Uniformly Accelerated Motion
College Physics Lab
PH 141
Uniformly Accelerated Motion
Purpose: To investigate the motion of a particular system; to determine whether or not the
acceleration is uniform, and, if it is, to determine the value of the acceleration.
Discussion: We will investigate the motion of two objects connected by a string which passes
over a pulley. The object with the larger mass will fall toward the ground, while the other object
will rise away from the ground. In this experiment we will only be concerned with describing the
motion (kinematics). In a later experiment we will investigate the relationship between the
masses and the motion (dynamics).
Since the masses move in the vertical direction we will use y to designate the position of the
larger mass (choose up to be the positive y-direction), with the floor corresponding to = 0.
Ideally we would like to use the same initial position , and change the final position . In
practice it is easier to change
and use the same . Therefore, we assume that
= 0, vi= 0,
and that a = - a1. According to the equations of uniformly accelerated motion:
1
2
1
2
(1)
(2)
Or
1
2
(3)
where a1 is the magnitude of acceleration. Notice that yi is proportional to t2, with +a1/2 playing
the role of the constant of proportionality. Theoretically, a graph of yi vs. t is a parabola.
However, a graph of yi vs. t2 is a straight line which passes through the origin!
Uniformly Accelerated Motion
Procedure:
1. Set up the pulley system, masses, and meter stick as instructed. Suggested values for the two
masses are 220 g and 200 g, although you may need to vary this. We want the masses to be
sufficiently different so that the friction does not interfere with the experiment. On the other
hand, we do not want the masses to differ so much that the time intervals are too short to
measure accurately.
2. Raise the larger mass to an initial height of yi = 130 cm from the ground. Make sure both
masses stop swinging before proceeding.
3. Use a stopwatch to measure the time required for the large mass to reach the ground (yf = 0).
Repeat the measurement three times (or until you get consistent results). Calculate an average
value for the time. You are going to have to be very careful in how you release the masses and
measure the time. One consistent way to release the masses is to "brake" the pulley wheel with
your finger, and then remove your finger to begin the motion.
4. Repeat steps 2 and 3 for yi decreasing from 120 cm to 50 cm. For each average t calculate t2
and enter it into the data table. Notice that t2 has units of s2. Record all your data in an
appropriate data table which includes columns for yi, t, and t2.
5. Make a graph of yi (vertical axis) vs. t (horizontal axis). Notice that the data points fall more or
less along a parabola. Draw a smooth curve which best fits the data points.
6. We would like to somehow produce a straight line graph from our data. Make a graph of yi
(vertical axis) vs. t2 (horizontal axis). Does the data fall reasonably close to a straight line? If it
does then you can conclude that the acceleration is constant. Draw in the "best" line through the
data points, but do not force the line to pass through the origin. Does your line pass reasonably
close to the origin?
7. Use two points on your line to calculate the slope of the line. Notice that the slope will have
units of cm/s2. Calculate the acceleration of the object in cm/s2 from a1 = 2*(slope). We do not
have another value with which to compare this result. Your acceleration will depend on your
masses and pulley, but values of 30 to 70 cm/s2 are common.