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 non-uniform 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 one-meter 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 6-7 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 vav in the table and calculate the overall average speed by averaging all the vav’s.

Example

 Dt(s) Dx(cm) vave(cm/s) 0.1 1.1 11 0.1 1.2 12 0.1 1.1 11 0.1 1.1 11

overall vave = 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 Dx1, Dx2, etc.  Neglect the first interval.

Δx2                Δx4

Δx1             Δx3

4.   Calculate the velocity for each interval:  vi = Dxi/ Dti  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) Δxi (cm) total distance  x(cm) vi (cm/s) Dv (cm/s) a = (cm/s2) 0.0 0.0 0.1 0.1 0.5 0.5 v1 = 0.5/0.1 = 5.0 0.1 0.2 0.9 1.4+0.5=1.4 v2 = 0.9/0.1 =9.0 v2 – v1 = 4.0 40. 0.1 0.3 1.2 1.2+1.4=2.6 v3=1.2/0.1=12.0 v3-v2=3.0 30. 0.1 0.4 1.6 1.6+2.6=4.2 v4=1.6/0.1=16.0 v4 – v3 = 4.0 40. 0.1 0.5 2 2+4.2=6.2 v5 = 2.0/0.1=20.0 v5 – v4 = 4.0 40. 0.1 0.6 2.4 2.4+6.2=8.6 v6 = 2.4/0.1=24.0 v6 – v5 = 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 velocity-time 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 v-t graph.  Which one is smaller? Why?