PH 105 The University of Alabama Physics Labs Kinematics Problem answer the lab questions, every week there are physics labs. Everything is explained in th

PH 105 The University of Alabama Physics Labs Kinematics Problem answer the lab questions, every week there are physics labs. Everything is explained in the attachment Course and Section_______
Names ___________________________
Date___________________
___________________________
ERROR ANALYSIS SIMULATION
Introduction
In this online experiment we are interested in learning how to treat data. The main point here is that
any time a scientist measures a number; he/she must be able to tell his colleagues the accuracy of that
number. Otherwise its not possible to tell whether the number agrees with the predictions of a theory;
or for another scientist to check the experimental results.
Submit your answers using Blackboard.
1 – Preliminary Questions
1. Suppose you measure the circumference of a circle and its diameter, then divide the circumference
by the diameter. The result ought to be π. If your result is 3.15 did you just proved that π is 3.15?
2. Suppose you want to find the length of a rod. Do you think that increasing the number of times you
take a measurement of its length would improve the precision of your result?
3. You take twenty measurements in order to find the length of a rod, you calculate the average and
obtain the value L0. Supposed that now a different person takes twenty measurements as well of the
same rod, then calculates the average and obtains the same L0 as you. Does it mean that both of you
obtain a result with the same precision?
2 – Pendulum
Open the simulation below and select Intro
(https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html)
On the top right corner select set Length = 1 m and Gravity = Moon. Use the cursor to drag the
pendulum away about 20° from its equilibrium position (at the bottom). Then press play, the pendulum
will start to oscillate. Your goal is to find its period of oscillation T (how long it takes to get back to the
initial position). To do so select the Stopwatch. You are not expected to measure the perfect ‘true’
value, instead the best estimate of the ‘true’ value is given by the average over N measurements
N
1
T̄ = ⋅∑ T i
N i=1
Measure T ten times and keep a record of your data (on a piece of paper for example).
4. What is the average value T that you have found ? Use three digits
Next, we need to find a way to quantify how inaccurate were your measurements. First let’s introduce
d, the deviation from the average value
d i=T i−T̄
Calculate di for each of your measurements Ti and keep a record of your data. Now calculate the
average of d
N
1
d̄= ⋅∑ d i
N i=1
5. What is the average value d that you have found ? Use three digits
Clearly, the average of the deviations di cannot be used as the error estimate, since it gives us zero (or
very close to zero, depending on how you have rounded your digits). This is because the deviations
with positive sign are always canceled by the deviations with negative sign.
In order to evaluate the inaccuracy of T, indicated as σaverage, first we need the standard deviation σT
which is an estimate of the statistical dispersion of your measurements Ti about the average T . The
standard deviation is given by
σ T=
√
N
1
2
⋅∑ d i
( N−1) i=1
6. What is the standard deviation σ T of your T i ? (Use three digits)
σ average which is the error of the measurement of T is related to the standard deviation σ T as
σ average =
σT
√N
7. What is σ average of your measurement? Use three digits
In this way the measurement of the period is expressed as
T =T̄ ±σ average
8. If you were to increase the number of measurements what happens to the standard deviation?
9. If you were to increase the number of measurements what happens to the error of the average?
10. Are your answers to question 9 and question 2 consistent?
3 – The Gaussian distribution
You can use online tools to calculate several statistical quantities, as for example here
(https://www.mathsisfun.com/data/standard-deviation-calculator.html)
A physicist uses a particular device to take measurements of the length L of a quantity. The following
table shown the N = 16 different values (in centimeters) obtained for L
8.30 7.64 6.96 8.34 7.06 9.64 8.79 9.18 7.77 7.02 8.92 8.73 6.40 7.32 8.93 7.54
11. Calculate the average value of the length.
12. Calculate the standard deviation of the length.
The distribution of the possible measurements of L is supposed to follow a Gaussian distribution, that is
a plot where the x-axis contains the values of L and the y-axis indicates how frequent that value was
obtained during the measurement. Use this simulation to visualize the distribution of the values of L
(http://digitalfirst.bfwpub.com/stats_applet/stats_applet_7_norm.html)
Input your average value of L and relative standard deviation.
Two numbers are displayed at the top of the green dots, report those two green numbers
13. Lower green number is
14. Bigger green number is
The numbers 0.1587 ≈ 0.16 at the bottom indicates the number of measurements with a value not
contain in the range given by the two green numbers. Since the plot is symmetric that means 0.16 x 2 =
0.32 or 32% of the measurements have a value outside the range defined by the two green numbers. In
Using the language of statistics those values “are outside one standard deviation”.
15. Look again at the table, how many measurements have a value outside one standard deviation ?
16. To what % of the total 16 measurements does the answer to question 14 correspond to ?
17. Is your answer to question 16 indicating that the distribution is a Gaussian ?
Course and Section_______
Date.
Names: ___________________________
__________
___________________________
KINEMATICS SIMULATION
Introduction
In this simulation you will study motion in one and two dimensions. More specifically the relations
between position, velocity and acceleration to describe the motion of an object.
Submit your answers using Blackboard.
1 – Preliminary Questions
1. Are the directions of the displacement and velocity always same ?
2. Are the directions of velocity and acceleration always same ?
3. If the acceleration is zero, does it mean that the object is not moving ?
4. Is it possible for the velocity of an object to be zero and its acceleration not zero ?
2 – Motion Graphs at Constant Acceleration
Open the following simulation (https://ophysics.com/k4.html)
You can change the values of initial position x0, velocity v0 and acceleration a0 using the bar at the
bottom.
Answer the following questions by looking at the graphs or by using the kinematic
equations (and use the graphs to verify your solution).(Note: For the questions 5-13, use
only numerical value; No units)
Set x 0 = -2.0, v 0 = 1 and a 0 = 0
5. What is the potion at t = 3?
6. Do the velocity or the acceleration ever change?
Set x 0 = 0, v 0 = -2 and a 0 = 2
7. At what time the velocity = 0?
8. At what time the position = 3?
Set x 0 = -1, v 0 = 0 and a 0 = 1
9. What is the position at t = 3?
10. At what time the position = 0?
Set x 0 = 2, v 0 = 1 and a 0 = -1
11. What is the velocity at t = 2.5?
12. What is the position at t = 3?
13. At what time the position = 0?
3 – Motion at Constant Acceleration
Open the following simulation (https://ophysics.com/k6.html)
Set x 0 = -5, v 0 = 2 and a 0 = 0
14. What is the position of the car at t = 3?
15. What is the velocity of the car at t = 3?
Set x 0 = -3, v 0 = 2 and a 0 = -0.5
16. What is the velocity of the car at t = 2?
17. What is the velocity of the car at t = 6?
18. What is the position of the car at t = 1.5?
The car changes its direction at the location x =1
19. If instead v 0 = 2.5 in which location now does the car charges direction?
For the next two questions use a 3 digits answer (you have to make the calculations while
the simulation can be used to check).
20. If instead v 0 = 2.27 in which location now does the car charges direction?
21. Which v 0 will make the car change its direction at x = 4?
4 – Projectile motion
Open the simulation (https://phet.colorado.edu/en/simulation/projectile-motion) and select Vector.
Uncheck the ‘Air Resistance’ for this entire simulation. Set the Initial Speed to 15 m/sec, Mass 2 kg,
Diameter 2.5 m. You can drag the blue box on the right top corner to any point on the path of projectile
to measure time, range and height.
Now, fire the ball at initial angle 300.
22. How far did it go?
23. What is the time of flight?
24. What height did it reach?
Fire the ball again but not select Slow motion
25. Which components of the velocity are changing?
26. What is the value of y-component of velocity at maximum height?
27. What is the value of x-component of velocity?
28. Does the acceleration change?
Now add air resistance.
29. Is your answer to question 25 still valid?
30. How is the time that it takes to move upward relative to the time it takes to fall down?
Keep the same initial speed of 15 m/s. (Uncheck air resistance)
31. What is the initial angle for the ball to reach the greatest distance?
32. What is the initial angle for the ball to reach the maximum height?
Keep same initial speed of 15 m/s, set initial angle = 60°
33. Does the time of flight depend on mass of the ball?
34. Does the maximum height depend on the mass of the ball?
There is target on the ground at distance 15.0 m. If you hit the target the simulation shows three stars. If
it only shows one star your shot is not precise enough, repeat.
35 If the initial speed is 13 m/s at what angle must the ball be fired to hit the target?
36 If the initial angle is 45° what initial speed is necessary to hit the target?
5 – Free Fall
Open the simulation (http://physics.bu.edu/~duffy/HTML5/1Dmotion_graphs.html)
Choose ‘Lunch up at 20 m/sec’. The coordinate x(m) indicates the vertical height. The initial speed is
20 m/s.
Look at the velocity graph and fill out the table below (try your best estimate, three points
are quite obvious). Plot the velocity-time graph on Excel (or any program you prefer). Fit it linearly.
Velocity(m/s)
Time (s)
37. What physical quantity does the slope represent?
38. What is value of the slope?
If we do theoretical calculations using the given initial conditions above, we get the following data.
Plot the velocity-time graph on Excel (or any program you prefer). Fit it linearly.
Velocity(m/s)
Time (s)
16
0.4
12
0.8
8
1.2
4
1.6
0
2.0
39. What is value of the slope?
40. Find the % error with the result you obtained in question 38.
|A p p r o x i m at e V a lu e−E x a c t V a lu e|
×100 %
|E x a c t V a l u e|
-4
2.4
-8
2.8

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