Over the weekend, my son and I were trying to use the Video Physics app to take data of marbles flying off the kitchen table, but they were moving too fast for the iPad camera in the low light so we headed outside and got some amazing data. So for class today (and possibly all future experiments using Video Physics) , the students took their data outside.The red dots in the image mark the location of the ball in each frame of the video. Most kids just took data for the initial drop but this one got a nice bounce and as you’l see below, the data for the bounce turned out better than the initial drop.
When working with projectiles we can break the physics into two problems, motion along the horizontal X-axis and motion along the vertical, Y-axis. The only force on the ball after it leaves the track is the force of gravity which equals the mass of the ball times the acceleration due to gravity (-9.8 m/s2), F = mg, which only pulls on the ball along the Y-axis. So the velocity of the ball in the horizontal direction (X) should be constant, which it was. Graphs of X position as a function of time, were very linear, and the slopes of those graphs gave the horizontal velocity of the ball, which also happened to be the initial velocity of the ball. In the example on the left the horizontal velocity was 160 cm/s or 1.6 m/s. The linear fits were done with the Graphical Analysis app.
In the top graph below is the Y position or height of the ball for the data taken in the first photograph, measured in meters (m) as a function of time and the second graph is the velocity of the ball along the Y-axis (vertical).
You can see that vertical, Y, position of the ball is NOT linear with respect to time, but its velocity while in the air (bottom graph) can be fit very nicely by a line, especially after the first bounce. The slope of a velocity vs time graph gives you the acceleration of the ball, which in this case came out to be -9.9 m/s2, very close to the expected value of -9.8 m/s2.
The students took data for 3 different marble drops, just dropping the ball, with no horizontal velocity, and using the marble runs to give it two different initial velocities. They determined that the time it took the ball to fall for all three was about the same and the range (total horizontal distance traveled) increased, as expected, as the initial velocity (along horizontal axis) was increased.