a. First, we drew a visual representation of the ramp. The materials we used are two wooden blocks, motion detector, ramp, ruler, cart, chalk, metronome, and the table. We used the block to prop up the table and create a ramp that is on an angle.
b. Then our group took a series of trials and marked the location of the back of the cart (so that the data was consistent) every second on the table with chalk. The metronome counted the seconds and indicated when we should mark. We did five trials and then entered the data into excel to make a graph. In column A, we entered the increments of time and in column B we entered the distance per second that the cart traveled.
c. In order to make the data linear, we square the B column. This also helped us find the equation of the line and to calculate our slope. The equation of the line is y=mx+b, so we plugged in the variables from our graph. Based on our graph, the equation of the line is
y=5.6958x+14.564.
y=5.6958x+14.564.
Above is the table before we graphed our data.
d. Lastly, we calculated the acceleration by using the formula slope=1/2a. In order to calculate this, we changed the units to meters.
Our predicted acceleration is
.113916m/s^2. The prediction appears high because we calculated it in centimeters as opposed to meters.
.113916m/s^2. The prediction appears high because we calculated it in centimeters as opposed to meters.
To solve for t=4:
y=5.6958(4)+14.564
=.1056968 m/s^2 after 4 seconds
y=5.6958(4)+14.564
=.1056968 m/s^2 after 4 seconds
I learned that by squaring the data you can make the line of the graph appear linear. You also can plug in an x,y coordinate pair to solve for b in the equation of the line. (y+mx+b)
The actual acceleration was .197m/s^2. Our group was not within 10%.
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