One-Dimensional Motion of a Dynamics Cart
Purpose: To graph the position and velocity as a function of time of an object experiencing one-dimensional motion, both for zero and nonzero acceleration, and to use best-fit lines to predict velocities and accelerations.
Apparatus & Set up: Tape timer (60 Hz setting)
3 meter length of tape (approx.)
Carbon discs
Meter stick
String
Ring stand, clamps etc.
Dynamics cart and track
Base and Support with clamps
Part 1 – Constant Velocity
Theory:
Procedure:
Arrange the dynamics cart on the track as shown below. You will need to attach the timer tape to one end of the cart. Make sure the carbon disk is pointed face up, and that the timer tape is laid flat across the carbon disk, but below the needle. The timer makes 40 dotted impressions in one second. By attaching the timer tape to the dynamics car, and then pushing the dynamics cart into motion, you can determine how many dots “long” it took the cart to travel the length of the tape. However, since we do not know the initial velocity (you are just going to give the cart a push) the speed at the instant when the cart moves cannot be known. So you will use the dots to calculate the average speed of the cart since an instantenous recording of the velocity is more difficult to obtain.
Steps:
Bring the cart to one side of the track, and attach the tape. Turn on the timer.
Lightly push the cart.
When the cart hits the end stop, turn off the timer and remove that is now laid out on the track (as much as have marks on it).
Since the timer makes 60 dots every second, make a slash THROUGH every sixth dot. This will tell you each 0.1 second.
Make a slash THROUGH the first dot on the tape. Mark this as "START".
Measure the distances between the START and each slash (in m) on the tape. Record the distances in the "d" column of the data table.
CALCULATIONS and GRAPHS:
Calculate the Δt for each time interval. Record your answers down the "Δt" Column.
Calculate the Δd for each time interval. Record your answers down the "Δd" Column.
Find the average speeds during each 0.1 second of the trip.
Use the total distance and the total time to calculate the average speed for the whole trip.
Plot a Distance vs Time graph in EXCEL. Plot the best-fit line for the data. Use a linear fit. Be sure to include the equation of the line, and to write it as d = di+vt. Comment on the R2 value. Is the slope constant?
Plot a graph of Average Velocity (Vavg) vs Time in EXCEL. Use your results from the last column of the data Table and use time measurements between the marked seconds. (ie. 0.05, 0.15, 0.25, etc.) Calculate the slope of the best straight line from your Velocity vs Time graph. What is the value of slope? Does it make sense? Why or why not
t (sec)
Δt (sec)
d (m)
Δd (m)
Vavg (m/s)
0
-------
0
0.1
0.2
0.3
0.4
0.5
0.6