Unit 5 - Work and EnergyCHAPTER 8 CONCEPTUAL PHYSICS BOOKCHAPTER 6 PHYSICS BOOK

Part 2CONSERVATION OF ENERGY AND POWER

Conservative vs. Nonconservative Forces

Conservative force – total Work on a closed path is zero. (ex: gravity)

Nonconservative force – total Work on a closed path is NOT zero. (ex: friction)

Energy

3

-W +W

-W

-W

Gravity- downMotion- up

Friction – leftMotion - right

Friction - rightMotion- left

Gravity- downMotion- down

Conservation of Energy

Law of Conservation of Energy – Energy cannot be created or destroyed, only converted from one form to another.

This means the amount of energy when everything started is still the amount of energy in the universe today! (Just in different forms!)

Conservation of Mechanical Energy

If non-conservative forces are NOT present (or are ignored) the total Mechanical Energy initially is equal to the total Mechanical Energy final.

OR

Conceptual Example 1: Pendulum

Pendulum - Kinetic and Potential Energy In the absence of air resistance and friction…

the pendulum would swing forever example of conservation of mechanical energy Potential → Kinetic → Potential and so on…

In reality, air resistance and friction cause mechanical energy loss, so the pendulum will eventually stop.

Conceptual Example 2: Roller Coaster Roller Coaster - Kinetic and Potential Energy

With Non-Conservative Forces…

If non-conservative forces (such as friction or air resistance) ARE present:

Be careful: Work done by friction is always negative! (Friction always opposes the motion)

So if friction is present, there is mechanical energy loss. (The energy is converted into heat and sound.)

Conceptual Example 3: Downhill Skiing Downhill Skiing - Kinetic and Potential Energy

This animation neglects friction and air resistance until the bottom of the hill.

Friction is provided by the unpacked snow. Mechanical energy loss (nonconservative force) Negative work

Problem Solving Insights

Determine if non-conservative forces are included. If yes: MEf = ME0 + Wnc (We won’t be solving this

type) If no: MEf = ME0

Eliminate pieces that are zero before solving Key words: starts from rest (KE0 = 0), ends on the ground

(PEf = 0), etc.

Example 1

A 2.00kg rock is released from rest from a height of 20.0 m. Ignore air resistance & determine the kinetic, potential, & mechanical energy at each of the following heights: 20.0 m, 12.0m, 0m (Round g to 10 m/s2 for ease)

Example 1 - Answers

Height KE PE ME

20.0 m 0 J 2*10*20 = 400 J 400 J

12.0 m 400-240 = 160 J 2*10*12 = 240 J 400 J

0 m 400-0 = 400 J 2*10*0 = 0 J 400 J

Start Here

ThenUseThis

Energy

13Example 2

Find the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations below. ma

x

14Example 2 - Answers

1. , so

2. , so

so

3. at the top, so

so

Power

Power: Rate of doing work. The work done per unit time.

Equation: P is power (Watts, ft lb/s , ft lb/min)

Horsepower: another unit for measuring power. 1 horsepower = 746 Watts (or 1 horsepower = 550 ftlb/s)

Power Example #1

A weight lifter lifts a 75 kg weight from the ground to a height of 2.0 m. He performs this feat in 1.5 seconds. Find the weight lifter’s average power in A) Watts and B)Horsepower.

A. B.

Power Example #2

A runner sprints 100 m in 25 seconds. Her average power during this run is 800 Watts. Find the force that the runner exerts during the run.

Power Example #3

A car accelerates from rest to 20.0 m/s is 5.6 seconds along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if the weight of the car is 9,000 N

Power Example #4

Bob pushes a box across a horizontal surface at a constant speed of 1 m/s. If the box has a mass of 30 kg, find the power Bob supplies if the coefficient of kinetic friction is 0.3.

Since a=0, the pushing force must be equal to the kinetic friction.

1 m/s implies that after 1 second the distance is 1 meter, so…