Chapter 5: Work and Energy

Today’s Objectives

What do you think? List five examples of things you have done in the last year that you would consider work. List five examples of things you have done in the last year that you would consider work. Based on these examples, how do you define work? Based on these examples, how do you define work?

Work In physics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force. In physics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force. W = F d

Work Done by a Constant Force What are the SI units for work? What are the SI units for work? Force units (N)  displacement units (m)Force units (N)  displacement units (m) N m are also called joules (J).N m are also called joules (J). How much work is 1 joule? How much work is 1 joule? Lifting an apple weighing about 1 N from the floor to the desk, a distance of about 1 m, is equivalent to 1 J of work.Lifting an apple weighing about 1 N from the floor to the desk, a distance of about 1 m, is equivalent to 1 J of work.

Question? How much work is done in pushing this Barack Obama Ice Statue with 20 N of Force a distance of 10 meters? How much work is done in pushing this Barack Obama Ice Statue with 20 N of Force a distance of 10 meters? Answer: Work = Fd (20 N) x (10 m) = 200 N x m

Question 2 No work on it. Why?! How much work is done carrying a 10 kg bag a distance of 10 meters? Work only depends on Force that is in the same direction as the movement!!!

Work What is the component of F in the direction of d? What is the component of F in the direction of d? F cos  If the angle is 90°, what is the component of F in the direction of d? If the angle is 90°, what is the component of F in the direction of d? F cos 90° = 0 If the angle is 0°, what is the component of F in the direction of d? If the angle is 0°, what is the component of F in the direction of d? F cos 0° = F How would you calculate the work in this case? More Accurate Equation Equation W = F d cos()

Work Done by a Constant Force Work done by forces that oppose the direction of motion, such as friction, will be negative. Centripetal forces perpendicular Centripetal forces do no work, because they are always perpendicular to the direction of motion.

How mu How much work is done by friction if the vacuum is 25 kg and the kinetic coefficient of friction is.4 when the vacuum is dragged across a rug 4 m?

Work is a Scalar Work can be positive or negative but does not have a direction. Work can be positive or negative but does not have a direction. What is the angle between F and d in each case? What is the angle between F and d in each case?

Now what do you think? Based on the physics definition, list five examples of things you have done in the last year that you would consider work. Based on the physics definition, list five examples of things you have done in the last year that you would consider work. (Show your List to Mr. P. before you leave.)

Energy is traditionally defined as the ability to do work. Energy appears in many forms. Light, Electricity, Nuclear Energy, Heat, and Mechanical Energy are all examples. Mechanical Energy is energy due to position or movement.

2 Types of Mechanical Energy Energy due to Motion Kinetic Energy – Energy due to Motion Any moving object has the ability to do work on another object. Therefore every moving object has Kinetic Energy. M = mass V 2 = velocity squared

2 Types of Mechanical Energy Potential Energy Potential Energy - energy due to position. Any object can have potential energy due to its position or because of its surroundings. Familiar examples of potential energy: A wound-up spring A stretched elastic band An object raised to some height over the ground

Water Mill

Gravitational Potential Energy Work is done in order to lift an object up off the ground: Work is done in order to lift an object up off the ground: W = Fd = (mg)h W = Fd = (mg)h By doing work on the object, we have given it energy. By doing work on the object, we have given it energy. We therefore define the gravitational potential energy: We therefore define the gravitational potential energy: P.E. = mgh m: massg: 9.8 m/s 2 h: height

Potential Energy This potential energy can become kinetic energy if the object is dropped. Potential energy is a property of a system as a whole, not just of the object (because it depends on external forces). We usually measure h from the ground. So at the ground, h = 0, which means the P. E. is zero.

Potential Energy Potential energy can also be stored in a spring when it is compressed; the figure below shows potential energy changing into kinetic energy.

Weekly Homework Due on Tuesday Pg. 184 #’s: 1, 7, 8, 9, 12, 19, 21, 23, 33

Recap – so far… Work = Fd(cos ) Work = Fd(cos ) Energy is the ability to do work. Energy is the ability to do work. Kinetic Energy – Energy due to motion – K.E. = 1/2mv 2 Kinetic Energy – Energy due to motion – K.E. = 1/2mv 2 Potential Energy – Energy due to position – (gravitational P.E. = mgh) Potential Energy – Energy due to position – (gravitational P.E. = mgh) Units for work and energy: joules (j) Units for work and energy: joules (j)

Kinetic Energy, and the Work- Energy Principle The amount of work that can be done on an object, is equal to the amount of kinetic energy or potential energy it gains or loses: If the net work is positive, energy increases. If the net work is negative, energy decreases. Work = change in energy

Kinetic Energy, and the Work-Energy Principle Because work and kinetic energy can be equated, they must have the same units: kinetic energy is measured in joules.

Mechanical Energy and Its Conservation Energy cannot be created or destroyed. It can only transfer from one form to another or be passed from one object into another. This is the Law of conservation of energy. bowling ball pendulum ball Bowling Ball Pendulum – You Tube

Pendulum Analysis Questions Where does the bowling ball in the pendulum have the highest velocity? Where does the bowling ball in the pendulum have the highest velocity? How does the original height of the pendulum compare to its final height before it begins to come back? How does the original height of the pendulum compare to its final height before it begins to come back? Is energy in the pendulum? Why or why not? Is energy conserved in the pendulum? Why or why not?

Conservation of Energy in a Pendulum

Energy Conservation Example 2 Roller Coasters!!! Another Example: /Dynamics/Coaster/CoasterApplet.html

Energy Conservation Example 3

Other Forms of Energy; Energy Transformations and the Conservation of Energy Work is done whenever energy is transferred from one object to another. Work is also done whenever energy changes forms. Accounting for all forms of energy, we find that the total energy neither increases nor decreases. Energy as a whole is conserved.

30 Power Power is the rate at which work is done. Power is the rate at which work is done. Power = Work * /Time Power = Work * /Time * (force x distance) * (force x distance) The unit of power is the watt. The unit of power is the watt.