# Theoretical velocities at different heights sliding down an inclined plane

• helloworld2941
helloworld2941
Homework Statement
For a report, I am trying to work out the theoretical velocity of a person at different points on a slide based on height. Disregarding frictional forces and air resistance and assuming a uniform acceleration (straight slide), can I work out somewhat accurate velocities using the principle of conservation of mechanical energy?
Max slide height 6m and weight of person 80kg
I have done two calculations, one at height 3m and one at bottom.
Relevant Equations
U = mgh
k = 1/2 mv^2
At 3m:
U = 3 x 9.8 x 80
= 2352J

U at 6m = 6 x 9.8 x 80
= 4704J

k = 1/2mv^2
(4704-2352)J = 1/2 (80) v^2
v = 7.67 m/s

At 0m (bottom):
U = 0
4704J = 1/2 (80) v^2
= 10.84 m/s

Okay so what is bothering me here is just that my working doesn't take into account the steepness of the slope? And in my mind from the seemingly "logical" thinking wouldn't a steeper slope produce different speeds in the middle of the slide (though bottom is the same?)
Thank you for any help! This has really confused me (struggling high school student)

helloworld2941 said:
Okay so what is bothering me here is just that my working doesn't take into account the steepness of the slope? And in my mind from the seemingly "logical" thinking wouldn't a steeper slope produce different speeds in the middle of the slide (though bottom is the same?)
Welcome to Physics Forums!

The acceleration down the slide depends on the steepness. Maybe you've studied this? The speed depends not only on the acceleration but also on the duration of the acceleration. For different amounts of slope, does it take different amounts of time to reach the middle of the slide? Can you see how it might be possible for the speed to be the same at the middle for two different slopes even though the acceleration is different for the two slopes?

Watch this classic "Racing balls" demonstration. It will inform your intuition.

helloworld2941
kuruman said:
Watch this classic "Racing balls" demonstration. It will inform your intuition.

That's such a simple but informative video! Thank you

kuruman
TSny said:
Welcome to Physics Forums!

The acceleration down the slide depends on the steepness. Maybe you've studied this? The speed depends not only on the acceleration but also on the duration of the acceleration. For different amounts of slope, does it take different amounts of time to reach the middle of the slide? Can you see how it might be possible for the speed to be the same at the middle for two different slopes even though the acceleration is different for the two slopes?
So they are not mutually exclusive factors? I think I understand it now. Thanks for your help!

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