Lab 3
2 years ago 10
Report3.docx
PHY2048LExp3Theory.pdf
PHY2048LExp3Dataandinstructions28129.pdf
Report3.docx
Experiment 3:
Student name:
Pre-lab section:
1) Introduction: Explain the theory behind this experiment in a paragraph between 150 and 250 words. (2.5 Points)
Suppose you are using external resources; include the reference. It would be best if you had any relevant formulas and explanations of each term. You may use the rich formula tools embedded here.
2) Hypothesis: In an If /Then statement, highlight the purpose of the experiment.
For instance: If two same shape objects with different masses are dropped from the same height, they will hit the ground simultaneously. (2 points)
Post-lab section:
3) Attach an image of your signed data sheet here. (3 Points)
4) Attach your analysis here, including any table, chart, or plot image. (4 points)
This should include
Table 1: 3 points
Table 2: 1 point
Table 3: 1 point
5) Attach the image of samples of your calculation here. (2 points)
6) In a paragraph between 100 and 150 words, explain what you Learn. What conclusion can you draw from the results of this lab assignment? (2 points)
7) In one sentence, compare the results of the experiment with your Hypothesis. Why? (1 point)
8) Attach your response to the questions in the lab manual here. (5 points)
Question 1: 3 points (each part, 0.5 points)
Question 2: 1 point
Question 3: 1 point
PHY2048LExp3Theory.pdf
Illustration and equations
Decompose motion into two motions: Along y-axis: Motion with initial velocity ϑ
0 y = ϑ 0 sinθ under accelerationg . Along x-axis: Motion with initial velocity ϑ
0 x = ϑ 0cosθ with no acceleration.
Studying the motions along the two axes
Motion along y-axis: Follows Newton’s second law, as it has accelerationg owing to
gravitational force acting downwards along y-axis.
Governed by Eqn. (5): y = y 0 + (ϑ
0 sinθ)t−
1
2 g t
2 .
Solving Eqn. (5), we find total time of flightT , which gives the stopping condition for overall projectile motion.
NOTE: ThisT is different from the instantaneous time t .
Motion along x-axis: Follows Newton’s first law, as there is no force in x-direction. Velocity in x-direction does not change. Range of flight R is
given by using total flight timeT in Eqn. (4): R= (ϑ 0 cosθ)T .
Experimental setup and procedure
Measure initial shooting height and height of timing pad from ground to findy
0
with ruler.
Measure launching angle θ from the angular graduation on projectile launcher.
Measure range of flight R with a tape measure.
Measure initial velocity v 0 and the total flight time T with
computer.
Computation of ymax Motion in y-direction is guided only by gravity it is similar to→
throwing something upwards. Hence, the y-component of velocityϑ y becomes
instantaneously 0 at topmost point of flight. Then, we have: ϑ y = 0 when y = ymax . Substituting this fact in Eqn. (3) : ϑ y 2 = ϑ
0 y
2 − 2g( y − y 0 )
we then obtain: 0 = ϑ
0 y
2 − 2 g( ymax − y 0 )
Solving for ymax , we then get:
ymax = y 0 + ϑ 0 y
2
2 g
End of Theory
PHY2048LExp3Dataandinstructions28129.pdf
Provided data for Exp 3 and instructions for data analysis and lab report
1. Provided data for Exp 3 are given in Table A (attached below).
2. Instruction for data analysis
(a) Calculate the average values of “Initial speed ( 0 (m/s)”, “Flight Time T (s)”, “Flight Range R (m)”
for all of the 4 measurements, and record them in the corresponding boxes in Table A.
(b) Fill out the portion of “Measured quantities” in Table B with the corresponding data from Table A.
(c) Fill out the portion of “Quantities Related to the measured quantities” in Table B with your
answers using the concepts reviewed in the theory section of Exp 3.
(d) Calculate maxy (see Fig. 1) using Eq. (3) & the measured values of ,
0 from Table A. Record
the calculated values of maxy in Table C.
3. Instructions for lab report
(a) Tables A, B and C with all the analyzed data must be included in your Exp 3 lab report.
(b) Answers to the 3 questions at the end of Exp 3 lab manual must be included in your Exp 3 report.
(c) Other required contents and format for your lab report can be found in the syllabus.
Table A: Data from Measurements #1 to #4.
Height from floor to shooting point = 1.004 m
Height from floor to top of timing pad = 0.014 m Short or medium Angle
Repeat # Initial speed
0 (m/s)
Flight Time
T (s)
Flight Range
R (m)
Short
Measurement #1
0
degree
1 3.319 0.426 1.371
2 3.332 0.427 1.373
3 3.327 0.426 1.376
Average
Medium
Measurement #2
0
degree
1 4.958 0.421 2.071
2 4.948 0.418 2.080
3 4.960 0.419 2.091
Average
Short
Measurement #3
30
degree
1 3.209 0.594 1.742
2 3.216 0.593 1.744
3 3.222 0.594 1.751
Average
Short
Measurement #4
45
degree
1 3.167 0.708 1.735
2 3.167 0.708 1.736
3 3.169 0.707 1.734
Average
Table B: Analysis on the equality of flight times obtained from Measurements #1 and #2.
Measurements #1 Measurements #2
Measured
quantities
Average flight time T (s)
Average flight range R (m)
Average initial speed 0 (m/s)
Initial height y0 (m)
Quantities
Related to
the
measured
quantities
xF on the ball
yF on the ball
xa of the ball
ya of the ball
Type of motion in x direction Type of motion in y direction
Table C: Determination of maxy (Fig. 1) from the measured values of ,
0 and using Eq. (3).
00 030 045
maxy
Report3.docx
Experiment 3:
Student name:
Pre-lab section:
1) Introduction: Explain the theory behind this experiment in a paragraph between 150 and 250 words. (2.5 Points)
Suppose you are using external resources; include the reference. It would be best if you had any relevant formulas and explanations of each term. You may use the rich formula tools embedded here.
2) Hypothesis: In an If /Then statement, highlight the purpose of the experiment.
For instance: If two same shape objects with different masses are dropped from the same height, they will hit the ground simultaneously. (2 points)
Post-lab section:
3) Attach an image of your signed data sheet here. (3 Points)
4) Attach your analysis here, including any table, chart, or plot image. (4 points)
This should include
Table 1: 3 points
Table 2: 1 point
Table 3: 1 point
5) Attach the image of samples of your calculation here. (2 points)
6) In a paragraph between 100 and 150 words, explain what you Learn. What conclusion can you draw from the results of this lab assignment? (2 points)
7) In one sentence, compare the results of the experiment with your Hypothesis. Why? (1 point)
8) Attach your response to the questions in the lab manual here. (5 points)
Question 1: 3 points (each part, 0.5 points)
Question 2: 1 point
Question 3: 1 point
PHY2048LExp3Theory.pdf
Illustration and equations
Decompose motion into two motions: Along y-axis: Motion with initial velocity ϑ
0 y = ϑ 0 sinθ under accelerationg . Along x-axis: Motion with initial velocity ϑ
0 x = ϑ 0cosθ with no acceleration.
Studying the motions along the two axes
Motion along y-axis: Follows Newton’s second law, as it has accelerationg owing to
gravitational force acting downwards along y-axis.
Governed by Eqn. (5): y = y 0 + (ϑ
0 sinθ)t−
1
2 g t
2 .
Solving Eqn. (5), we find total time of flightT , which gives the stopping condition for overall projectile motion.
NOTE: ThisT is different from the instantaneous time t .
Motion along x-axis: Follows Newton’s first law, as there is no force in x-direction. Velocity in x-direction does not change. Range of flight R is
given by using total flight timeT in Eqn. (4): R= (ϑ 0 cosθ)T .
Experimental setup and procedure
Measure initial shooting height and height of timing pad from ground to findy
0
with ruler.
Measure launching angle θ from the angular graduation on projectile launcher.
Measure range of flight R with a tape measure.
Measure initial velocity v 0 and the total flight time T with
computer.
Computation of ymax Motion in y-direction is guided only by gravity it is similar to→
throwing something upwards. Hence, the y-component of velocityϑ y becomes
instantaneously 0 at topmost point of flight. Then, we have: ϑ y = 0 when y = ymax . Substituting this fact in Eqn. (3) : ϑ y 2 = ϑ
0 y
2 − 2g( y − y 0 )
we then obtain: 0 = ϑ
0 y
2 − 2 g( ymax − y 0 )
Solving for ymax , we then get:
ymax = y 0 + ϑ 0 y
2
2 g
End of Theory
PHY2048LExp3Dataandinstructions28129.pdf
Provided data for Exp 3 and instructions for data analysis and lab report
1. Provided data for Exp 3 are given in Table A (attached below).
2. Instruction for data analysis
(a) Calculate the average values of “Initial speed ( 0 (m/s)”, “Flight Time T (s)”, “Flight Range R (m)”
for all of the 4 measurements, and record them in the corresponding boxes in Table A.
(b) Fill out the portion of “Measured quantities” in Table B with the corresponding data from Table A.
(c) Fill out the portion of “Quantities Related to the measured quantities” in Table B with your
answers using the concepts reviewed in the theory section of Exp 3.
(d) Calculate maxy (see Fig. 1) using Eq. (3) & the measured values of ,
0 from Table A. Record
the calculated values of maxy in Table C.
3. Instructions for lab report
(a) Tables A, B and C with all the analyzed data must be included in your Exp 3 lab report.
(b) Answers to the 3 questions at the end of Exp 3 lab manual must be included in your Exp 3 report.
(c) Other required contents and format for your lab report can be found in the syllabus.
Table A: Data from Measurements #1 to #4.
Height from floor to shooting point = 1.004 m
Height from floor to top of timing pad = 0.014 m Short or medium Angle
Repeat # Initial speed
0 (m/s)
Flight Time
T (s)
Flight Range
R (m)
Short
Measurement #1
0
degree
1 3.319 0.426 1.371
2 3.332 0.427 1.373
3 3.327 0.426 1.376
Average
Medium
Measurement #2
0
degree
1 4.958 0.421 2.071
2 4.948 0.418 2.080
3 4.960 0.419 2.091
Average
Short
Measurement #3
30
degree
1 3.209 0.594 1.742
2 3.216 0.593 1.744
3 3.222 0.594 1.751
Average
Short
Measurement #4
45
degree
1 3.167 0.708 1.735
2 3.167 0.708 1.736
3 3.169 0.707 1.734
Average
Table B: Analysis on the equality of flight times obtained from Measurements #1 and #2.
Measurements #1 Measurements #2
Measured
quantities
Average flight time T (s)
Average flight range R (m)
Average initial speed 0 (m/s)
Initial height y0 (m)
Quantities
Related to
the
measured
quantities
xF on the ball
yF on the ball
xa of the ball
ya of the ball
Type of motion in x direction Type of motion in y direction
Table C: Determination of maxy (Fig. 1) from the measured values of ,
0 and using Eq. (3).
00 030 045
maxy