Finding swing speed using energy conservation with different height references

[dnt]

a girl on a swing, which is 4 m long, is 2.0 m high at her highest point (all the way back) and 0.5 m above the ground at the closest point (at the bottom).

question is how fast is she going and when?

im pretty sure her fastest point is at the bottom.

to solve it i think you set potential energy equal to kinetic (mgh = 1/2mv^2) and solve for v. but what h do you use? is it 2.0 m or 1.5 m (the difference in heights from top to lowest point)?

also, what's the point in mentioning the 4 m long string?

 

[cscott]

Have you considered rotational energy? [itex]PE_{top} = RE_{bottom} - PE_{bottom}[/tex]<br /> <br /> Just an idea..[/itex]

 

[mathmike]

well the height you use is atbitrary just as long as you use it all the way through the problem.

the reason they tell you the length of the swing is you need it to figure out angular velocity

 

[dnt]

angular velocity? we haven't done that yet. why can't i just solve setting potential and kinetic equal to each other (mgh = 1/2mv^2) and solving for v?

 

[jtbell]

Try thinking of the problem using the complete statement of conservation of energy:

$${PE}_{bottom} + {KE}_{bottom} = {PE}_{top} + {KE}_{top}$$

The information that you're given fits perfectly into this approach. (except for the length of the string, which isn't needed)

Note that in this approach, you can measure the height from whatever point you like, when calculating the PE, so long as you're consistent about it.

 

[BobG]

a girl on a swing, which is 4 m long, is 2.0 m high at her highest point (all the way back) and 0.5 m above the ground at the closest point (at the bottom).
question is how fast is she going and when?
im pretty sure her fastest point is at the bottom.
to solve it i think you set potential energy equal to kinetic (mgh = 1/2mv^2) and solve for v. but what h do you use? is it 2.0 m or 1.5 m (the difference in heights from top to lowest point)?
also, what's the point in mentioning the 4 m long string?

Use the difference in the height (you want to know how much potential energy you lost, not how much potential energy you have at any given point)

Did they give you the formula for the period of a pendulum? This would allow you to attach a time to each position (starting from 2 m high to the bottom of her swing, to the highest point all the way forward, bottom on the way back, etc).