Solving Frictionless Slides: No Mass Required!

[runningirl]

Homework Statement

A water slide can be though of as being frictionless. Let's say a slider starts from rest and goes down a slide that is 30 m long and is set at a 25 degree incline.

a) determine the speed of the slider at the bottom of the slide.

b) Explain why you don't need to know the mass of the slider.

Homework Equations

f=ma

The Attempt at a Solution

sin(25)*30=a
a=12.7 m/s/s.

i don't know if that's right.
would i not need the mass for the acceleration?

 

[tiny-tim]

hi runningirl!

sin(25)*30=a
a=12.7 m/s/s.

you can solve this either by F = ma or by conservation of energy

i assume you want to use F = ma (in the direction of the slope) …

ok, if the mass is m, then what is F? ​

 

[p21bass]

As the slide is frictionless, this is a fairly simple constant-acceleration problem. The only acceleration is in the y-direction, you can use a constant-acceleration equation to determine the downward velocity. Since you know the angle, you can then calculate/convert v_y to v.

 

[runningirl]

hi runningirl!


you can solve this either by F = ma or by conservation of energy

i assume you want to use F = ma (in the direction of the slope) …

ok, if the mass is m, then what is F? ​

uh... I'm not quite sure if i can find the acceleration since i have two unknown variables with f=ma.

 

[tiny-tim]

why are you using distance?

use F = ma (in the direction of the slope)

 

[runningirl]

but then i'll have two unknowns.

 

[tiny-tim]

write it out anyway … something should cancel

 

[runningirl]

uh...

f=m(12.7m/s/s)?

 

[tiny-tim]

where does the 12.7 come from?

start from the beginning

 

[runningirl]

then it would just be f=ma because i don't have a force, mass, or acceleration.

 

[runningirl]

where does the 12.7 come from?

start from the beginning

i think i figured it out.

i did ma=m(9.8)(sin25)
a=4.14

but i did it another way and got a different answer...

m(h)=.5(ma^2)
30/sin(25)=.5ma^2

a=5.96 m/s/s.

 

[tiny-tim]

(just got up :zzz: …)

i think i figured it out.

i did ma=m(9.8)(sin25)
a=4.14

yes that's completely correct

(an alternative way is simply to say that the acceleration is the component of the gravitaitonal acceleration in the direction of the slope, ie 9.8cos65°)

but i did it another way and got a different answer...

m(h)=.5(ma^2)
30/sin(25)=.5ma^2

a=5.96 m/s/s.

i think you're thinking of conservation of energy …

mgh = .5mv²

(i can't think of any formulas with a² in them)