Galileo’s Inclined Plane
The Galileo project was interesting to me because it allowed me to use a more
hands
on approach. We recreated Galileo’s water clock by using an incline,
a marble,
and a cup to measure the
water.
You put the marble on the
incline.
You let it roll down the incline.
Our
conclusion is that accelleration occured because the mable rolled four times the
distance in only twice the time.
We have learned that acceleration is the change in velocity per unit
time. We have an equation
a = Δv / Δt
The change in velocity, Δv, is the difference between the velocity at
the end of the interval and the velocity at the start of the interval, or
in equations:
Δv = vfinal - vinitial = vf - vi
In previous activities we found the average speed as distance over
time (and because all distances and speeds are positive here, this
is also the average velocity). To calculate the acceleration we need
the instantaneous velocity at the start and end of the interval.
Because we do not have a speedometer, we will have to use our
knowledge of motion, and some math to calculate the
instantaneous velocity at each location.
An equation to calculate average velocity is to use the
“mathematical” average. The equation below calculates the
average of two velocities (the initial and final velocities):
v(final) + v(initial) = average velocity
2
We can use algebra to rearrange this:
v(final) + v(initial) = 2 * average velocity
or (rearrange once more):
v(final) = 2 * average velocity - v(initial)
Using this equation and the data from our table above, we can
calculate the velocity at the end of each marked location (for our
exploration the initial velocity is zero). Once we have found all the
instantaneous velocities we can use them to calculate acceleration.
hands
on approach. We recreated Galileo’s water clock by using an incline,
a marble,
and a cup to measure the
water.
You put the marble on the
incline.
You let it roll down the incline.
Our
conclusion is that accelleration occured because the mable rolled four times the
distance in only twice the time.
We have learned that acceleration is the change in velocity per unit
time. We have an equation
a = Δv / Δt
The change in velocity, Δv, is the difference between the velocity at
the end of the interval and the velocity at the start of the interval, or
in equations:
Δv = vfinal - vinitial = vf - vi
In previous activities we found the average speed as distance over
time (and because all distances and speeds are positive here, this
is also the average velocity). To calculate the acceleration we need
the instantaneous velocity at the start and end of the interval.
Because we do not have a speedometer, we will have to use our
knowledge of motion, and some math to calculate the
instantaneous velocity at each location.
An equation to calculate average velocity is to use the
“mathematical” average. The equation below calculates the
average of two velocities (the initial and final velocities):
v(final) + v(initial) = average velocity
2
We can use algebra to rearrange this:
v(final) + v(initial) = 2 * average velocity
or (rearrange once more):
v(final) = 2 * average velocity - v(initial)
Using this equation and the data from our table above, we can
calculate the velocity at the end of each marked location (for our
exploration the initial velocity is zero). Once we have found all the
instantaneous velocities we can use them to calculate acceleration.