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class notes; 4.26.11. Work and Horsepower NO Quiz TODAY Personal Horsepower Lab Lab Due Wednesday Thursday More information coming tomorrow!! A couple more tickets available.-------------------Twins Physics Day Early bus stuff Dress for the weather Leave at 8:30 http://www.ftexploring.com/energy/energy-1.htm Lab is due tomorrow Today during work time Find out answers to questions • Reading Notes (1 page ) – Gravitational Potential Energy • Homework: – Physics: Work (no angles) – Check your understanding of Potential Energy Mechanical Work Equals ZERO no change in speed no work no change in height no work Force is ┴ to motion no Work W=F*d 1 N m = 1 Joule F 90° • W = 0! Carrying a weight corresponds to W = 0. • F is perpendicular to d, θ = 90°: • W = 0. IF you are pushing against an immovable object, d =0 so W = 0!! d d =0 Gravitational Potential Energy Both blocks acquire the same gravitational potential energy, mgh. The same work is done on each block. What matters is the final elevation, not the path followed Work = F * d Using the force and the distance along the ramp • The amount of work done by a force on any object is given by the equation Work = F d cosΘ • F is the Applied force, • d is the displacement • θ is the angle between the F & d Work and Potential Energy The work done on the ball gives the ball gravitational potential energy. Gravitational potential energy = mgh Which Path Requires the Most WORK? • Suppose that a car traveled up three different roadways (each with varying incline angle or slope) from the base of a mountain Vertical distance only affects the PE • • • • The PE at the top of each is 30 J, The work to move up each would be 30 J. How can this be???? For Work use Force || to displacement!! Fg UP d Fg UP d Fg UP d Calculations: Watts and Horsepower • James Watt patented the steam engine in 1769. • To sell it, he needed to tell people how many horses it would replace. • He measured how quickly farm horses could do work. • There are few horses that actually produce exactly one horsepower of power. POWER Work, Power and Energy • Notebooks 30 pts + 5 EC for vertical loops • More Equations and Notes today • Tomorrow is the last day to bring in Valleyfair $$$41.50 and permission slip. Work: The Transfer of Mechanical Energy • The baseball pitcher does work on the ball. The ball gains kinetic energy. • To do the greatest possible amount of work, the greatest possible force the greatest possible distance Kinetic energy • The amount of translational kinetic energy (from here on, the phrase kinetic energy will refer to translational kinetic energy) which an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object. • • where m = mass of object • v = speed of object Units of work and energy • Like work and potential energy, the standard metric units of measurement for kinetic energy is the Joule. As might be implied by the above equation, 1 Joule is equivalent to 1 kg*(m/s)^2. Analyze the animation and use the principles of work and energy to answer the given questions. • Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends from a height of 0.60-meters to a height of 0.00 meters. Assume negligible air resistance. • • Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends halfway down a 0.60-meter high hill (i.e., to a height of 0.30 meters). Assume negligible air resistance. • • If the mass of the Hot Wheels car was twice as great (0.100 kg), then what would be the speed at the bottom of the 0.60meter high hill? • • If the 0.050-kg Hot Wheels car is brought to a rest over a distance of 0.40 meters, then what is the magnitude of the frictional force acting upon the car? Which Path Requires the Most Energy? • Suppose that a car traveled up three different roadways (each with varying incline angle or slope) from the base of a mountain Analyze the animation and use the principles of work and energy to answer the given questions. • Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends from a height of 0.60-meters to a height of 0.00 meters. Assume negligible air resistance. • • Use energy conservation principles to determine the speed of a 0.050-kg Hot Wheels car that descends halfway down a 0.60-meter high hill (i.e., to a height of 0.30 meters). Assume negligible air resistance. • • If the mass of the Hot Wheels car was twice as great (0.100 kg), then what would be the speed at the bottom of the 0.60meter high hill? • • If the 0.050-kg Hot Wheels car is brought to a rest over a distance of 0.40 meters, then what is the magnitude of the frictional force acting upon the car? Work Work = Force x Distance F = 500 pounds (2000 N) D = 8 feet (2.5 meters) ----------------------------------- W = 2000 N x 2.5 m = 5000 N-m ----------------------------------Alternative unit: Joule 1 N-m = 1 joule (J) Work Work = Force x Distance If the wall doesn't move, the prisoner does no work. Energy Work is done on the bow. The work done is stored in the bow and string as elastic potential energy. After release, the arrow is said to have kinetic energy, 1/2 mv2. Energy is measured in the same units (joules) as work. Energy Transformation The work done in lifting the mass gave the mass gravitational potential energy. Potential energy then becomes kinetic energy. Kinetic energy then does work to push stake into ground. Energy Transformation • Power = Work/ Time 1 joule / second = 1 watt Power Total mechanical energy • As discussed earlier, there are two forms of PE discussed in our course gravitational potential energy and elastic potential energy. Given this fact, the above equation can be rewritten: • TME = PEgrav + PEspring + KE Total Mechanical energy stays the same until it hits the water. Work and Energy How High Will It Go? The motion of the sled in the animation below is similar to the motion of a roller coaster car on roller coaster track. • As on a roller coaster, energy is transformed from potential energy to kinetic energy and vice versa. Provided that external forces (such as friction forces and applied forces) do not do work, the total amount of mechanical energy will be held constant. Energy Conservation on an Incline • If air resistance is neglected, then it would be expected that the total mechanical energy of the cart would be conserved. The animation below depicts this phenomenon (in the absence of air resistance). • Total mechanical energy is constant conservative force gravity transfers PE-KE • The diagram below depicts the motion of Li Ping Phar (esteemed Chinese ski jumper) as she glides down the hill and makes one of her record-setting jumps. Measurement of Horsepower • The maximum horsepower developed by a human being over a few seconds time can be measured by timing a volunteer running up the stairs in the lecture hall. • If a person of weight W runs up height h in time t, then h.p. = Wh/t X 1/550 ft-lbs/sec. • A person in good shape can develop one to two horsepower. It will be entertaining to the students if the professor tries it too. • Should the person be allowed a running start? http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html http://www.physics.ucla.edu/demoweb/demomanual/mechanics/uniform_circular_motion/index.html Height at A = 60m The car's mass is 500kg. • A roller coaster with two loops and a small hill, see diagram below • In the diagram A is the highest point of the coaster, B is 3/4 height of A, C is 1/2 of A, D is 1/4 of A, E is the ground level, and F is 1/8 of A. Point (A-F) Height (m) PE (J) KE (J) TME (J) Speed (m/s) PE = mgh HA = 60m 2 Speed use KE = ½ m v m =500kg KE = TME (previous) – PE A to F A h (m) 60 B 45 C 30 D 15 E 0 F 7.5 PE (J) KE (J) (500(9.8)(60) = 294,000-294,000= 294,000 J 0 Joules TME (J) Speed (m/s) 294,000J 0 m/s PE = mgh KE = ½ m 2 v HA = 60m m =500kg A to F A PE (J) h (m) 60 B 45 PE = mgh Speed use KE = ½ m v2 KE = TME (previous) – PE KE (J) TME (J) Speed (m/s) 0 m/s (500(9.8)(60) = 294,000-294,000= 294,000 J 0 Joules 294,000J (500(9.8)(45) = 294,000-220,500 = 294,000J 220,500 J 73,500J 17.1 m/s Equation: KE = ½ m v2 Substitute: 73,500J = ½ 500kg v2 X 2 …/ by 500…take √ .. v= 17.1 m/s Mechanical Energy Equations Page 7 section #3 W1Force of Gravity pulls down W1 Mechanical Work PE KE TME does not change W4 W2 W4 The transfers W1 of energy during the 1st Bounce W4 W2 W3 W2Force of Gravity pulls down W1 Mechanical Work PE KE TME does not change W4 W2 W3 W3ball compressed W1 Mechanical Energy lost to HEAT TME does change W2 W4 W3 W1 W4Force of Gravity pulls down Mechanical Work KE PE TME does not change W4 W2 W3 Notice the speed change Missing mechanical energy?? Energyinitial – Energyfinal = Energylost Frictional Work • According to the Cedar Point website the maximum speed of the Magnum XL-200 is 72 mph not 76 mph as we calculated above. • The difference is due to frictional forces acting on the roller coaster cars. • Assuming that the mass of a loaded roller coaster car is 600 kg what is the frictional (nonconservative) work done on the car by the track? Analyze the transfers of energy during the 1st Bounce Work on incline • Answer the following about the above picture: • Draw the three forces acting on the object. • If the object slides down the incline, what work was done with gravity? • What work is done against the motion? • What is the net work done? • Predict the final velocity of the object. Mechanical Energy Follow the bouncing ball Bouncing balls • • When a ball is dropped, it transfers its GPE to kinetic energy. As the ball hits the floor, its kinetic energy is turned into elastic potential energy (and some heat, and noise). High speed photography can show how the ball gets deformed. • The elastic potential energy is transferred to kinetic energy as the ball bounces. Some energy is lost as heat as the ball bounces, so it does not achieve the height from which it was dropped. Bouncing balls • different types of balls at room temperature and when they are frozen. • When a ball is dropped on a surface, molecules in the ball can deform or absorb the kinetic energy of the fall. If they return to their original shape they push the ball away from the surface. If the energy is absorbed, the ball does not bounce. Bouncing balls Bouncing balls Conservative and non-conservative work • Forces can be categorized as internal forces or external forces. There are many sophisticated and worthy ways of explaining and distinguishing between internal and external forces. Many of these ways are commonly discussed at great length in physics textbooks. For our purposes, we will simply say that external forces include the applied force, normal force, tension force, friction force, and air resistance force. And for our purposes, the internal forces include the gravity forces, magnetic force, electrical force, and spring force. Internal Forces External Forces Fgrav Fspring Fapp Ffrict Fair Ftens Fnorm In the following descriptions, the only forces doing work upon the objects are internal forces - gravitational and spring forces. Thus, energy is transformed from KE to PE (or vice versa) while the total amount of mechanical energy is conserved. Read each description an indicate whether energy is transformed from KE to PE or from PE to KE. • Description of Motion KE to PE or PE to KE? Explain. • 1. A ball falls from a height of 2 meters in the absence of air resistance. • • 2.A skier glides from location A to location B across a friction free ice. • • 3.A baseball is traveling upward towards a man in the bleachers. • • 4.A bungee cord begins to exert an upward force upon a falling bungee jumper. • • 5.The spring of a dart gun exerts a force on a dart as it is launched from an initial rest position. resistance and tension forces) doing work upon an object. Read the description and indicate whether the object gained energy (positive work) or lost energy (negative work). (NOTE: If this is part is difficult, review the section on work.) Then, indicate whether the gain or loss of energy resulted in a change in the object's kinetic energy, potential energy, or both. Click the buttons to view answers. Description + or - Work? Change PE or KE or Both? • Megan drops the ball and hits an awesome forehand. The racket is moving horizontally as the strings apply a horizontal force while in contact with the ball. • A tee ball player hits a long ball off the tee. During the contact time between ball and bat, the bat is moving at a 10 degree angle to the horizontal. • • Rusty Nales pounds a nail into a block of wood. The hammer head is moving horizontally when it applies force to the nail. • The frictional force between highway and tires pushes backwards on the tires of a skidding car. • A diver experiences a horizontal reaction force exerted by the blocks upon her feet at start of the race. Work out due to friction 6th section Mechanical Energy Equations A boulder resting at the top of a hill has potential energy. Potential energy changes to kinetic energy due to work done by gravity PE Roller coaster W/P/E • The Work pulling the coaster to the top of the 1st hill is the Potential Energy at the top of the hill and the Energy available for the entire ride. • The total mechanical energy at any point of the roller coaster is the PE + KE if there were no frictional forces KEinitial + PEinitial + Wexternal = KEfinal + PEfinal Energy Transformation on a Roller Coaster A GIF Animation A roller coaster ride also illustrates the work-energy theorem. • The theorem is often stated in the form of the following mathematical equation. • KEinitial + PEinitial + Wexternal = KEfinal + PEfinal • The left side of the equation includes the total mechanical energy (KEinitial + PEinitial) for the initial state of the object plus the work done on the object by external forces (Wexternal) while the right side of the equation includes the total mechanical energy (KEfinal + PEfinal) for the final state of the object. A roller coaster ride also illustrates the work-energy theorem. • KEinitial + PEinitial + Wexternal = KEfinal + PEfinal Frictional Work • Frictional Work • According to the Cedar Point website the maximum speed of the Magnum XL-200 is 72 mph not 76 mph as we calculated above. The difference is due to frictional forces acting on the roller coaster cars. Assuming that the mass of a loaded roller coaster car is 600 kg what is the frictional (nonconservative) work done on the car by the track? Test Form A Mass = 800 kg Test Form B • 1. Find the Total Mechanical Energy at the end of the first horizontal platform. • 2. Find the Acceleration on platform • vf 2= vi 2+ 2ad • Then Find g’s • 6. radius = 30 meters Height at A = 60m • a roller coaster with two loops and a small hill, see diagram below • In the diagram A is the highest point of the coaster, B is 3/4 height of A, C is 1/2 of A, D is 1/4 of A, E is the ground level, and F is 1/8 of A. The car's mass is 500kg. Point Height(m) PE(J) KE(J) TME(J) Speed (m/s) coaster Roller coaster W/P/E • The Work pulling the coaster to the top of the 1st hill is the Potential Energy at the top of the hill and the Energy available for the entire ride. KEinitial + PEinitial + Wexternal = KEfinal +PEfinal • The Total Mechanical Energy at any point of the roller coaster is the PE + KE if there were no frictional forces Energy Transformation on a Roller Coaster A GIF Animation Height at A = 60m The car's mass is 500kg. • A roller coaster with two loops and a small hill, see diagram below • In the diagram A is the highest point of the coaster, B is 3/4 height of A, C is 1/2 of A, D is 1/4 of A, E is the ground level, and F is 1/8 of A. Point (A-F) Height (m) PE (J) KE (J) TME (J) Speed (m/s) PE = mgh HA = 60m 2 Speed use KE = ½ m v m =500kg KE = TME (previous) – PE A to F A h (m) 60 B 45 C 30 D 15 E 0 F 7.5 PE (J) KE (J) (500(9.8)(60) = 294,000-294,000= 294,000 J 0 Joules TME (J) Speed (m/s) 294,000J 0 m/s PE = mgh KE = ½ m 2 v HA = 60m m =500kg A to F A PE (J) h (m) 60 B 45 PE = mgh Speed use KE = ½ m v2 KE = TME (previous) – PE KE (J) TME (J) Speed (m/s) 0 m/s (500(9.8)(60) = 294,000-294,000= 294,000 J 0 Joules 294,000J (500(9.8)(45) = 294,000-220,500 = 294,000J 220,500 J 73,500J 17.1 m/s Equation: KE = ½ m v2 Substitute: 73,500J = ½ 500kg v2 X 2 …/ by 500…take √ .. v= 17.1 m/s TME = KE + PE 800 kg h (m) PE (J) Speed m/s KE (J) TME (J) Top of 1st hill (Need to first find the TME available) 80 m 10 m/s 800(9.8)(80)= 627,200 J PE = mgh ½ (800)(10)2= 40,000 J 667,200 J KE = ½ m v2 TME = KE + PE 800 kg h (m) Stays same if no friction PE (J) Speed m/s KE (J) TME (J) Speed at the bottom of the 1st hill 0 m ?? 0 J PE = mgh 667,200 J 667,200 J KE = ½ m v2 TME = KE + PE 800 kg h (m) Speed m/s PE (J) KE (J) TME (J) Speed at the bottom of the 1st hill 0 m 40.8 0 J 667,200 J 667,200 J Equation: KE = ½ m v2 Substitute: 667,200 J= ½ 800kg v2 X 2 …/ by 800…take √ .. v= 40.8 m/s Coaster g’s Back side: Save for tomorrow Weight Equation A boulder resting at the top of a hill has potential energy. Potential energy changes to kinetic energy due to work done by gravity PE Use: To convert from Newtons to kg And from kg to Newtons The Total Mechanical Energy • As already mentioned, the mechanical energy of an object can be the result of its motion (i.e., kinetic energy) and/or the result of its stored energy of position (i.e., potential energy). The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy. This sum is simply referred to as the total mechanical energy (abbreviated TME). • TME = PE + KE • As discussed earlier, there are two forms of potential energy discussed in our course gravitational potential energy and elastic Mechanical Energy as the Ability to Do Work Sample PE calculation A boulder resting at the top of a hill has potential energy. Gravitational Potential Energy is the energy stored due to height. Work can change the height of the Boulder Work can change the potential energy of the Boulder Potential energy changes to kinetic energy due to work done by gravity PE 4.17.09.notes WPE Introduction & Equation sheet Hand in Valley Fair $$ and slip Lab Question: Who had the highest Horsepower?? You may turn Lab in today or Monday…. 1st 0.73 Mike 3rd 0.95 Joey 4th 0.88 Parker 5th 1.01 Chris 6th 0.91 Seth WPE Introduction TODAY: 4-17-09 Notes and Equation Sheet Valleyfair: Friday, May15th --Passing by Friday 5pm Cash By 7:30 am Friday May 15th Book notes Pg. 224-231 ½ page New sheet Mechanical Work Equations in any direction Page 7 section #1 To Do Work, Forces Must Cause Displacements • • To Do Work, Forces Must Cause Displacements Let's consider Scenario C above in more detail. Scenario C involves a situation similar to the waiter who carried a tray full of meals above his head by one arm straight across the room at constant speed. It was mentioned earlier that the waiter does not do work upon the tray as he carries it across the room. The force supplied by the waiter on the tray is an upward force and the displacement of the tray is a horizontal displacement. As such, the angle between the force and the displacement is 90 degrees. 5th section Mechanical Work Equations Page 7 section #2 Who or What is applying the Force?? Mechanical work and Energy work is done upon an object whenever a force acts upon it and changes the height or changes the speed The amount of work done is dependent height A boulder resting at the top of a hill has potential energy. • Gravitational Potential Energy is the energy stored due to height. • Work can change the height of the Boulder • Work can change the potential energy of the Boulder Mechanical Energy Equations Page 7 section #3 Horizontal displacement does not affect the gravitational PE • Knowing that the potential energy at the top of the tall pillar is 30 J, what is the potential energy at the other positions shown on the hill and the stairs. Assignment 4.17.09 Lab report due MONDAY NOTEBOOK: Book notes Pg. 224-231 (½ page) Work and Energy Problems Work and energy are Scalar, so we do not use +/- on numbers for direction Potential energy (height) Work Kinetic energy (speed) Work and Energy Problems Work and energy are Scalar, so we do not use +/- on numbers for direction PE = mgh W=F*d KE = 1/2 mv2 • A ball starts from rest on top of a tall pillar and falls to the ground below. Assume the effect of air resistance is negligible. • PEi = KEf • (Since initially at rest, KEi = 0 and cancels. Since the final height is 0, PEf = 0 and cancels.) Example from 6. A 50-kg platform diver hits the water below with a kinetic energy of 5000 Joules. The height (relative to the water) from which the diver dove was approximately ____ meters. *the potential energy change *the work done. 5000 J 5000 J Work and Energy Problems Work and energy are Scalar, so we do not use +/- on numbers for direction PE = mgh PE = 5000J • W=F*d • KE = 1/2 mv2 • KE = 5000 J 5000J=50(9.8)h h=5000 /490 h= 10.2 m • W = 5000 J transferring PE to KE Example from 7. Using 1000 J of work, a small object is lifted from the ground floor to the third floor of a tall building in 20 seconds. What power was required in this task? • the potential energy change • the work done • the power delivered Work and Energy Problems Work and energy are Scalar, so we do not use +/- on numbers for direction • PE = mgh • PE = 1000J • W=F*d • KE = 1/2 mv2 • W = 1000 J transferred to PE P=W/t P=1000J / 20sec=50 Watts 4.20.09 notes Work, Potential Energy & Problems NOW. . . . . Hand in Personal Horsepower Lab by 2:15 Hand in Valleyfair $$ and Slips together by 2:15 hOMEWORK Worksheet Work time A boulder resting at the top of a hill has potential energy. • Gravitational Potential Energy is the energy stored due to height. • Work can change the height of the Boulder • Work can change the potential energy of the Boulder Potential energy changes to kinetic energy due to work done by gravity PE Work to PE or PE to work • a force acts upon it and changes the height Measurement of Horsepower • The maximum horsepower developed by a human being over a few seconds time can be measured by timing a volunteer running up the stairs in the lecture hall. • If a person of weight W runs up height h in time t, then h.p. = Wh/t X 1/550 ft-lbs/sec. • A person in good shape can develop one to two horsepower. It will be entertaining to the students if the professor tries it too. • Should the person be allowed a running start? http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html A bouncing basketball captured with a stroboscopic flash at 25 images per second. Ignoring air resistance, the square root of the ratio of the height of one bounce to that of the preceding bounce gives the coefficient of restitution for the ball/surface impact. Bouncing of ball • If a soccer ball is dropped on a hard surface, it will bounce back to a height lower than its initial position. Such kind of motion is called the bouncing of the soccer ball, which plays an important role in the motion of the ball. Let us study the mechanism of the bouncing of the ball in • The relative details. bounciness of different types of balls • The coefficient of restitution is how you quantify bounciness or give bounciness a number, and you do that by dividing the bounce height by the drop height, then finding the square root of that. When... Read more: http://wiki.answers.com/Q/What_is_the_C oefficient_of_Restitution_of_bouncing_a_b asketball#ixzz1JW73FiKE • As a result, a ball with smaller coefficient of restitution rebounds to lower height in successive bounces and a shorter time is required for the ball to stop. • For example, grass reduces the coefficient of restitution of a soccer ball since the bending of blades causes further loss of its kinetic energy. • Therefore, it would take a shorter time for the soccer ball to stop if it is kicked on grass instead of hard floor. changing its temperature. • We can also change the bounciness of a ball by changing its temperature. Take two baseballs that bounce to about the same height. Put one in the freezer for an hour and leave the other at room temperature. Then compare their bounciness again. You should notice that the room temperature ball bounces a little bit higher. The cold ball would bounce about 80 percent as high as the room temperature ball. Although the difference of bounciness is not dramatic, it's enough to see that temperature can be a factor: it could make the difference between a home run and a pop fly. • However, the change in bounciness due to the change in temperature is taken for granted for some sport. For example, squash player rely on the pre-game warm up to warm up the ball as well as the players. Surface bounced on • Example…grass reduces the coefficient of restitution of a soccer ball since the bending of blades causes further loss of its kinetic energy. Therefore, it would take a shorter time for the soccer ball to stop if it is kicked on grass instead of hard floor. COR • Coefficient of restitution of a tennis ball is 0.712. Thanks ... • 1910 soccer ball [ii] 1950 soccer ball [ii] 2004 Euro Cup ball [ii] • In the late 1980s, the leather casing ball was replaced by totally synthetic ball in soccer competitions. The covering material of the totally synthetic ball is synthetic leather made from polymer. For high quality ball, the casing is made of the synthetic leather panels stitched together through pre-punched holes by waxed threads. The bladder of a totally synthetic ball is usually 1910 ball [ii]The ball is then 1950 soccer ball [ii] 2004through EuroaCup ball [ii] latexsoccer or butyl bladder. inflated by pumping air into its bladder tiny hole on the casing. The totally synthetic ball could resist water absorption and reliably maintain its shape. • The Internal structure of a totally synthetic soccer ball [ii] • Nowadays, the official soccer rules called the "Laws of the game", which are maintained by the International Football Association Board (IFAB), specify the qualities of the ball used in soccer matches. According to the laws, the soccer ball should satisfy the following descriptions: • it is spherical in shape, • its casing is made of either leather or other suitable material, • its circumference is not more than 70 cm and not less than 68 cm, • its weight is not more than 450 g and not less than 410 g at the start of the match. • its pressure inside equal to 0.6 - 1.1 atmosphere at sea level. Figure explaining the extra pressure inside the soccer ball. The relative bounciness of different types of balls [iii] • Energy change in the falling ball after release until hitting on the ground. (Note that here "G.P.E." and "K.E." stand for the gravitational potential energy and kinetic energy respectively.) Work must be done in order to distort an elastic object • . Therefore, if you pull a spring outward so that it become longer, some energy must have been transferred from yourself to the spring. The energy stored in an distorted object due to its deformation is called the elastic potential energy. So, when talking about the elasticity of the ball, we are indeed talking about the spring-like behavior of the ball. In other words, we are considering the tendency of the ball to return to its original spherical shape when it is being squeezed. Where does the elasticity of the ball come from? The elasticity of a solid ball arises from the elasticity of the constituting material which is due to the interatomic or intermolecular force inside. In contrast, for air-filled ball like soccer ball, its elasticity is resulted from the extra air pressure inside the ball. What happens to a ball after you dropped it above a hard floor? The gravity pulls the ball toward the ground and thus the ball falls leading to the lost of its gravitational potential energy. By the law of conservation of energy, the ball must gain kinetic energy and so it falls towards the ground with an increasing speed. Subsequently, the ball hits the hard floor with a high speed. (Note that the ball always moves with the downward acceleration of g = 9.8 m/s2 as it falls.) The elasticity of an object means • the tendency of the object to return to its equilibrium shape, the natural shape of the object with no net force applied on it, when it is being deformed. And the force for the object to restore to its equilibrium shape is called the restoring force, which is always directed in opposite to the deformation of the object. Almost all real rigid body are elastic, i. e. having certain extent of elasticity. A trivial example of an elastic object is the spring. You probably have the experience that a spring would tend to restore to its original size when you stretch it to be longer. Scientist found that, providing the deformation is not too large, the relationship between the distortion and the restoring force is given by the Hooke's law: "The restoring force exerted by an elastic object is proportional to how far it has been distorted from its equilibrium shape." The restoring force Fs on a spring in case of different extension. Law of conservation of energy • In the law of conservation of energy, it was stated that: "Energy can neither be created or destroyed but can only be changed from one form to another." Therefore, the amount of total energy in an isolated system must be constant. For example, let us consider a piece of charcoal placed in an isolated room. If we burn the charcoal, the chemical energy inside the charcoal is changed into the thermal energy of the room. Then the temperature inside the room would be increased. When the ball hits the ground, the ball exerts force on it. By the Newton's 3rd law of motion, the ground exerts a force on the ball as well. The motion of the ball would be stopped by the (stationary) hard floor resulting in the compression of the ball. So the work done on the ball leads to the increase of the elastic potential energy of the ball. That means some of the kinetic energy of the ball (which is converted from the gravitational potential energy of the ball) is converted into the elastic potential energy when the ball hits the ground. On the other hand, some of the kinetic energy is lost as thermal energy during the impact due to either the internal friction of the ball or the heating of the surface. • Energy change in the falling ball during the impact After losing all the kinetic energy, the ball becomes momentarily at rest. • The squashed ball would simply act like a compressed spring. The ball pushes the ground with a restoring force proportional to its displacement from the equilibrium position (Hooke's law). In consequence, the ground pushes back the ball with a force of equal magnitude but opposite in direction. Thus the ball bounces back in upward direction. During the rebound, the stored elastic potential energy is released as the kinetic energy of the ball which is then converted to gravitational potential energy as the ball moves up. Moreover, some of the elastic potential energy is lost again due to friction or heat which results in slight heating of the ball. The ball keeps on going upward until it comes to rest after losing all its kinetic energy again. Due to the lost of some of the initial gravitational potential energy into thermal energy, the ball cannot bounce back to the original height. What is the Coefficient of Restitution? (also called: Elastic Coefficient) What is the slope of each of the graphs? • Use the slope of the graphs to find the Coefficient of Restitution, just like we did for the Spring Constant. • The Coefficient of Restitution tells us how “springy” the ball is. • The slope of the graph represents this constant. The constant will be the same for a given ball. PE Bouncing Ball Lab Work and Potential Energy and Problems Patterns in graphs Increasing/decreasing/ no change Linear or curved line of best fit. Bouncing ball lab measure height at the first bounce up and the second bounce Work to PE or PE to work • a force acts upon it and changes the height Measurement of Horsepower • The maximum horsepower developed by a human being over a few seconds time can be measured by timing a volunteer running up the stairs in the lecture hall. • If a person of weight W runs up height h in time t, then h.p. = Wh/t X 1/550 ft-lbs/sec. • A person in good shape can develop one to two horsepower. It will be entertaining to the students if the professor tries it too. • Should the person be allowed a running start? http://www.physics.ucla.edu/demoweb/demomanual/mechanics/energy/faith_in_physics_pendulum.html Bouncing Ball Bouncing a Ball • • • • What you need: a tennis ball a basketball a room without breakables • Instructions: Drop the tennis ball from waist height and see how high it bounces. Drop the basketball from the same height and see how high it bounces. Put the tennis ball on top of the basketball and drop them both at arms length from waist height. • Results & Explanation: The tennis ball should bounce a lot higher than before. When the balls hit the ground, momentum from the basketball was transferred to the tennis ball making it go much higher than before. Mechanical Work Equals ZERO no change in motion no work Force is ┴ to motion no Work W=F*d F 90° d 1 N m = 1 Joule • W = 0! Carrying a weight corresponds to W = 0. • F is perpendicular to d, θ = 90°: • W = 0. IF you are pushing against an immovable object, d =0 so W = 0!! d =0 Which Path Requires the Most Energy? • Suppose that a car traveled up three different roadways (each with varying incline angle or slope) from the base of a mountain Vertical distance only affects the PE • • • • The PE at the top of each is 30 J, The work to move up each would be 30 J. How can this be???? For Work use Force || to displacement!! Fg UP d Fg UP d Fg UP d Work = F * d Using the force and the distance along the ramp • The amount of work done by a force on any object is given by the equation Work = F d cosΘ • F is the Applied force, • d is the displacement • θ is the angle between the F & d Force not in same direction as displacement: we use the component in the direction of the motion • Let be an unbalanced force applied to an object, and let d be a resulting displacement. Concepts Involving Work F || = F * cos Θ If F|| is the component of F along d, then the WORK done by F, is given by W = F|| x d Work = F * cos Θ * d Work = F * d * cos Θ Work is of the nature of a force times a distance ! Work = F║ d But if Force not Parallel to motion: Work done by a force parallel to the displacement is Work = F d cos Θ Add Page 7 section #1 Mechanical Work Equations Work on incline • Answer the following about the above picture: • Draw the three forces acting on the object. • If the object slides down the incline, what work was done with gravity? • What work is done against the motion? • What is the net work done? • Predict the final velocity of the object. Units of Work • Whenever a new quantity is introduced in physics, the standard metric units associated with that quantity are discussed. In the case of work (and also energy), the standard metric unit is the Joule (abbreviated J). One Joule is equivalent to one Newton of force causing a displacement of one meter. In other words, • The Joule is the unit of work. • 1 Joule = 1 Newton * 1 meter • 1J=1N*m • In fact, any unit of force times any unit of displacement is equivalent to a unit of work. Some nonstandard units for work are shown below. Notice that when analyzed, each set of units is equivalent to a force unit times a displacement unit. • • • • • • • • • • • • • • • • • • • A trolley of mass 10 kg is pulled along the floor. The pulling force is 36 N, at an angle of 30� above the horizontal. Ignore friction. What other forces are acting on the trolley? Gravity and normal reaction force. What is the total vertical force acting on the trolley? Why can we say this? Zero. No vertical motion � zero vertical acceleration � Fy = 0. What is the magnitude of the normal force? The vertical forces are gravity, the normal force, and the vertical component of the pulling force. Let's find the horizontal and vertical components of the pulling force: Px = P cosq = 36 cos30 = 31 N Py = P sinq = 36 sin30 = 18 N The gravitational force (ie the weight of the trolley) is: w = mg = 10 ×9.8 = 98 N Now we either say that the total vertical force is zero: Fy = w + N + Py 0 = -98 + N + 18 80 N = N or we can say that the forces up equal the forces down (but be careful with sign and direction!) up = down N + Py = w N + 18 = 98 N = 80 N What is the total force acting on the trolley? The vertical forces add to zero, the total force must be the horizontal pulling force, equal to 31 N horizontally. What is the acceleration of the trolley? F = ma 31 = 10 a 3.1 m/s2 = a The acceleration is 3.1 m/s2 horizontally, in the direction the trolley is being pulled. diagram showing the forces acting on a block that is resting on an inclined plane Measuring the coefficient of friction on a flat surface Measuring the coefficient of friction on an inclined surface. ://en.wikibooks.org/wiki/How_To_Build_a_Pinewood_Derby_Car/Physics FRICTION VS. PULLING ANGLE • PURPOSE: To demonstrate how pulling angle affects the frictional force, and to show that the minimum force required to pull an object occurs when pulling at the angle of repose a, where the coefficient of friction u=tana. • DESCRIPTION: A wooden board of weight w, lying on a sandpaper surface, is pulled at an angle a by a string connected to a spring scale. The force F required to move the board is given by: F = w / [ (1/u)cosa + sina]. Differentiating F with respect to a, the minimum force is seen to occur at the angle of repose, u=tana. Pulling horizontally is definitely not the most efficient angle! • SUGGESTIONS: Pull horizontally to determine u, then check the angle of repose by tilting the sandpaper surface. Then pull at a variety of angles to demonstrate that pulling at the angle of repose requires the least force. Moving objects can do work (bowling ball displaces pins; hammer pushes in nail; car creams cow) energy of motion = kinetic energy. Energy is the ability to do work • Suppose a "bullet" of mass m moving at vo mushes into a block of soft clay and experiences a constant force F (decelerating at a constant rate, a). • • The force required to slow down the bullet is F = ma, where a is the deceleration. The work done through the distance s, W = Fs = mas. • During the deceleration, v2 = vo2 + 2as; or as = 1/2(v2 vo2) • or Work done ON OBJECT = . (would get same result for non-constant F and a). Potential energy changes to kinetic energy due to work done by gravity PE A boulder resting at the top of a hill has potential energy. • Gravitational Potential Energy is the energy stored due to height. • Work can change the height of the Boulder • Work can change the potential energy of the Boulder Example: PEKE • You are standing on the edge of a cliff and decide to push a rock that has a mass of 2kg off the edge with your foot. Using conservation of mechanical energy, determine how fast the rock is going just before it impacts the ground 75m below. Assume that there is no air resistance. If you dropped a 20kg rock from the same spot would the velocity be the same? Driver’s Training and braking • Speed of a car increased by 50%. By what factor will minimum braking distance be increased (ignore reaction time)? • Braking force same. Therefore: • Distance = 2.25times original Mechanical Energy: traditional definition = the ability to do work. Work done in stopping a car: The mechanical work done on the object = the change in kinetic energy; If W is positive, KE increases; IF W is negative, KE decreases. -- often called Work-Energy Theorem (Net work done = change in kinetic energy Work done by gravity • Suppose a car of mass 1200 kg falls vertically a distance of 24 m (starting from rest; i.e., voy = 0). • (a) What is the work done by gravity on the car? • Fgrav = mg; Dy = 24 m; Force and displacement in same direction (down). • Fgrav = Fnet • because gravity is only force acting on car. Using Work-Energy Theorem • (b) Find final velocity of car. • Using constant acceleration (g): • Using Work-Energy Theorem: • • • Plug in: v = 22 m/s. A mass m is moving in a straight line at velocity vo. It comes into contact with a spring with force constant k. How far will the spring compress in bringing the mass to rest? A spring exerts F proportional to x in both compression and extension (for reasonable x). Driver’s Training and braking • Speed of a car increased by 50%. By what factor will minimum braking distance be increased (ignore reaction time)? • Braking force same. Therefore: Distance = 2.25 times original Both cases body uses chemical energy for muscles to exert these forces (you get tired, need more Twinkies to keep going)--in terms of mechanical work performed: ZIP! Work done holding the box up Work, PE, KE • In the diagram at left no work is done moving an object along a horizontal direction when there is no friction (recall Galileo's principle of inertia. No force is required to keep an object moving. A small amount of work is necessary to start it moving and an equal amount is "given back" when it is stopped.) • Whether the motion is circular (as with the pendulum), up a series of steps, or in one horizontal movement followed by lifting the height h, the work done is the same to raise the object to a height h. This is what we mean by "Path Independence". Work, PE, KE The spring has more mechanical (elastic) potential energy when compressed. Pendulum graph with low friction • Energy slowly "leaks away" from mechanical system Pendulum --graph with high friction KE -- PE • Assume the track is frictionless and the car starts from rest. • 1. At what position is kinetic energy the greatest? • 2. When placed in order of least amount of kinetic energy to greatest, positions of the roller coaster are; 3. At what position does ET = EP only? Work, KE,PE • 4. A 50.0 kg crate is pushed 4.00 m across a level frictionless surface with a force of 58.0 N. The kinetic energy of the moving crate is? • 5. An object is dropped from rest a certain height above the floor. Its speed at the moment before it hits the floor is independent of: • 6. When work done on a frictionless horizontal surface, all the work is transformed into: Work, KE,PE • 7. A sled slides down a snowy hill. As the sled descends the hill the total mechanical energy; • 8. A boy rides up a hill on his bike. As he ascends the hill his kinetic energy; • 9.Friction makes molecules vibrate with; • 10. As potential energy of a closed or isolated system increases, __________ decreases Work, KE,PE • 11. This type of energy is called "energy of position"? 12. This type of energy is called the energy of motion? • 13. Which of the following is a unit for work? • 14. A figure skater exerts an upward force of 25.0 N on his skating partner while he glides 35.0 m on the ice. How much work is done on the lifted skater? Work, KE,PE • 15. Work is done when a rubber band is stretched. Energy is then stored in the band until it snaps back. The stored energy is best known as ___________ energy • 16. A crane raises a 20.0 N object above the ground in 2.50 seconds. The work done by the crane is 500 N. What is the power output of the crane? Work, KE,PE • 17. For a free falling object, the ratio of the force of gravity to the acceleration is: • 18. Which two quantities are measured in the same units? 19. A moving body must undergo a change of: 20. Two objects of equal mass are a fixed distance apart. If the mass of each object would be tripled, the gravitational force between the objects would? • Gravitational Potential Energy Elastic Potential Energy The Potential Energy in figures a, b, and c are: The Kinetic Energy is the energy an object has by virtue of its motion. The kinetic energy of an object of mass m moving at a velocity v is , for pure transitional motion. II. Total Mechanical Energy The Total Mechanical Energy of an object is the sum of its kinetic and potential energies, . total mechanical energy of the system is conserved • Law of Conservation of Energy: When the work done on a system by non-conservative forces is zero, then the total mechanical energy of the system is conserved (i.e., constant). Energy Transformation for a Pendulum KE PE No friction!! • The conservation of mechanical energy is demonstrated in the animation below. Observe the KE and PE bars of the bar chart; their sum is a constant value. • Read each description and indicate whether energy is transformed from KE PE or from PE KE • A ball falls from a height of 2 meters in the absence of air resistance. Read each description and indicate whether energy is transformed from KE PE or from PE KE • A skier glides from location A to location B across the friction free ice. Read each description and indicate whether energy is transformed from KE PE or from PE KE • A baseball is traveling upward towards a man in the bleachers. Read each description and indicate whether energy is transformed from KE PE or from PE KE • A bungee chord begins to exert an upward force upon a falling bungee jumper. Read each description and indicate whether energy is transformed from KE PE or from PE KE • The spring of a dart gun exerts a force on a dart as it is launched from an initial rest position. The following descriptions involve external forces indicate whether the gain or loss of energy resulted in a change in the object's kinetic energy, potential energy, or both • Megan drops the ball and hits an awesome forehand. The racket is moving horizontally as the strings apply a horizontal force while in contact with the ball. Read each description and indicate whether energy is transformed from KE to PE or from PE to KE • A baseball player hits the ball into the outfield bleachers. During the contact time between ball and bat, the bat is moving at a 10 degree angle to the horizontal. Read each description and indicate whether energy is transformed from KE to PE or from PE to KE • Rusty Nales pounds a nail into a block of wood. The hammer head is moving horizontally when it applies force to the nail. Read each description and indicate whether energy is transformed from KE to PE or from PE to KE • The frictional force between highway and tires pushes backwards on the tires of a skidding car. Read each description and indicate whether energy is transformed from KE to PE or from PE to KE • A diver experiences a horizontal reaction force exerted by the blocks upon her feet at start of the race. Read each description and indicate whether energy is transformed from KE to PE or from PE to KE • A weightlifter applies a force to lift a barbell above his head at constant speed. law of conservation of the total mechanical energy • (i.e. if Wnc=0 then ET= constant). • And then, Work - Energy Theorem • Let be the total mechanical energy of an object at position one (1). • Let be its total mechanical energy at position two (2). The change in the total mechanical energy, from position one to position two, is . non-conservative forces. • Work - Energy Theorem: The change in the total mechanical energy of a system (or object), from position one to position two, is equal to the work done on the system (or object) by the non-conservative forces. How Far Will It Skid? • This mathematical relationship between initial speed and stopping distance is depicted in the animation Work and Energy--Energy Transformation for a Dart • The animation shows that the energy of the dart/gun system is initially present in the form of the elastic potential energy (PEs) and gravitational potential energy (PEg). The springs of the dart gun are compressed which accounts for the elastic potential energy. Furthermore, the dart is initially elevated at a height of 1-meter above the ground which accounts for the gravitational potential energy. The presence of these two initial forms of energy are shown by the PEg and PEs bars of the bar chart. External-internal forces We categorize a force as internal or external because: • internal forces conserve mechanical energy (keep same) • external forces either add or remove mechanical energy Internal Forces External Forces Fg Fsp FA Ffr Fair FT F┴ The Work-Energy Theorem Internal vs. External Forces Forces can be categorized as internal forces or external forces. External-internal forces • The significance of categorizing a force as internal or external is related to the ability of that type of force to change an object's total mechanical energy when it does work upon an object. • When work is done upon an object by an external force, the total mechanical energy changes of that object is changed conservation of mechanical energy-practice • Example 1 • You are standing on the edge of a cliff and decide to push a rock that has a mass of 2kg off the edge with your foot. Using conservation of mechanical energy, determine how fast the rock is going just before it impacts the ground 75m below. Assume that there is no air resistance. If you dropped a 20kg rock from the same spot would the velocity be the same? conservation of mechanical energy-practice • Example 2 • A 4kg block slides across a frictionless table with a velocity of 5m/s into a spring with a stiffness of 2500N/m. How far does the spring compress? Net force— net work • In the picture above, answer the following: The picture represents a 2 kg object which starts from rest. The force represents the net force. – Describe the motion of the object for its first 10 m. – Describe the motion of the object for the distance interval of 10 m to 15 m. – Determine the acceleration of the object for the first 10 m. – How long will it take the object to go the 10 m? – What is the net work done over the 10 m interval? – What is the object's speed at the end of the 10 m interval? – What is the net work done from 10 m to 15 m? – What is the object's speed at the end of the 15 m? PE and KE and work • In the picture above, the object is rolling along the horizontal surface. Answer the following: • Describe the motion of the object when it leaves the edge of the surface. • How long does it take the object to reach the ground? • What is the speed of the object the instant before it hits? • What is the initial gravitational U of the object? • What is the initial EK of the object? • What is the initial mechanical energy of the object? • Draw a graph representing the change in EK of the object. • On your graph, when will gravitational U equal EK. • Draw a graph representing the mechanical energy of the object. Elastic PE and KE • Two blocks, one with mass M and the other with mass m, are connected by a light frictionless spring. You hold mass m and compress mass M. When mass M is released, it rebounds with speed v. Mass M is compressed a distance d. Using only the given variables and constants, answer the following: • What is the spring constant? • What work is done to compress mass M? • Draw a graph of the change in elastic U as the spring is compressed and then released. • What is the maximum speed of the object? • What is its speed when it is compressed 1/3 d? Work on incline • Answer the following about the above picture: • Draw the three forces acting on the object. • If the object slides down the incline, what work was done with gravity? • What work is done against the motion? • What is the net work done? • Predict the final velocity of the object. Variables for power The standard metric unit of power is the Watt. • Power is the rate at which work is done. It is the work/time ratio. Mathematically, it is computed using the following equation. Variables for power Energy Transformation for Downhill Skiing • Along the inclined section of the run, the total mechanical energy of the skier is conserved provided that: • there is a negligible amount of dissipative forces (such as air resistance and surface friction), and • the skier does not utilize her poles to do work and thus contribute to her total amount of mechanical energy Stopping Distance of a Hot Wheels Car When the Hot Wheels car collides with the box and skids to a stop, external forces do a significant amount of work upon the car. The force of friction acts in the direction opposite the car's motion and thus does negative work upon the car. This negative works contributes to a loss in mechanical energy of the car. Summary of Energy Forms Mechanical Energy Type Formula Kinetic Gravitational Elastic PEg = mgh KE.PE and pendulum http://www.hcc.hawaii.edu/distance/sci122/Programs/p19/p19.html more there Energy Tranformation E = mgh3 E = mgh2 + 1/2 mv22 E=1/2mv12 E = mgh3 Energy Conservation • TME is the sum of both types of energy. • TME is the same at all points if there is NO friction. Elastic force • the amount of force is directly proportional to the amount of stretch or compression (x); the constant of proportionality is known as the spring constant (k). Elastic potential energy • There is a special equation for springs which relates the amount of elastic potential energy to the amount of stretch (or compression) and the spring constant. The equation is Use 9.8 m/s/s to determine the gravitational PE. gravitational potential energy • These relationships are expressed by the following equation: • PEgrav = mass * g * height PEgrav = m * g * h • In the above equation, m represents the mass of the object, h represents the height of the object and g represents the acceleration of gravity (approximately 10 m/s/s on Earth). PE to KE in freefall Forces on a spring PE- gravitational and elastic Kinetic energy • • • • • The amount of kinetic energy which an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object. • • where m = mass of object • v = speed of object Units of work and energy • Like work and potential energy, the standard metric units of measurement for kinetic energy is the Joule. As might be implied by the above equation, 1 Joule is equivalent to N-m N = kg m/s/s For elastic force, F= kx, Area under curve from 0 to xf = PE and KE for pendulum PE and KE for horizontal spring Elastic potential energy The second form of potential energy which we will discuss in this course is elastic potential energy. Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs, an arrow drawn into a bow, etc. The amount of elastic potential energy stored in such a device is related to the amount of stretch of the device - the more stretch, the more stored energy. (a) Show that the system is nonconservative (b) How much work is done by the non-conservative force? • Skier with Friction • A skier of mass 80 kg starts from rest down a slope where h = 110 m. The speed of the skier at the bottom of the slope is 20 m/s. Potential energy problem • 1. A cart is loaded with a brick and pulled at constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top? Work problem • . If a force of 15.0 N is used to drag the loaded cart (from previous question) along the incline for a distance of 0.90 meters, then how much work is done on the loaded cart? Kinetic energy problem • 1. Determine the kinetic energy of a 1000kg roller coaster car that is moving with a speed of 20.0 m/s • If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy? Kinetic energy problem • Missy Diwater, the former platform diver for the Ringling Brother's Circus had a kinetic energy of 15 000 J just prior to hitting the bucket of water. If Missy's mass is 50 kg, then what is her speed? Kinetic energy problem • 4. A 750-kg compact car moving at 100 km/hr has approximately 290 000 Joules of kinetic energy. What is the kinetic energy of the same car if it is moving at 50 km/hr? Ben's power rating. • Suppose that Ben Pumpiniron elevates his 80-kg body up the 2.0 meter stairwell in 1.8 seconds. If this were the case, then we could calculate Ben's power rating. It can be assumed that Ben must apply a 800-Newton downward force upon the stairs to elevate his body. By so doing, the stairs would push upward on Ben's body with just enough force to lift his body up the stairs. It can also be assumed that the angle between the force of the stairs on Ben and Ben's displacement is 0 degrees. With these two approximations, Ben's power rating could be determined as shown below. • the expression for power can be rewritten once more as force*velocity. This is shown below. • This new expression for power reveals that a powerful machine is both strong (big force) and fast (big velocity). Work and power practice • 1. Two physics students, Will N. Andable and Ben Pumpiniron, are in the weightlifting room. Will lifts the 100-pound barbell over his head 10 times in one minute; Ben lifts the 100pound barbell over his head 10 times in 10 seconds. Which student does the most work? Which student delivers the most power? Explain your answers. Work and power practice • During the Personal Power lab, Jack and Jill ran up the hill. Jack is twice as massive as Jill; yet Jill ascended the same distance in half the time. Who did the most work? Who delivered the most power? Explain your answers. Work and power practice • 3. A tired squirrel (mass of 1 kg) does push-ups by applying a force to elevate its center-of-mass by 5 cm. Determine the number of push-ups which a tired squirrel must do in order to do a mere 1.0 Joule of work. If the tired squirrel does all this work in 4 seconds, then determine its power. Work and power practice • 3. A tired squirrel (mass of 1 kg) does pushups by applying a force to elevate its center-ofmass by 5 cm. Determine the number of pushups which a tired squirrel must do in order to do a mere 1.0 Joule of work. If the tired squirrel does all this work in 4 seconds, then determine its power. Work and power practice • 4. If little Nellie Newton lifts her 40-kg body a distance of 0.25 meters in 2 seconds, then what is the power delivered by little Nellie's biceps? Work and power practice • Your monthly electric bill is expressed in kilowatt-hours, a unit of energy delivered by the flow of l kilowatt of electricity for one hour. Use conversion factors to show how many joules of energy you get when you buy 1 kilowatt-hour of electricity. Work and power practice • An escalator is used to move 20 passengers every minute from the first floor of a department store to the second. The second floor is located 5-meters above the first floor. The average passenger's mass is 60 kg. Determine the power requirement of the escalator in order to move this number of passengers in this amount of time. • 9. Calculate the potential, kinetic, and mechanical energies, velocity, work, and power of the ball at the various locations. Important equations used throughout this lab packet are listed below for reference. PE mgh Eo E f W KE • Important equations used throughout this lab packet are listed below for reference. • % KELOST = 100g = -9.8 m/s2 1 KE mv 2 2 1 2 y v o t gt 2 KE KE f KE o 1 2 x v o t at 2 KE % KELOST = KE o Key Terms • • • • • • • • • • • • • energy chemical energy sound energy light energy nuclear energy potential energy heat energy mechanical energy gravitational potential energy point of reference kinetic energy Work-Energy Theorem Law of Conservation of Energy An Eskimo pulling a sled with a rope at an angle θ to the horizontal. • Problem An Eskimo returning from a successful fishing trip pulls a sled loaded with salmon. The total mass of the sled and salmon is 50.0 kg, and the Eskimo exerts a force on the sled by pulling on the rope. The coefficient of kinetic friction between the sled and the ground is 0.200. (a) The Eskimo pulls the sled 5.40 m, exerting a force of 1.10 102 N at an angle of θ = 0°. Find the work done on the sled by friction, and the net work. (b) Repeat the calculation if the applied force is exerted at an angle of θ = 30.0° with the horizontal. Figure 5.6 An Eskimo pulling a sled with a rope at an angle θ to the horizontal. Strategy See Figure 5.6. The frictional work depends on the magnitude of the kinetic friction coefficient, the normal force, and the displacement. Use the y-component of Newton's second law to find the normal force , calculate the work done by friction using the definitions, and sum with the work done by the applied force without friction to obtain the net work on the sled. Part (b) is solved similarly, but the normal force is smaller because it has the help of the applied force app in supporting the load.
