+ What do you think? 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?
+ Work Inphysics, work is the magnitude of the force (F) times the magnitude of the displacement (d) in the same direction as the force. W = Fd What are the SI units for work? Force units (N) distance units (m) N•m are also called joules (J). How much work is 1 joule? Liftan apple weighing about 1 N from the floor to the desk, a distance of about 1 m.
+ Work Pushing this car is work because F and d are in the same direction. Why aren’t the following tasks considered work? A student holds a heavy chair at arm’s length for several minutes. A student carries a bucket of water along a horizontal path while walking at a constant velocity.
+ Work At an angle you can use the below equation to calculate the work being done Ifthe angle is 90°, what is the component of F in the direction of d? Fcos 90° = 0 Ifthe angle is 0°, what is the component of F in the direction of d? Fcos 0° = F
+ Example How much work is being done on a vacuum cleaner pulled 3.0 m by a force of 50.0 N at an angle of 30° above the horizontal? Given: F= 50.0N d= 3.0 m θ=30°
+ Classroom Practice Problem A 20.0kg suitcase is raised 3.0 m above a platform. How much work is done on the suitcase? Answer: 5.9 x 102 J or 590 J
+ Work is a Scalar Work can be positive or negative but does not have a direction.
+ Sign of Work is Important Work is positive Force is in the same direction as the displacement Work is negative Forceis in a different direction as the displacement Sign of the net work lets you know if the object is speeding up or down + for speeding up and work is being on object - for slowing down and work is done by object
+ What do you think? You have no doubt heard the term kinetic energy. What is it? What factors affect the kinetic energy of an object and in what way? Youhave no doubt heard the term potential energy. What is it? What factors affect the potential energy of an object and in what way?
+ Kinetic Energy Energy associated with an object in motion Wnet = Fd = mad Since v2f = v2i + 2ad v2 f vi2 2 2 Wnet m( ) Then v f v i 2 ad 2 Finally 1 2 1 2 Wnet mv f mvi 2 2
+ Kinetic Energy Kinetic energy depends on speed and mass The net work done on a body equals its change in kinetic energy SI units for KE kg•m2/s2 or N•m or Joule (J)
+ Example A 7.0 Kg bowling ball moves at 3.0 m/s. How fast must a 2.45g ping pong ball move in order to have the same kinetic energy as the bowling ball? Is the speed reasonable for the ping pong ball? Given: Bowling ball: m= 7.0 kg v= 3.0m/s Ping pong: m= 2.45 g (this= 0.00245kg) v=??
+ Example 2KE KE= ½ mv2 v m KE= ½ (7)(32) 2(31.5) KE= 31.5 J v 0.00245 Rearrange Equation v = 160.36 m/s to get v by itself
+ Classroom Practice Problems A 6.00 kg cat runs after a mouse at 10.0 m/s. What is the cat’s kinetic energy? Answer: 3.00 x 102 J or 300 J Suppose the above cat accelerated to a speed of 12.0 m/s while chasing the mouse. How much work was done on the cat to produce this change in speed? Answer: 1.32 x 102 J or 132 J
+ Work and Kinetic Energy KEis the work an object can do if the speed changes. Wnet is positive if the speed increases. You must include all the forces that do work on the object in calculating the net work done
+ Potential Energy Energyassociated with an object’s potential to move due to an interaction with its environment; basically its stored energy A book held above the desk An arrow ready to be released from the bow Some types of PE are listed below. Gravitational Elastic Electromagnetic
+ Gravitational Potential Energy Energy associated with an object due to the object’s position relative to a gravitational source SI unit is still a Joule Theheight (h) depends on the “zero level” chosen where PEg= 0.
+ Elastic Potential Energy Theenergy available for use in deformed elastic objects Rubber bands, springs in trampolines, pole-vault poles, muscles For springs, the distance compressed or stretched = x
+ Elastic Potential Energy The spring constant (k) depends on the stiffness of the spring. Stiffer springs have higher k values. Measured in N/m Force in newtons needed to stretch a spring 1.0 meters
+ Example A 70.0kg stuntman is attached to a bungee cord with an unstretched length of 15m. He jumps off a bridge from a height of 50m. When he finally stops the cord has a stretched length of 44m. Assuming the spring constant is 71.8 N/m, what is the total PE relative to the water when the man stops falling?
+ Example PEg= mgh PEelastic = ½ k x2 PEg= (70)(10)(6) PEelastic= ½ (71.8)(292) PEg= 4200 J PEelastic= 30191.9J PEtotal= PEg + PEelastic PEtotal= 4200 + 30191.9 PEtotal= 34391.9J
+ Classroom Practice Problems When a 2.00 kg mass is attached to a vertical spring, the spring is stretched 10.0 cm such that the mass is 50.0 cm above the table. What is the gravitational potential energy associated with the mass relative to the table? Answer: 9.81 J What is the spring’s elastic potential energy if the spring constant is 400.0 N/m? Answer: 2.00 J
+ What do you think? Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed? Explain your reasoning. Would your answer change if the slide were not frictionless? If so, how?
+ What do you think? What is meant when scientists say a quantity is conserved? Describe examples of quantities that are conserved. Are they always conserved? If not, why?
+ Mechanical Energy (ME) ME = KE + PEg + PEelastic Doesnot include the many other types of energy, such as thermal energy, chemical potential energy, and others ME is not a new form of energy. Just a combination of KE and PE
+ Conservation of Mechanical Energy The sum of KE and PE remains constant. One type of energy changes into another type. For the falling book, the PE of the book changed into KE as it fell. As a ball rolls up a hill, KE is changed into PE.
+ Example Starting from rest, a child zooms down a frictionless slide from an initial height of 3.0m. What is her speed at the bottom of the slide? Her mass is 25kg. Given: vi= 0m/s hi= 3m m=25kg vf= ?? hf=0m
+ Example *Choose your equations PE= mgh KE= ½ mv2 PEf= (25)(10)(0) KEf= ½ (25)v2 PEf= 0J KEf= ?? PEi= (25)(10)(3) KEi= ½ (25)(02) PEi= 750J KEi= 0J
+ Example *Put together PEi+ KEi= PEf+ KEf 750 + 0 = 0 + ½ (25)vf2 750= 12.5 vf2 vf2 = √60 vf= 7.75m/s
+ Classroom Practice Problems Suppose a 1.00 kg book is dropped from a height of 2.00 m. Assume no air resistance. Calculate the PE and the KE at the instant the book is released. Answer: PE = 19.6 J, KE = 0 J Calculate the KE and PE when the book has fallen 1.0 m. (Hint: you will need an equation from Chapter 2.) Answer: PE = 9.81 J, KE = 9.81 J Calculate the PE and the KE just as the book reaches the floor. Answer: PE = 0 J, KE = 19.6 J
+ Table of Values for the Falling Book h (m) PE(J) KE(J) ME(J) 0 19.6 0 19.6 0.5 14.7 4.9 19.6 1.0 9.8 9.8 19.6 1.5 4.9 14.7 19.6 2.0 0 19.6 19.6
+ Conservation of Energy Acceleration does not have to be constant. ME is not conserved if friction is present. If friction is negligible, conservation of ME is reasonably accurate. A pendulum as it swings back and forth a few times Consider a child going down a slide with friction. What happens to the ME as he slides down? Answer: It is not conserved but, instead, becomes less and less. The “lost” energy? is converted into nonmechanical energy (thermal energy).
+ Classroom Practice Problems A small 10.0 g ball is held to a slingshot that is stretched 6.0 cm. The spring constant is 2.0 102 N/m. What is the elastic potential energy of the slingshot before release? What is the kinetic energy of the ball right after the slingshot is released? What is the ball’s speed at the instant it leaves the slingshot? How high does the ball rise if it is shot directly upward?
+ Now what do you think? Imagine two students standing side by side at the top of a water slide. One steps off of the platform, falling directly into the water below. The other student goes down the slide. Assuming the slide is frictionless, which student strikes the water with a greater speed? Explain your reasoning. Would your answer change if the slide were not frictionless? If so, how?
+ Now what do you think? What is meant when scientists say a quantity is “conserved”? Describe examples of quantities that are conserved. Are they always conserved? If not, why?
+ What do you think? Twocars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently? What does power mean? What units are used to measure power?
+ Power Therate at which work is done or energy is transferred Energy used or work done per second If we substitute W for Fd then Fd P t
+ Power SI units for power are J/s. Calledwatts (W) Equivalent to kg•m2/s3 Horsepower (hp) is a unit used in the Avoirdupois system. 1.00 hp = 746 W
+ Watts These bulbs all consume different amounts of power. A 100watt bulb consumes 100 joules of energy every second.
+ Example A 193kg curtain need to be raised 7.5m, at a constant speed, in as close to 5 sec as possible. Unsure which motor would be the best 3 motors were bought. Power ratings are 1.0kW, 3.5kW, and 5.5kW. Which motor is best for the job? Given: m= 193kg d= 7.5m t= 5 sec P=??
+ Example W Fd mgd P t t t (193)(10)(7.5) P 5 P=2895 W or 2.895kW So the best motor would be the 3.5kW motor
+ Classroom Practice Problems Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min. Calculate the power delivered by the horses. How much work is done by the two horses? Answers: 1.0 x 103 W and 6.0 x 105 J
+ Now what do you think? Twocars are identical with one exception. One of the cars has a more powerful engine. How does having more power make the car behave differently? What does power mean? What units are used to measure power?