Physical Measurements Lab 2:
Uniform and Accelerated Motion
Introduction:
The purpose of this experiment is to learn the concepts of average velocity, acceleration, uniform motion and nonuniform motion in a straight line or one dimension. You will also gain some experience in working with data.
The average speed of a moving object during a time t is
_{} (1)
In the case of constant acceleration, the velocity (same as speed for linear motion in one direction) changes by a constant amount during equal time intervals.
acceleration = _{} (2)
and
_{} (3)
Equipment:
Dynamic cart, spark timer, cart track, pulley and weight.
EXPERIMENT:
A. Constant
Speed.
1. Cut a onemeter long ticker tape and pass it through the spark timer. Attach the ticker tape to the dynamic cart. The timer and the cart should be properly aligned and must be at the same level. The ticker tape should be parallel to the tabletop.
2. Set the spark timer at 10 Hz mode. Position the cart close to the timer, and give the cart a gentle push immediately after the timer is switched on. You should practice a couple of times before you switch on the spark timer. Note that 10 Hz means 10 cycles/second and the time for one cycle is 0.1 sec. Therefore, the time interval between consecutive dots on the ticker tape is thus 0.1s (Dt in equation 1 is 0.1 sec).
3. Measure and record Dx, the length of each interval between two consecutive spark marks. Make at least 67 consecutive measurements. Do not use the first several dots.
4. Calculate the speed for each interval, using equation (1).
5. Record your results of Dt, Dx, and v_{av} in the table and calculate the overall average speed by averaging all the v_{av}’s.
Example
Dt(s) 
Dx(cm) 
v_{ave}(cm/s) 
0.1 
1.1 
11 
0.1 
1.2 
12 
0.1 
1.1 
11 
0.1 
1.1 
11 












overall v_{ave} = 11.25
B. Constant Acceleration.
1. Use the same setting as in procedure A. 1. Connect the cart to a mass of 50 grams (just the hanger, do not need to add weight) that passes over a pulley as shown below.
2. Gently release the cart right after you switch on the spark timer and catch the cart before it hits the pulley.
3. Measure and record the distance between consecutive spark marks as Dx_{1}, Dx_{2}, etc. Neglect the first interval.
Δx_{2} Δx_{4}
Δx_{1} Δx_{3}
4. Calculate the velocity for each interval: v_{i} = Dx_{i}/ Dt_{i} where i = 1, 2, 3..... and determine the other values for the table below
Example of how to prepare your data table:
1 
2 
3 
4 
5 
6 
7 
Dt(s) 
t (s) 
Δx_{i} (cm) 
total distance x(cm) 
v_{i} (cm/s) 
Dv (cm/s) 
a = _{}(cm/s^{2}) 

0.0 

0.0 



0.1 
0.1 
0.5 
0.5 
v_{1} = 0.5/0.1 = 5.0 


0.1 
0.2 
0.9 
1.4+0.5=1.4 
v_{2} = 0.9/0.1 =9.0 
v_{2} – v_{1} = 4.0 
40. 
0.1 
0.3 
1.2 
1.2+1.4=2.6 
v_{3}=1.2/0.1=12.0 
v_{3}v_{2}=3.0 
30. 
0.1 
0.4 
1.6 
1.6+2.6=4.2 
v_{4}=1.6/0.1=16.0 
v_{4} – v_{3} = 4.0 
40. 
0.1 
0.5 
2 
2+4.2=6.2 
v_{5} = 2.0/0.1=20.0 
v_{5} – v_{4} = 4.0 
40. 
0.1 
0.6 
2.4 
2.4+6.2=8.6 
v_{6} = 2.4/0.1=24.0 
v_{6} – v_{5} = 4.0 
40. 
Example of finished table :
t(s) 
Δ x(cm) 
x(cm) 
v(cm/s)=Δ x/Δ t 
Δ v(cm/s) 
a(cm/s/s)=Δ v/Δ t 
0 

0 



0.1 
0.5 
0.5 
5 


0.2 
0.9 
1.4 
9 
4.0 
40 
0.3 
1.2 
2.6 
12 
3.0 
30 
0.4 
1.6 
4.2 
16 
4.0 
40 
0.5 
2 
6.2 
20 
4.0 
40 
0.6 
2.4 
8.6 
24 
4.0 
40 
5. Make the following graphs on graph paper using the values from your data table above.
a)total distance (column 4) vs. total time (2)
b) Instantaneous velocity vs. time graph (this is a bar graph as shown below). Note that for constant accelerated motion, the instantaneous
velocity in the middle of a time
interval is the average velocity for that time interval. To obtain the instantaneous velocity
versus time graph, simply mark the middle point at the top of each bar, and
connect them with a best straight line
possible. Use a graph paper (ask the
instructor a copy), or computer to generate the graph.
c) acceleration (7) vs. total time (2)
6. Determine the acceleration a by finding the slope of your velocitytime graph (b).
7. Compare it to the average value of acceleration determined in your table for section B.
8. Calculate the theoretical value (refer to your lecture notes, we worked it out as an example) of the acceleration and compare with the slope of the vt graph. Which one is smaller? Why?