Lab 5

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31.05.2024
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Report5.docx
Atwoodsmachinelab5PowerPoint.pdf
Lab5dataandinstructions.pdf
Exp5_questions.pdf

Report5.docx

Experiment 5:

Student name:

Pre-lab section:

1) Introduction: Explain the theory behind this experiment in a paragraph between 150 and 250 words. (2 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. (1 point)

Post-lab section:

3) Attach an image of your signed data sheet here. (4 Points)

4) Attach your analysis here, including any table, chart, or plot image. (3 points)

Table 1 (3 point)

5) Attach the image of samples of your calculation here. (1 point)

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. (7 points)

Question 1: 1 point for each part, 0.5 points

Question 2: 1.5 points

Question 3: 1.5 points

Question 4: 2 points

Optional exercise: +1

Atwoodsmachinelab5PowerPoint.pdf

Concept of the experiment

Two masses slung over a pulley, linked through a string of negligible mass.

Since they are linked by string, they have the same magnitude of acceleration, with heavier mass moving downwards and lighter mass moving upwards.

Theoretical acceleration: Free body diagram

Key Idea: Draw each of the bodies separately, detached from the system, and draw all forces acting on it to find resultant force, and hence, resultant acceleration.

Deriving the equation for m2

For m2 :

Acceleration is upward Net force is upward Magnitude of tension is bigger than magnitude weight of m2 So equation is: T − m

2 g= m

2 a → T = m

2 g + m

2 a . (1)

Deriving the equation for m1

For m1 :

Acceleration is downwards Net force is downwards Magnitude tension is smaller than magnitude weight of m1 So equation is: m 1 g − T = m

1 a . (2)

Deriving the equation for acceleration a

Solving for acceleration a:

Substituting tension from (1) into (2), we get:

m 1 g −m

2 g − m

2 a = m

1 a

→ a = m 1 − m

m 1 + m

g (3)

NOTE: We use the values we get from this equation as the accepted values for computing the % errors in Table 1.

Outline of procedure

We will taking different values of masses for m1 and m2 and releasing the heavier mass to measure the acceleration.

In order to do so, we measure the change of velocity of the mass over time and then plot magnitude of velocity versus time, with the help of the computer. Then, we find the acceleration from the slope of the plot.

Slope → acc.

End of Theory

Lab5dataandinstructions.pdf

Provided data for Exp 5 and instructions for data analysis and lab report

1. Provided fitting data for Exp 5 are given in Fig. 1 in which the #’s correspond to the Measurement #.

Measurement #1: 1m = 0.060 kg,

2m = 0.050 kg

Measurement #2: 1m = 0.060 kg,

2m = 0.040 kg

Measurement #3: 1m = 0.055 kg,

2m = 0.045 kg

Measurement #4: 1m = 0.065 kg,

2m = 0.035 kg

2. Instruction for data analysis

(a) Determine (exp.)a from the fitting parameters shown in Fig. 1.

Record (exp.)a with its units in Table 1.

(b) Calculate (3)( .)calca from Eq. (3) using the values of

1m and 2m listed in column 1 of Table 1.

Record (3)( .)calca with its units in Table 1.

Attention: Point deduction will be given to your report if the recorded data have no units.

Record the % error in Table 1.

(#1)

(#3)

(#2)

(#4)

Figure 1 Plots and fittings of data from the 4 measurements in Exp 5

Table 1 Comparison of (exp.)a with (3)( .)calca

Measurement

Masses (kg)

Slope (exp.)a

(3)( .)calca

% error between

(exp.)a and (3)( .)calca

Measurement #1

1 m = 0.060,

2 m = 0.050

Measurement #2

1 m = 0.060,

2 m = 0.040

Measurement #3

1 m = 0.055,

2 m = 0.045

Measurement #4

1 m = 0.065,

2 m = 0.035

3. Instructions for lab report

(a) Tables 1 with all the analyzed data and units must be included in your Exp 5 lab report.

(d) The required other contents and format for your lab report can be found in the syllabus.

Report5.docx

Experiment 5:

Student name:

Pre-lab section:

1) Introduction: Explain the theory behind this experiment in a paragraph between 150 and 250 words. (2 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. (1 point)

Post-lab section:

3) Attach an image of your signed data sheet here. (4 Points)

4) Attach your analysis here, including any table, chart, or plot image. (3 points)

Table 1 (3 point)

5) Attach the image of samples of your calculation here. (1 point)

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. (7 points)

Question 1: 1 point for each part, 0.5 points

Question 2: 1.5 points

Question 3: 1.5 points

Question 4: 2 points

Optional exercise: +1

Atwoodsmachinelab5PowerPoint.pdf

Concept of the experiment

Two masses slung over a pulley, linked through a string of negligible mass.

Since they are linked by string, they have the same magnitude of acceleration, with heavier mass moving downwards and lighter mass moving upwards.

Theoretical acceleration: Free body diagram

Key Idea: Draw each of the bodies separately, detached from the system, and draw all forces acting on it to find resultant force, and hence, resultant acceleration.

Deriving the equation for m2

For m2 :

Acceleration is upward Net force is upward Magnitude of tension is bigger than magnitude weight of m2 So equation is: T − m

2 g= m

2 a → T = m

2 g + m

2 a . (1)

Deriving the equation for m1

For m1 :

Acceleration is downwards Net force is downwards Magnitude tension is smaller than magnitude weight of m1 So equation is: m 1 g − T = m

1 a . (2)

Deriving the equation for acceleration a

Solving for acceleration a:

Substituting tension from (1) into (2), we get:

m 1 g −m

2 g − m

2 a = m

1 a

→ a = m 1 − m

m 1 + m

g (3)

NOTE: We use the values we get from this equation as the accepted values for computing the % errors in Table 1.

Outline of procedure

We will taking different values of masses for m1 and m2 and releasing the heavier mass to measure the acceleration.

Slope → acc.

End of Theory

Lab5dataandinstructions.pdf

Provided data for Exp 5 and instructions for data analysis and lab report

1. Provided fitting data for Exp 5 are given in Fig. 1 in which the #’s correspond to the Measurement #.

Measurement #1: 1m = 0.060 kg,

2m = 0.050 kg

Measurement #2: 1m = 0.060 kg,

2m = 0.040 kg

Measurement #3: 1m = 0.055 kg,

2m = 0.045 kg

Measurement #4: 1m = 0.065 kg,

2m = 0.035 kg

2. Instruction for data analysis

(a) Determine (exp.)a from the fitting parameters shown in Fig. 1.

Record (exp.)a with its units in Table 1.

(b) Calculate (3)( .)calca from Eq. (3) using the values of

1m and 2m listed in column 1 of Table 1.

Record (3)( .)calca with its units in Table 1.

Attention: Point deduction will be given to your report if the recorded data have no units.

Record the % error in Table 1.

(#1)

(#3)

(#2)

(#4)

Figure 1 Plots and fittings of data from the 4 measurements in Exp 5

Table 1 Comparison of (exp.)a with (3)( .)calca

Measurement

Masses (kg)

Slope (exp.)a

(3)( .)calca

% error between

(exp.)a and (3)( .)calca

Measurement #1

1 m = 0.060,

2 m = 0.050

Measurement #2

1 m = 0.060,

2 m = 0.040

Measurement #3

1 m = 0.055,

2 m = 0.045

Measurement #4

1 m = 0.065,

2 m = 0.035

3. Instructions for lab report

(a) Tables 1 with all the analyzed data and units must be included in your Exp 5 lab report.

(d) The required other contents and format for your lab report can be found in the syllabus.

Report5.docx

Experiment 5:

Student name:

Pre-lab section:

1) Introduction: Explain the theory behind this experiment in a paragraph between 150 and 250 words. (2 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. (1 point)

Post-lab section:

3) Attach an image of your signed data sheet here. (4 Points)

4) Attach your analysis here, including any table, chart, or plot image. (3 points)

Table 1 (3 point)

5) Attach the image of samples of your calculation here. (1 point)

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. (7 points)

Question 1: 1 point for each part, 0.5 points

Question 2: 1.5 points

Question 3: 1.5 points

Question 4: 2 points

Optional exercise: +1

Atwoodsmachinelab5PowerPoint.pdf

Concept of the experiment

Two masses slung over a pulley, linked through a string of negligible mass.

Since they are linked by string, they have the same magnitude of acceleration, with heavier mass moving downwards and lighter mass moving upwards.

Theoretical acceleration: Free body diagram

Key Idea: Draw each of the bodies separately, detached from the system, and draw all forces acting on it to find resultant force, and hence, resultant acceleration.

Deriving the equation for m2

For m2 :

Acceleration is upward Net force is upward Magnitude of tension is bigger than magnitude weight of m2 So equation is: T − m

2 g= m

2 a → T = m

2 g + m

2 a . (1)

Deriving the equation for m1

For m1 :

Acceleration is downwards Net force is downwards Magnitude tension is smaller than magnitude weight of m1 So equation is: m 1 g − T = m

1 a . (2)

Deriving the equation for acceleration a

Solving for acceleration a:

Substituting tension from (1) into (2), we get:

m 1 g −m

2 g − m

2 a = m

1 a

→ a = m 1 − m

m 1 + m

g (3)

NOTE: We use the values we get from this equation as the accepted values for computing the % errors in Table 1.

Outline of procedure

We will taking different values of masses for m1 and m2 and releasing the heavier mass to measure the acceleration.

Slope → acc.

End of Theory

Lab5dataandinstructions.pdf

Provided data for Exp 5 and instructions for data analysis and lab report

1. Provided fitting data for Exp 5 are given in Fig. 1 in which the #’s correspond to the Measurement #.

Measurement #1: 1m = 0.060 kg,

2m = 0.050 kg

Measurement #2: 1m = 0.060 kg,

2m = 0.040 kg

Measurement #3: 1m = 0.055 kg,

2m = 0.045 kg

Measurement #4: 1m = 0.065 kg,

2m = 0.035 kg

2. Instruction for data analysis

(a) Determine (exp.)a from the fitting parameters shown in Fig. 1.

Record (exp.)a with its units in Table 1.

(b) Calculate (3)( .)calca from Eq. (3) using the values of

1m and 2m listed in column 1 of Table 1.

Record (3)( .)calca with its units in Table 1.

Attention: Point deduction will be given to your report if the recorded data have no units.

Record the % error in Table 1.

(#1)

(#3)

(#2)

(#4)

Figure 1 Plots and fittings of data from the 4 measurements in Exp 5

Table 1 Comparison of (exp.)a with (3)( .)calca

Measurement

Masses (kg)

Slope (exp.)a

(3)( .)calca

% error between

(exp.)a and (3)( .)calca

Measurement #1

1 m = 0.060,

2 m = 0.050

Measurement #2

1 m = 0.060,

2 m = 0.040

Measurement #3

1 m = 0.055,

2 m = 0.045

Measurement #4

1 m = 0.065,

2 m = 0.035

3. Instructions for lab report

(a) Tables 1 with all the analyzed data and units must be included in your Exp 5 lab report.

(d) The required other contents and format for your lab report can be found in the syllabus.

other Questions(10)