you have a right angled triangle. The hypotenuse is the full length of the rope, let's call it L. The vertical side is the full length of the rope minus h, that's (L - h)

The length of the vertical side is Lcosθ
where
L is the length of the rope
θ is the angle of the rope with the vertical

...

Now I really am going!
 
  • #11
catkin said:
Thanks for the diagram. Yes you have to use the angle.

Draw a horizontal from the mid point of the grey seat. Now you have a right angled triangle. The hypotenuse is the full length of the rope, let's call it L. The vertical side is the full length of the rope minus h, that's (L - h)

The length of the vertical side is Lcosθ
where
L is the length of the rope
θ is the angle of the rope with the vertical

...

Now I really am going!


Hm...Is this what you mean??
I wasn't sure what you mean by vertical...b/c you state vertical twice ..once as L-h then 2nd as Lcos theta...

http://img100.imageshack.us/img100/1567/88164147ft0.th.jpg [Broken]


What I got from your explanation was that...

L-h ==> the line that was drawn from the 2 different points of the swing...

Lcos theta = L? do I plug that into L in the L-h ??
 
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  • #12
swing.jpg


this is what he meant by a right triangle.

Use [tex]cos(\theta) = adjacent/hypotenuse[/tex] to find x.

Then, to find how high the child has risen, subtract x from 2m.
 
  • #13
Thank You both I get how to do the problem now :smile:
 

1. What is "400N Child in Swing: Calc Potential Energy"?

"400N Child in Swing: Calc Potential Energy" is a scientific experiment that involves calculating the potential energy of a 400N child on a swing. This experiment helps to understand the relationship between weight, height, and potential energy.

2. How is potential energy calculated in this experiment?

In this experiment, potential energy is calculated using the formula PE = mgh, where PE is potential energy, m is the mass, g is the acceleration due to gravity, and h is the height. The value of g is usually taken as 9.8 m/s^2.

3. Why is the child's weight important in this experiment?

The child's weight is important because it determines the amount of potential energy that will be generated when the child is on the swing. The heavier the child, the more potential energy will be generated at the highest point of the swing.

4. What are the factors that affect potential energy in this experiment?

The factors that affect potential energy in this experiment are the weight of the child, the height of the swing, and the acceleration due to gravity. These factors follow a direct relationship with potential energy, meaning that an increase in any of these factors will result in an increase in potential energy.

5. What is the significance of this experiment?

This experiment is significant because it helps to demonstrate the concept of potential energy and its relationship with weight, height, and gravity. It also highlights the importance of understanding potential energy in various real-life scenarios, such as amusement park rides and sports activities.

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