PRELAB
VIDEO
Look at a preview of the lab activities.
PURPOSE
To study the concepts of distance and velocity through graphical analysis.
MATERIALS human subjects, motion detector w/interface, masking tape
RELEVANT EQUATIONS
v = ( x - x_{o}) / t | ||
v = v_{o} + a t | [for constant a] | |
x = v_{o} t + 1/2 a t^{2} | [for constant a] |
DISCUSSION
The concepts associated with motion are central to all of physics. It is important to understand exactly what is meant by position, time, time interval, average velocity, instantaneous velocity, and acceleration. The concept of velocity as the time rate of change in the position covered is fundamental. In graphical terms, the velocity of a body can be calculated from a plot of position vs. time. In order to do this, the graphical concept of the slope must be understood. Consider the plots illustrated in Figure 3-1.
In plot (a), the x-position
of the body does not change with time. You can see that the velocity
of such a body is zero. This is illustrated by the slope of the line that
represents x vs. t, or x(t). The slope is defined as the rise (Δx)
over the run (Δt),
and since we have zero rise everywhere on the plot, the velocity is zero
everywhere.
Figure 3-1: Plots of Position vs. Time
In plot (b), the body is definitely moving, and the curve that represents x(t) is a straight line. Calculating the slope is indicated for a particular spot on the curve where the rise and the run have been drawn. You will notice that the slope would be the same no matter where along the line we choose to calculate it. The velocity is therefore constant for this plot. Actually it was also constant for plot (a), with a value of zero. Any time the x(t) vs. t plot is a straight line (linear), the velocity is constant during that interval.
Next, in plot (c), we see that the variation of x(t) vs. t is curved. This presents a problem if we want to find the slope - where's the straight line? The answer is to draw the tangent line at a given point on the curve. This is a unique straight line that touches the curve at one and only one point. The slope of the tangent line is the velocity at that point. In this context, the velocity is referred to as instantaneous, because it's the value at that particular instant. You can qualitatively verify this fact by sketching in tangent lines near t = 0 and near the maximum value of t that is plotted. The slope of the tangent line, and therefore the velocity, starts out small but continues to increase as time elapses. This motion is one where the body is continuously speeding up, or accelerating.
Bear in mind that as a vector quantity, velocity also has direction associated with it. In motion along a straight line path, we distinguish the two possible directions with a plus or minus sign.
In this experiment you will explore these concepts in a direct, graphical way. You will use a motion detector interfaced to a computer to collect and display data. The following features are important for this experiment:
The motion detector will not properly record any object closer than about 0.5 meter. Be sure the distances to be measured are larger than this minimum.
The motion detector "sees" the closest object in its observational cone of about 15° around a centerline directly in front it. Be sure this zone is free of extraneous objects and motions while taking readings.
The motion detector is the origin of the coordinate system for graphs displayed on the computer. The velocity is positive if you move away from the detector and negative if you move toward it.
The position is equal to the "distance from the detector to the object being detected".
Print out and complete the
Prelab questions.