Power, Efficiency, and Potential Energy Class Lectures 11: 3.6 & 7 Today’s Objective 1.Power and Efficiency 2.Potential Energy 3.Conservation of Energy Method

Power Power is defined as the rate at which work is done, Units of power are: Watts and HP

Efficiency Efficiency is defined as the ratio of work output to the work input: If there are energy losses due to electrical and thermal energy, the resultant efficiency is the product of all.

Problem 3/131 Given: W A = 1000 kg, v A = 3 m/s upward Required: Power required for the motor, if the efficiency e = 0.8

Potential Energy Two types of potential Energy: 1.Gravitational potential energy 2.Elastic potential energy Gravitational potential Energy Potential energy is measured from a datum plane Datum can be selected arbitrarily If the Particle’s position is above the Datum, it has a positive potential energy and if its position is below the datum it has a negative potential energy

Potential Energy Potential energy can be converted to work Potential energy = work done by the weight As the potential energy is used up, it decreases in value and produces positive work, thus The increase in potential energy will produce a negative work, and vice versa.

Potential Energy Elastic potential energy When a spring is extended or compressed, it stores a positive potential energy The stored potential energy = potential work by the spring force x 1 and x 2 are the initial and final deflections in the spring.

Work and Energy Equation The equation for work energy with the potential energy included can be written as, Expanding it, we can write, Work energy equation

Conservation of Energy If the forces are conservative, i.e., independent of the path travelled (non-conservative forces: forces produced by friction, heat, sound, etc.), then, conservation of energy equation

Problem 3/139 Given: 2-lb collar released from rest at A. No friction. k = 1.6 lb/ft, upstretched length = 15 in. Required: Velocity at point B

Problem 3/141 Given: released from rest at position A. Neglect friction Required: Velocity at B, Maximum deflection in the spring

Problem 3/152 Given: Released from rest. Neglect friction Required: Speed of mass A and B after B moved 1 m.

Midterm Exam Review Date and Time: Thursday, March 5, 2015 Time:4:30 – 5:45 Material Covered: Chapters 1, 2, and 3 Number of Problems: 8 – 10 How graded: 1. No partial credit given for solutions based on wrong concepts. 2. Partial credit given only if there is a math error.