Traveling ice

In this part, the student will make a simple design of an incline with a thin board (cardboard, clip-board,…) and aluminum foil (smoothly placed over the board). You will document your work on a pdf file neatly and as organized as possible.

1. The ice-board interface should be extremely smooth. Friction can easily be neglected. Make sure the ice dry before each experimental trial. Thus, when its removed, be ready to do the experiment.

2. The pieces of ice should be similar. You will need several. First thing is to take a (typical) piece and measure to about where the center of mass is located (from the bottom of a piece to where you believe it is located). Place this value clearly labeled in meters including your error (
±
±
). The initial potential energy will be determined using a measurement from the table up to (where you place the ice every trial) the center of mass point. Thus, you will need to place a mark at the top of your incline so you know what the height is relative from the table to the center of mass of a typical piece of ice. Thus, when freezing the water, make sure the level is the same so the ice is the same. Measure from the table top upwards to the mark and add in your distance from the mark to the center of mass to get the height
h
h
in meters. Include error in this value.

3. Below is a simple sketch. The equations for the experiment are the all too familiar conservation of energy equation and the projectile with solely horizontal launch (see video).

From the top of the incline to it reaches the bottom, the transformation is
m g h ⟶ 1 2 m v 2
m g h ⟶ 1 2 m v 2
. Thus, one may easily “predict” the speed of the ice as it reaches the table (see video for proper launch trajectory).

4. Using your height, calculate the predicted speed for the launch. Make sure its in m/s and it is clearly labeled on your upload pdf file.

The length it will travel along the horizontal (base of the table to the point on the floor) can then be calculated using
x = v o x t
x = v o x t
, where
v o x
v o x
is the speed you just calculated, and
t
t
is the time of flight during projectile motion. Using simple kinematics, we find that
t = 2 y g
t = 2 y g
,
y
y
is the height from the top of the table straight down to the floor. The ice will launch and travel vertically a distance
y
y
. Measure what y is and note your error (
±
±
). Make sure this is clearly labeled as well in your work. Therefore,
x = v o x 2 y g
x = v o x 2 y g
.

5. Calculate the predicted length of horizontal travel and clearly label it.

6. When obtaining the experimental value, keep in mind the following:

Place the ice long ways (if it is not a perfect cube) at the marked position of height measurement.
ALWAYS START FROM REST! There should be no kinetic energy initially (only potential) for this to work. So, just hold the ice with one finger and op up the finger to set it in motion. NO PUSHING!!
Do a few trial runs and make sure the ice DOES NOT rotate, but just proceeds in simple translation down the incline until it smashes on the floor.
Clearly note all of your variables and observations DURING these practice trials.
Film this process of the ice landing and then refer back to the film to get a precise landing point to measure your horizontal length
x
x
.

7. Measure this value for three trails and take the average. Note all trial values, in meters, and then clearly label the average along with your average error (e.g.
x a v g = 0.15 ± 0.01 m
x a v g = 0.15 ± 0.01 m
).

8. Compare with prediction and calculate the percent difference. Note your error for all the measurements and note how reasonable the result is based on that.

9. Based on your result, were you able to demonstrate the conservation of mechanical energy? List all factors that would not allow a pure transformation of gravitational potential energy to kinetic energy.

10. Tale pictures of your set-up and include them in the pdf file.

11. Make sure the file is extremely neat, organized and labeled, Finally, upload the file.