How Does the Angle of an Incline Affect the Time of Descent?

[VooDoo]

Hi Guys,

For a physics practical investigation I will be investigating the change in height (angle) of an inclined plane and the time taken to travel down the incline.
Now for my hypothesis and results I am a bit stuck. For the hypothesis I will be using the following formula.

x=ut+.5at^2

Where:
x=distance down the incline plane (meters)
u=Initial velocity (m/s)
t=time taken to travel down (seconds)
a=acceleration down the incline plane (m/s/s meters per second per second)

Now for our situation
x=1.58
u=0
t=?
a=gSinΦ (Φ varies with different heights)

So now I can build a relationship between the height (or the angle of inclination) and the time taken to travel.

Now I substitute values into the formula to get:

x=.5at^2 (because u=0)

Then transpose:
2x=at^2
t^2=(2x)/(gsinΦ)

Now we know that the values of 2x and g (g = 9.8 = acceleration due to gravity) remain constant (well we assume they do). How do I create a direct proportionality between t and Φ ?? So I get a straight line graph when I plot the two?

Have I gone about things the wrong way?

Edit - Here is a graph of the angle versus time

 

[Nylex]

You could simply plot t vs. (sin Φ)^1/2 to give you a straight line.

 

[VooDoo]

You could simply plot t vs. (sin Φ)^1/2 to give you a straight line.

Hi Nylex,
is t on the vertical axis or horizontal axis?

I ploted (sinΦ)^1/2 but that just gives me a curved graph. Then I ploted (sinΦ)^-1/2 which gave me a sort of straight graph. Have I found proportionality? I got the excel spreadsheet if anyone needs it?

 

[whozum]

Given x and g to be constants your function will become
t^2 = (2x/g) * sin(phi)
t = (2x/g)^.5 * sin(phi)^.5

(2x/g)^.5 is just a scalar coefficient, don't worry about it.

Your function is reflecting the relationship t = sin(phi)^.5, there shouldn't be a linear trend because the relationship si the square root of a periodic function, so at the least it will curve. You could try logarithms in which case

log t = (log sin(phi))/2, that should be somewhat linear.

 

[VooDoo]

Hi whozum,

Is that log base to e or log base to 10?

 

[whozum]

Any base will work just as long as you use the same base for both sides.