course Phy 201
I was looking on my access page and did not see this homework assignment on there so i am resubmiting it just in case.
Galileo Experiment
Use the fastest pendulum you can reliably count.
Count your pendulum for a minute.
The instructor will operate the experiment. You just watch and time.
Time the ball as it moves down 10 feet of ramp, using a pendulum.
Repeat for 9 feet, then for 6 feet, then for 4 feet.
Graph position vs. clock time for the ball rolling down the ramp, with clock time in units of half-cycles.
Sketch the graph pretty carefully and sketch a smooth curve that you believe represents the actual position vs. clock time behavior of the ball.
The speed of the ball is constantly changing, so your graph will not contain any straight lines.
There is some uncertainty in your timing, so while your curve will probably come close to your data points, it shouldn't be expected to actually pass through any of them.
In other words, your curve should represent the actual behavior of the ball, as best you can infer it from the data points, but you shouldn't go out of your way to make your curve actually go through any of the points.
Based on your graph estimate the following:
The time required to travel down the first one-foot ramp. Due to the graph that I made earlier it looks like it would be around .5
The distance that would be traveled during each half-cycle of your pendulum (i.e., the distance from the start to the end of the first half-cycle, the distance from start to end of the second half-cycle, etc.). According to my graph and estimate the distance that would be traveled during each half cycle would be around 6 inches.
The average rate of change of position with respect to clock time on the first, the third, the fifth, the seventh and the ninth 1-foot ramps. The first would be .5/1=.5
The third would be 2.5/3=.83,
You appear to be calculating the average velocity for the first three feet, rather than the average velocity on just the third ramp.
How long did the ball spend on just the third ramp? It traveled a foot during that time so what was its average velocity?
The fifth would be 3.5/5.7, The ninth would be 5.0/9=.55
comments and questions similar to the above apply here as well
Trapezoids
Sketch a y vs. x coordinate system. The y axis is vertical (up and down the page), the x axis horizontal (left and right across the page).
You have a 'graph trapezoid' on your desk.
A 'graph trapezoid' has the property that one of its sides is perpendicular to two other sides.
Orient your trapezoid so that its base rests somewhere on the x axis. (The base is the side which is perpendicular to two other sides; not every trapezoid has a base in this sense, but a 'graph trapezoid' does).
Estimate the two 'graph altitudes' of your trapezoid, its 'altitude' and its 'base'. You can use any unit with which you are comfortable to make your estimate (e.g., centimeters, inches, feet, kilometers, nanometers, pounds, liters, gallons, kilograms, slugs, cubic feet, miles per hour; whatever you think works best for you is fine, though length units are probably most appropriate to this exercise). (The 'graph altitudes' are the sides which are parallel to the vertical axis when the base rests on the horizontal axis).
you need to include your estimates here
Make on fold in the trapezoid so that if you tear the paper along the fold, the two pieces can be reassembled to make a rectangle.
Answer the two questions below, and in your answers explain your reasoning by giving the estimated dimensions, and a complete description of what you did. Your explanation show how you proceeded from your estimates to your results.
What is the 'graph slope' associated with your trapezoid? 9.6/5=1.92
What would be the dimensions of this rectangle? 9.5 by 5
you didn't include your estimates of altitudes so it's not possible to tell whether you calculated these correctly
Definitions of average velocity and average acceleration:
These are the central definitions for the first part of your course.
� Everything you do in analyzing motion should come back to these definitions:
� The average velocity of an object on an interval is its average rate of change of position with respect to clock time on that interval.
� The average acceleration of an object on an interval is its average rate of change of position with respect to clock time on that interval.
Analyzing the motion of the Lego racer:
We estimated that the Lego racer traveled 60 cm in 1.5 seconds to rest as it traveled in the direction opposite our chosen positive direction, then 30 cm in 1.2 seconds to rest as it traveled in our chosen positive direction.
Applying the definition of average velocity to the second motion:
By the definition, we are finding average rate of change of position with respect to clock time.
The A quantity is the position of the racer.
The B quantity is the clock time.
The average rate is by definition of average rate equal to (change in A) / (change in B).
Having identified the A and B quantities we find that
average velocity = average rate of change of position with respect to clock time = (change in position) / (change in clock time).
According to our information, the change in position is +30 cm and the change in clock time is +1.2 seconds.
Thus our average velocity is
average velocity = average rate of change of position with respect to clock time = (change in position) / (change in clock time) = (+ 30 cm) / (+1.2 s) = +25 cm / sec.
Find the average velocity for the first motion, using similar steps to connect your result with the definition of average velocity.
If we sketch a graph of velocity vs. clock time for the second motion:
we know that the velocity ended up at zero
we know that the cart was moving in the positive direction as it slowed to rest
if we assume that the graph is a straight line, we conclude that the line decreases toward a point on the horizontal axis during the 1.2 second interval (you should have a sketch of the graph in your notes)
we know that the average velocity is 25 cm / s; since the final velocity is zero we conclude that the initial velocity is greater than 25 cm / s; and since we expect the average velocity to occur at the middle of the time interval we conclude that the initial velocity was 50 cm/s
Our graph therefore forms a trapezoid with base 1.2 seconds, and altitudes 50 cm/s and 0 cm/s (in this case the trapezoid is in fact a triangle). We could find the trapezoid's associated slope and area.
The slope is rise / run. The rise is the change in velocity. Velocity changes from 50 cm/s to 0, so the change in velocity is
change in velocity = final velocity - initial velocity = 0 cm/s - 50 cm/s = - 50 cm/s.
The run is 1.2 seconds. So the slope is
slope = rise / run = - 50 cm/s / (1.2 s) = -42 (cm / s) / (s) = -42 (cm / s) * ( 1 / s) = -42 cm / s^2.
Since the rise represents change in velocity and the run represents change in clock time, our calculation gives us (change in velocity) / (change in clock time).
This is the form of an average rate of change. Recalling the definition of average rate of change, we see that velocity is the A quantity, clock time the B quantity, so that this is the average rate of change of velocity with respect to clock time.
This is the definition of acceleration.
The slope of this graph represents the acceleration of the car.
Note that our reasoning requires that the v vs. t graph be a straight line. Otherwise we could not have concluded that the initial velocity is 50 cm/s.
What is the slope of the graph of the first motion (the distance was 30 cm and required 1.5 seconds)? Average Velocity=average velocity wrt clock time; which would be 30/1.2=25cm/s
1.2 s is the time interval associated with the second motion, not the first
Answer by duplicating the reasoning used above.
What is the area of the graph trapezoid corresponding to the first motion, and what does this area represent? The are of the rectangle would be length* width (9.5*5=47.5), the area of the small triangle would be length * with (4*1.5=6) so the area of the trapezoid would be 47.5+6=53.5, This are represents the dimensions in the space.
Your figures here don't seem to be related to the motion of the car. You should be analyzing the second motion of the car, as specified above.
Answer by identifying all the quantities you use to find the area, and as best you can reason out the meaning of your result. Reason in detail similar to that used above, though the reasoning process will be different for the question of area.
The first I thing I done to solve for the area I first started with the rectangle dimensions which by my drawing would be 9.5 length *5width=47.5area of rectangle. Then I took the length and width for the tip of the triangle and according to my drawing would be 4 length * 1.5 width= 6 area of triangle. Then I added the two sums together 47.5 area of rectangle + 6 area of triangle =53.5 total area of trapezoid. "
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