Chapter 5 notes

Exam answers : 

Exam answers

Exam answers : 

Exam answers

Exam answers : 

Exam answers

Announcements : 

Announcements Homework for Monday… (Ch. 5, Probs 6, 27, & 28) Office hours… MTWRF 11-noon

Chapter 5 : 

Chapter 5 Energy

Energy overview… : 

Energy overview… “It is important to realize that in physics today, we have no knowledge of what energy is.” Richard Feynmann Nobel Laureate The Newtonian formalism of Mechanics was unrivaled for over a hundred years. Beginning of 1800’s saw the advent of the concept of energy, which had enormous predictable power. Law of Conservation of Energy Scalars versus Vectors

Energy overview… : 

Energy overview… Energy… Property of all matter, not an entity in and of itself Force is the agent of change, Energy is a measure of the change

Different forms of Energy : 

Different forms of Energy Kinetic Potential Thermal Light (radiant) Sound

Section 5.1:Work : 

Section 5.1:Work 1D case… Work done on the body is positive since the direction of the force is the same as the displacement. What are the units of W? 

Work (done by a constant force) : 

Work (done by a constant force) 2D case… NOTICE:  is the angle between vectors ‘tail-to-tail’ What angle yields the maximum work? What angle yields the minimum work?

Quiz Question 1 : 

Quiz Question 1 A crate moves to the right on a horizontal surface as a woman pulls on it with a 10 N force. Rank the situations shown below according to the work done by the 10 N force, least to greatest. The displacement is the same for all cases. 1, 2, 3 2, 1, 3 2, 3, 1 1, 3, 2 3, 2, 1 10N 10N

Work done by Friction : 

Work done by Friction The block undergoes a displacement by sliding down the incline. What is the work done by friction? What is the work done by the normal force?

Dissipative Forces : 

Dissipative Forces Energy is ‘lost’ to friction by an object which goes into… … heating (both the object and its environment) … sound Friction is a dissipative or nonconservative force

Serway: Prob. 5 : 

Serway: Prob. 5 Starting from rest, a 5.00-kg block slides 2.50 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is k=0.436. Determine the work done by the force of gravity the work done by the friction force between the block and incline, and the work done by the normal force.

Section 5.2: Kinetic Energy & the Work-Energy Theorem : 

Section 5.2: Kinetic Energy & the Work-Energy Theorem Kinetic Energy The kinetic energy of a mass m moving with a velocity v Units? That’s all there is to it!

Work-Energy Theorem : 

Work-Energy Theorem Using the definition of KE, W becomes TOTAL work done on a body by all forces Change in kinetic energy of the body

Serway: Prob. 5 revisited.. : 

Serway: Prob. 5 revisited.. Starting from rest, a 5.00-kg block slides 2.50 m down a rough 30.0° incline. The coefficient of kinetic friction between the block and the incline is k=0.436. Determine the work done by the force of gravity the work done by the friction force between the block and incline, and the work done by the normal force. the total work done on the block. the speed of the block at 2.50 m

Work done by Gravity : 

Work done by Gravity What is the work done by gravity on the box which slides down the incline a distance ?

Conservative and Nonconservative forces : 

Conservative and Nonconservative forces Nonconservative force… Generally dissipative Work done by a nonconservative force depends on the path i.e. friction Conservative force… Work done by a conservative force is independent of the path Work they do can be recast as potential energy i.e. gravity

Quiz Question 2 : 

Quiz Question 2 The work done by gravity during the descent of a projectile is: positive negative zero sign depends on the direction of the y-axis sign depends on the direction of both the x- and y-axes.

Quiz Question 3 : 

Quiz Question 3 A baseball is hit high into the upper bleachers of left field. Over its entire flight, the work done by gravity and the work done by air resistance, respectively, are: positive; positive positive; negative negative; positive negative; negative unknown since vital information is lacking

Work-Energy Theorem : 

Work-Energy Theorem A rock is dropped off of a cliff from a height y. Calculate the work done by gravity by using the definition of work and the work-energy theorem. v y

Gravitational Potential Energy : 

Gravitational Potential Energy The work required to lift a box of mass m a height y is Wc = mgy. Where does this work go?  into Potential Energy y

Gravitational Potential Energy cont.. : 

Gravitational Potential Energy cont.. Notice: Potential energy is stored energy waiting to be ‘let loose’. Potential energy is a relative energy… The zero-reference level is arbitrary & must be chosen. Can only measure a change in PE.

Conservation of Mechanical Energy : 

Conservation of Mechanical Energy In any isolated system of objects interacting only through conservative forces, the total mechanical energy E = KE + PE, of the system, remains the same at all times

Quiz Question 4 : 

Quiz Question 4 Three identical balls are thrown from the top of the building, all with the same initial speed. The first ball is thrown horizontally, the second at some angle above the horizontal, and the third at some angle below the horizontal. Neglecting air resistance, rank the speeds of the balls as they reach the ground, from fastest to slowest. 1, 2, 3 2, 1, 3 3, 1, 2 All three balls strike the ground at the same speed

Quiz Question 5 : 

Quiz Question 5 Bob, of mass m, drops from a tree limb at the same time that Alice, also of mass m, begins her descent down a frictionless slide. If they both start at the same height above the ground, which of the following is true about their kinetic energies as they reach the ground? Bob’s KE is greater than Alice’s. Alice’s KE is greater than Bob’s. They have the same KE. The answer depends on the shape of the slide.

i.e. 5.5 : 

i.e. 5.5 Calculate the speed of a body falling straight down in the presence of gravity using… Conservation of Mechanical Energy the Kinetic Equations

Section 5.4:Spring Potential Energy : 

Section 5.4:Spring Potential Energy Hooke’s Law gives the force of a spring where k is the spring constant. Fs is a restoring force k depends on the properties of the spring

Elastic Potential Energy : 

Elastic Potential Energy The elastic potential energy associated with the spring force is In the absence of nonconservative forces, Conservation of Mechanical Energy becomes

Demo Question… : 

Demo Question… Immediately after I let go of the top of the spring, will the bottom of the spring move upwards move downwards remain stationary?

Energy Conservation : 

Energy Conservation This equation can be rearranged into the following forms… Energy “lost” (i.e. converted to heat, sound, light, etc.) Negative or ~0

How to solve ‘Conservation of Mechanical Energy’ problems… : 

How to solve ‘Conservation of Mechanical Energy’ problems… Pick a body Pick initial and final points of motion

Problem 1 : 

Problem 1 For a block of mass m to slide without friction up the ramp shown, it must have a minimum initial speed of: h  v0

Problem 2 : 

Problem 2

Section 5.6: Power : 

Section 5.6: Power Average Power is work done in a time t What are the units of Power?

Human Energy Consumption : 

Human Energy Consumption

Quiz Question 7 : 

Quiz Question 7 An escalator is used to move 20 people (~60 kg each) per minute from the 1st floor of a department store to the 2nd floor, h = 5m above. The power required is approximately? 100 W 200 W 1000 W 2000 W 60,000 W h 30

Quiz Question 8 : 

Quiz Question 8 What is the power output of a 70 kg sprinter who accelerates from rest to 10 m/s in 3.0 s? 120 W 230 W 1200 W 2100 W 10,500 W