Power, Efficiency, and Potential EnergyClass 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: WA = 1000 kg, vA = 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

• x1 and x2 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.