# Wheel and Axle Lab Report

By djvoice
Nov 27, 2011
596 Words

HERIOT-WATT UNIVERSITY SCHOOL OF ENGINEERING AND PHYSICAL SCIENCES (MECHANICAL ENGINEERING) MECHANICAL ENGINEERING SCIENCE 3 (B58EC1) DYNAMICS LABORATORY : WHEEL AND AXLE ACCELERATION

Objective: To predict the time taken for a wheel to roll on its axle, down a slope using energy methods Theory: Energy Method Release Ød or radius r After descent h v m/sec m kg I kg.m2 ØD or radius R

Figure 1. Energy in a rolling wheel Referring to Figure 1 when the wheel is released from rest and subsequently rolls down the slope, it accelerates and hence gains energy. Now for a rolling wheel the kinetic energy has two components, translational due to the bodily movement of the mass centre down the slope and rotational due to the wheel spin. Now the source of this energy is the loss in potential energy as the wheel moves down the slope. If it is reasonable to assume that friction effects are insignificant then no energy is lost. Thus the loss in potential energy becomes a gain in kinetic energy. Hence, Loss in potential energy = mgh, is equal to the Gain in kinetic energy = 0.5mv2 + 0.5Iω 2 where v = velocity of the mass centre down slope (m/sec) ω = angular velocity of wheel (rad/sec) = v/r, r is the axle radius when rolling I = Polar moment of inertia = mR2/2 (1) (2)

Applying conservation of energy, equate equations 1 and 2 to derive an expression for the velocity v at the bottom of the slope. Using the linear equations of motion, find the expression for time t. Show these derivations in your report.

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Experiment: Using the measured distances (100mm to 500mm, intervals of 100mm) travelled by the wheel and the expressions i.e. (1) velocity at bottom of slope and (2) acceleration down the slope, calculate the time taken for the wheel to roll down the slope. Compare the calculated values with the experimental data Discussions: Plot a graph of time t2 vs distance s for calculated and experimental data. Explain the discrepancies between calculated values and experimental data. Discuss and quantify sources of errors. Report format: The report for the labs must have the following sections: Introduction – give a background to the subject and experiment Aim/Objective – describe the aim or objective of the experiment Theory – detailed description of the theory and engineering principles. All equations used in the calculations must be shown. Apparatus – a description and diagrams of the apparatus, diagrams must be fully labelled. All variables used in the theory section must be identified. Procedures – a detailed record of the execution of the experiment, that a person could repeat the experiment by reading it. Results – Tabulation of raw readings and the calculated ones. A sample calculation must be shown. Calculated and experimental values must be shown and %errors between them derived. Discussion – discuss on the results obtained. Compare between experimental and calculated results and discuss on the errors. Identify the sources of error and explain with calculations or theory involved. Listing errors without justification is not sufficient and this will not gain any marks. Conclusion – conclude if the aim or objective is achieved. References – Books or publications to support theory and discussion. Lecture notes cannot be used as reference. Identify where the materials are used in your report. Appendix (Optional) – any other information to support the report. Attendance to lab session is compulsory. Any report does not have all the above sections will be rejected and returned, and it will be considered as non-submission. Marks will be deducted for late submission.

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Objective: To predict the time taken for a wheel to roll on its axle, down a slope using energy methods Theory: Energy Method Release Ød or radius r After descent h v m/sec m kg I kg.m2 ØD or radius R

Figure 1. Energy in a rolling wheel Referring to Figure 1 when the wheel is released from rest and subsequently rolls down the slope, it accelerates and hence gains energy. Now for a rolling wheel the kinetic energy has two components, translational due to the bodily movement of the mass centre down the slope and rotational due to the wheel spin. Now the source of this energy is the loss in potential energy as the wheel moves down the slope. If it is reasonable to assume that friction effects are insignificant then no energy is lost. Thus the loss in potential energy becomes a gain in kinetic energy. Hence, Loss in potential energy = mgh, is equal to the Gain in kinetic energy = 0.5mv2 + 0.5Iω 2 where v = velocity of the mass centre down slope (m/sec) ω = angular velocity of wheel (rad/sec) = v/r, r is the axle radius when rolling I = Polar moment of inertia = mR2/2 (1) (2)

Applying conservation of energy, equate equations 1 and 2 to derive an expression for the velocity v at the bottom of the slope. Using the linear equations of motion, find the expression for time t. Show these derivations in your report.

Page 1/2

Experiment: Using the measured distances (100mm to 500mm, intervals of 100mm) travelled by the wheel and the expressions i.e. (1) velocity at bottom of slope and (2) acceleration down the slope, calculate the time taken for the wheel to roll down the slope. Compare the calculated values with the experimental data Discussions: Plot a graph of time t2 vs distance s for calculated and experimental data. Explain the discrepancies between calculated values and experimental data. Discuss and quantify sources of errors. Report format: The report for the labs must have the following sections: Introduction – give a background to the subject and experiment Aim/Objective – describe the aim or objective of the experiment Theory – detailed description of the theory and engineering principles. All equations used in the calculations must be shown. Apparatus – a description and diagrams of the apparatus, diagrams must be fully labelled. All variables used in the theory section must be identified. Procedures – a detailed record of the execution of the experiment, that a person could repeat the experiment by reading it. Results – Tabulation of raw readings and the calculated ones. A sample calculation must be shown. Calculated and experimental values must be shown and %errors between them derived. Discussion – discuss on the results obtained. Compare between experimental and calculated results and discuss on the errors. Identify the sources of error and explain with calculations or theory involved. Listing errors without justification is not sufficient and this will not gain any marks. Conclusion – conclude if the aim or objective is achieved. References – Books or publications to support theory and discussion. Lecture notes cannot be used as reference. Identify where the materials are used in your report. Appendix (Optional) – any other information to support the report. Attendance to lab session is compulsory. Any report does not have all the above sections will be rejected and returned, and it will be considered as non-submission. Marks will be deducted for late submission.

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