Gravitational Potential Energy child swing Problem

[septum]

Homework Statement

A 140-N child is in a swing that is attached to ropes 2.00 m long. Find the gravitational potential energy associated with the child relative to her lowest position at the following times.

(a) when the ropes are horizontal

I get this one. I used PE=mgy; PE=(140-N)(2.00 m)= 280 J

However, I'm unsure how to approach part B, so if someone could just nudge me in the right direction I would really appreciate it (you certainly don't have to work it out--I'm not asking you to do my work).

(b) when the ropes make a 25.0° angle with the vertical

 

[Delphi51]

Sketch the rope, the angle and the height. Use trigonometry to find the height. Then use mgy again.

 

[aeroengineer]

Use trig to find the height of the child above the ground, using this number as variable "y" in the PE formula.

Think right triangles.

 

[septum]

T.T i don't understand this at all.

I drew a whole lot of right triangles solving for a h and o using 90 degrees and 25 degrees and 65 degrees (basically everything I can think of) and get small numbers such as 2.21 and when I add that in that gives you a.. LOT of joules which is nonsensical.

 

[Delphi51]

Certainly the height has to be less than 2 meters!

Show the swing rope at an angle of 25 degrees from vertical.
Draw a vertical line down from where the ropes are held at the top.
Draw a horizontal line across from the bottom of the child to the vertical line.
Now you have a right triangle with a 25 degree angle in it. You know the length of one side. You should be able to find the height . . .

 

[septum]

Even if I do 2.00m*cos25 degress it comes out as 1.81 m.

If I plug that into my 140 N * (1.81 m) = 153 which is far too large. It must be much less and that is what I'm failing to understand.

 

[Delphi51]

Oops - I forgot about something!
Your 1.81 m is the vertical distance from the top of the swing down to the child. The height above the ground will be 2 - 1.81.

 

[septum]

*facepalm*

Thank you so much for your help.