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.
The Essay on Renewable and Nonrenewable Energy
Energy can be explained as having the ability to do work. There are many forms of energy potential, electrical, chemical and magnetic just to name a few. Energy is used for everything an individual must do from preparing a meal to launching a rocket. There are two general categories of energy: potential energy and kinetic energy. Potential energy is energy that has been saved waiting to be ...
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.
The Term Paper on Nursing Theory 2
1. How does the Nursing Theory assist the practicing nurse in the delivery of care to patients? Explain your answer. Nursing theories are important to the lives of nurses because they help develop and understand further the nursing practice. These were formulated by the theorists because they believed that these will aid nurses in the holistic health care delivery and furthermore help in ...
