- #1
helloworld2941
- 6
- 2
- 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)
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)