Energy, Work, and Power

What is Energy? Energy, in physics, is defined as the capacity to do work. There are many different forms of energy. List some types of energy… In this chapter, we are going to focus on gravitational potential and kinetic energy.

If energy is the ability to do work, what is work? Mechanical energy transferred by a force (e.g. gravitational force, friction, applied force) acting on an object over a measured displacement I.e., if work is done on an object, the object’s mechanical energy changes as a result. Measured in Newton∙Metres (N∙m) or Joules (J) Scalar quantity Is work being done in these pictures? What force is doing work? What on?

Defining Work: When Force is Constant W = F Δd cosθ W = Work (N∙m or J) F = Force doing the work (N) Δd = displacement (m) Θ = angle between F and Δd when placed tail to tail, always less than 180˚

Positive Work W = F Δd cosθ When W > 0, the object has gained mechanical energy due to the force acting on it. W = F Δd cosθ If 0 ≤ θ < 90˚ (i.e., the force has a component that acts in the same direction as the displacement) Identify situations in which positive work is done.

Zero Work When W = 0, zero mechanical energy has been transferred to the object W = F Δd cosθ If F = 0 If Δd = 0 If θ = 90˚ (i.e., F Δd) Describe situations in which zero work is done.

Negative Work W = F Δd cosθ When W < 0, the object has lost mechanical energy due to the force acting on it W = F Δd cosθ If 90˚< θ ≤ 180˚ (i.e., the force has a component that acts in the opposite direction as the displacement) Describe situations in which zero work is done.

Work Examples A 0.90 kg book on a level table is pushed with a force of 15 N over a distance of 6.0 m. A force of friction of 2.0 N opposes this motion. How much work does the normal force do on the book? How much work does the applied force do on the book? How much work does friction do on the book?

Work Examples A hockey puck (m = 0.20 kg) slides along a patch of rough ice (µk = 0.060) and stops after travelling for 25 m. Draw a FBD for the puck. Determine the work done by the friction. What work is done by the normal force?

Defining Work: When Force Varies When force varies over the displacement, the work done is the area beneath the force-displacement graph Positive area = positive work done Negative area = negative work done

Homework on Work Pg. 229 # 1-5, 7-8

Kinetic Energy Kinetic Energy (Ek) is the energy of an object due to its motion. Ek = ½ mv2 Ek = kinetic energy (J) m = mass (kg) v = velocity (m/s)

KE Example A 95 g donut falls from a table and hits the floor. The maximum KE of the donut during its fall is 2.6 J. When does the donut achieve maximum KE? Calculate the donut’s maximum speed.

KE Conceptual Questions As a car leaves a small town, the driver presses on the accelerator until the speed doubles. By what factor did the car’s kinetic energy increase? Two cars are travelling at the same speed. Car A is twice the mass of car B. How does car A’s KE compare to car B’s?

KE Conceptual Questions Examine the pictures which follow, and answer the following questions: Which object has the greatest velocity? Work is being done on which of the objects in the photos? What force is doing the work in each case? Which objects are probably losing kinetic energy? Which object has the greatest amount of kinetic energy?

KE Conceptual Questions

Relating Kinetic Energy & Work W = ΔEk Assumptions: All work done gives the system kinetic energy only Constant force provides constant acceleration Force and displacement are parallel The formula for kinetic energy is derived using work

Homework on Kinetic Energy Pg. 207, 11A-D Pg. 216, 19-21 Pg. 226, 23-26

Gravitational Potential Energy Gravitational Potential Energy (Eg) is the energy of an object because of its position relative to a lower position. Δ Eg = mg Δh Δ Eg = change in gravitational potential energy (J) m = mass (kg) Δh = change in height (m)

GPE Examples Jose Guerra, an 85 kg Olympic diver from Cuba, climbs to the top of a diving platform at constant velocity. As a result, he gains 15 kJ of energy, with respect to the ground. How high is the platform from the ground?

The Importance of Reference Points Δ Eg = mg Δh E.g. A 75 kg skydiver jumps from a plane 1.5 km from the ground. What is her GPE with respect to: a) the airplane? b) the ground? The amount of GPE an object has is relative.

W = ΔEg Relating GPE and Work Assumptions: Work done gives system GPE only Object is lifted at constant velocity Force and displacement are parallel (θ = 0º) The formula for gravitational potential energy is derived using work.

GPE Conceptual Questions Object A has twice the mass of object B. B is 4.0 m above the ground, and A is 2.0 m above the ground. Which has the greater amount of GPE? For A and B of the previous question: Both A and B are lowered 1.0 m. Which has the greater amount of GPE now?

GPE Conceptual Questions You carry a heavy box up a flight of stairs at constant velocity. Your friend carries an identical box on an elevator to reach the same floor as you. Who did the greatest amount of work (against gravity)? Explain.

GPE Conceptual Questions Examine the pictures which follow, and answer the following questions: What object do you think has the greatest amount of GPE? Which objects clearly illustrate that GPE may be converted into KE? What other forms of potential energy can you think of, besides GPE?

GPE Conceptual Questions

Homework on GPE p. 235 # 3-6

Law of Conservation of Energy Energy is neither created nor destroyed. It may only be converted from one form to another or transferred from one object to another.

Law of Conservation of Mechanical Energy The total mechanical energy is the sum of the gravitational and potential energy. Total mechanical energy is conserved (so long as work is done by conservative forces): ET = ET’ Eg + Ek = Eg’ + Ek’ ET = total mechanical energy (J) Eg = gravitational potential energy (J) Ek = kinetic energy (J)

Conservation Conceptual Questions How does the car’s total mechanical energy, kinetic energy, and gravitational potential energy compare A, B and C? A C B

Conservation of Mechanical Energy

Conservation of Mechanical Energy

Conservation Conceptual Question The masses of the cars in the picture below are identical. All four cars are released from rest simultaneously from point A. Which car is travelling the fastest by point B?

Example Problem An astronaut on the moon, stands on a cliff and drops a 20 kg boulder from a height of 30 m. On the moon, g is 1.6 N/kg. Use conservation of energy to calculate the speed of the boulder: a) Just before it hits the ground. b) 10 m from the top of the cliff.

Homework on Energy Conservation p. 241 # 1-3

Conservative and Non-Conservative Forces The box shown can travel any one of four paths to get to its final destination, shown. A then B C then D E F In the absence of friction, how does the amount of work done by gravity compare along each path? If friction is present, how does the amount of work is done by friction compare along each path?

Conservative and Non-Conservative Forces The work done by a conservative force does not depend on the length of the path taken. E.g. Gravity The work done by a non-conservative force depends on the length of the path taken. E.g. Friction, air resistance The longer the path, the more work done (more energy removed) from the system by the force.

Non-Conservative Forces, Work and Energy The amount of work done by the non-conservative force equals the change in the total mechanical energy of the system: Wnc=ET’-ET Wnc = Work done by non-conservative force (N·m) ET’= Total energy after interaction (J) ET = Total energy before interaction (J)

Example A 65.0 kg skydiver jumps from an airplane at an altitude of 5.00 × 102 m from the ground. Several minutes later, she reaches the ground travelling at a terminal velocity of 8.00 m/s. What is the skydiver’s total mechanical energy, relative to the ground, just after she jumps? What is the skydiver’s total mechanical energy just before she lands? How much work did the non-conservative frictional force do?

Mid-Point Assessment What do the vocabulary terms below mean? Discuss in your small groups. Work Total Mechanical Energy Kinetic Energy Potential Energy Positive Work Zero Work Negative Work Constant Force Variable Force

How are these terms related? What do you know about these terms? Assessment How are these terms related? What do you know about these terms? Instructions: WITHOUT TALKING, in your small groups, you will pass around a piece of paper on which you will construct a mind map. Your mind maps will show how these terms are related AND what you’ve learned about the terms. After 10 minutes, you will be allowed to talk about what you’ve come up with as a group. Create a good copy in your groups to post in class. Don’t forget to copy down your good copy in your notes too!

Mid-Point Assessment Example of concept maps:

Mid-Point Assessment Some key questions to consider: How are work and energy related? If zero work is done on an object, does it affect the energy? What is positive work is done? Negative work? How do you calculate work?

POWER & EFFICIENCY

What is Power? Rate at which work is done Measured in Watts (W) (1 Watt = 1 Joule/second) or P = Power (W) W = work done (N∙m or J) ΔE = change in energy (J) Δ t = time (s)

Power Example When doing a chin-up, a physics student lifts her 40 kg body a distance of 0.25 m in 2.00 s. What is the power delivered by the student's biceps?

What is Efficiency? Transforming energy from one form to another always involves some “loss” of useful energy The efficiency of a device describes the amount of input energy that is converted into the intended output energy or work.

Efficiency Efficiency = x 100% Efficiency = x 100% How much of the input energy goes towards a “useful” output? Efficiency = x 100% Efficiency = x 100% Eo = useful output energy (J) Ei = input energy (J) Wo = useful output work (N∙m) Wi = input work (N∙m)

Efficiency Example An electric kettle uses 2000 J of electrical energy to produce 500 J of heat energy. What is the efficiency of the kettle?

Homework p. 254 # 1-5

Energy, Work & Power Equations 1) 2) 3) 4) 5) 6) 7)

Test your Knowledge with this MINI-TEST! Work, Energy & Power Test your Knowledge with this MINI-TEST!

MINI-TEST Question 1: Units for work are joules. This can also be written as: N/m N∙m N/m2 N2∙m

MINI-TEST Question 2: Which one of the following statements about work is correct? Work is a vector quantity Work has no units Work is a measure of how much energy is created in a process Work is a scalar quantity

MINI-TEST Question 3: Which one of these following statements about power is correct? Power is the rate of doing work Power is the rate of change of velocity Power is a vector Power is the potential energy gained when the mass is raised

MINI-TEST Question 4: The power used by a hoist lifting a 50.0 kg mass through a vertical distance of 4.5 m in 5.0 s is: 10W 45W 100W 450W

MINI-TEST Question 5: A theme park roller-coaster carriage starts to run down a slope. Which of the following statements are true, ignoring friction and air resistance? Kinetic energy is transformed to potential energy Energy is destroyed as heat Potential energy is transformed into kinetic energy The total energy at e beginning is bigger than at the end

MINI-TEST Question 6: Which one of the following statements is TRUE: An object at rest has no energy. Gravitational potential energy depends only on the height of an object. Doubling the speed of a moving object quadruples its kinetic energy. Things "use up" energy.

Agree or Disagree? “Heat”, “temperature” and “thermal energy” each describe the same thing. Heat is a substance that resides within an object. A piece of wood and a piece of steel, both removed from a pot of boiling water and placed in a sealed container, will cool to different temperatures. Increasing thermal energy will increase temperature.

Thermal Energy & Heat Heat: Kinetic molecular theory: Thermal energy: How do the motion of particles in solids, liquids and gases compare? Link 1, Link 2 Thermal energy: Measure of the kinetic energy of particles due to their constant random motion. Depends on mass, and number of particles in a substance. Heat: Transfer of thermal energy (through the collision of particles). Solid Liquid Gas

Discussion Question The picture shows a kettle of boiling water, and a mug of boiling hot tea. Compare these objects using kinetic molecular theory, thermal energy and heat.

Temperature Measure of the average speed (kinetic energy) of the atoms or molecules of a substance. Measured in units of Celsius (°C), Fahrenheit (°F) or Kelvin (K). 0°C and 100°C are defined by the freezing and boiling points of water. 0K is defined as absolute zero, when the kinetic energy of particles is zero (no movement). 0K = -273.15°C TK = TC + 273.15 T = temperature in Kelvin TC = temperature in Celsius

Kinetic Molecular Theory & Temperature

First Law of Thermodynamics The change in energy of a system is the sum of the work and heat exchanged between a system and its surroundings: ΔE = W + Q ΔE = change in energy (J) W = Work done on a system (J) Q = heat (J)

Heat & Temperature

Thermal Equilibrium Energy flows from “warmer” objects to “cooler” objects until they both achieve thermal equilibrium (the same temperature). Transfer of energy occurs through the collision of particles.

Specific Heat Capacity Amount of energy that must be added to raise 1.0 kg of a substance by 1.0 K. Larger masses require more heat to achieve a specific rise in temperature Different materials have varying capacities to absorb heat. Table 1: Some Specific Heat Capacities Substance Specific Heat Capacity (J/kg·°C) Aluminum (solid) 900 Ice (-15°C) 2000 Ethyl alcohol (liquid) 2450 Mercury (liquid) 139 Water (15°C) 4196 Substance Specific Heat Capacity (J/kg·°C) at Constant Pressure Carbon dioxide gas 833 Nitrogen gas 1040 Water vapour (100°C) 2020

Specific Heat Capacity

Heat Required for Temperature Change To calculate the amount of heat required to raise the temperature of a quantity of a substance: Q = mcΔT Q = heat transferred [J] m = mass of substance [kg] c = specific heat capacity of substance ΔT = temperature change [K or °C]* *Since K and °C are 1:1, when temperature changes are used, both scales give the same result.

Examples A 2.5 kg pane of glass, initially at 41°C, loses 4.2 × 104 J of heat. What is the new temperature of the glass? A 120 g mug at 21°C is filled with 210 g of coffee at 91°C. All the heat lost by the coffee is transferred to the mug. The specific heat capacity of the mug is 7.8 × 102 J/kg·°C. Write an equation representing the heat gained by the mug. Write an equation representing the heat lost by the coffee. Calculate the final temperature of the coffee.

Phase Changes A beaker of ice is placed on a hot plate. Its temperature is monitored with a thermometer. What will happen to the beaker of ice over time? How do you expect the beaker’s temperature to change, as more and more heat is added by the hot plate? Why? Temperature (K) Heat (J) Temperature (K) Heat (J) Temperature (K) Heat (J) Temperature (K) Heat (J)

Phase Changes As the ice is heated, Temperature (K) Heat (J) Thermal energy added to ice Increased av. kinetic energy of particles Increase in temperature Temperatures do not increase during phase changes When the ice temperature reaches 0°C, thermal energy goes towards melting the ice, instead of increasing temperature. Once the ice has melted, the temperature increases once more. Temperature (K) Heat (J)

Phase Changes Phase changes require a change in internal energy. The amount of energy needed for a phase change is called the latent heat.

Homework Pg. 287 #1-10