1. Energy MechanicalDissipated GravitationalElastic KineticPotential Energy – a property of an object which can be stored in different ways and transferred from one object to another, but never created or destroyed It is a property that is capable to produce “change” 1 Energy

2. 2 Four Basic Energy Storage Mechanisms Elastic Potential Energy (E s ) – energy stored in objects that return to their natural shape after being deformed (objects such as elastic cords, springs, etc) Gravitational Potential Energy (E g ) – energy stored in objects that have been raised to an elevated position from a pre- defined “zero” position typically at the lowest point in its overall motion Kinetic Energy (E k ) – energy stored in objects that are moving Dissipated Energy (E d ) – energy that is stored in non-mechanical ways such as sound, heat, light, etc

3. 3 When studying energy, you have to define the system. This is done by placing a dotted line around the object(s) in question. The line around object (a) defines the system as just the cart. The line around object (b) includes the track in the system The line around object (d) includes the earth in the system. If your system includes enough objects, energy will simply transfer from one object in your system to another. Since it stays inside your system, it is considered a closed system. A system is not closed when energy transfers out to or in from an object outside of the system. For now, we will limit our study to closed systems where energy is stored in different ways or by different mechanisms.

4. Potential Energy Potential energy -- energy that is stored in an object based on its position relative to another more “natural” position or its shape relative to another more “natural” shape A spring gains potential energy when it is deformed (compressed or stretched) from its original shape by a force. The spring responds with a restoring force based on Hooke’s Law The spring force increases as the displacement (deformation) increases 4

5. 5 A = ½bh = ½(x)F = ½(x)kx The area under the line is the amount of potential energy stored in the spring.

6. A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring. 3.26 J 6

7. As the cannon ball moves upward from its original position, it gains gravitational potential energy because it is continually moving upward from the lowest position. The amount of energy (Newton- meters) increases because the distance it travels upward increases (meters). The amount of force being applied to the ball is the gravitational force (Newtons). An object gains gravitational potential energy when it is positioned at a location above its lowest position in the defined system. 7

8. E g = gravitational potential energy (J) m = mass (kg) g = gravitational field constant (N/kg) Δy = vertical displacement (m) The gravitational potential energy is the product of the gravitational force acting on the object and the height of the object. 8 The gravitational potential energy is proportional to the vertical displacement of the object. The vertical displacement is measured from the zero point that you define in your system. Typically, it is the lowest point.

9. A roller coaster with a mass of 1000 kg travels from ground level up a 25 m hill and then back down 10 m. What is the potential energy at the top of the hill and at the position on the other side? 245 kJ 147 kJ 9

10. Kinetic Energy 10 Energy Speed When the energy in a system is used to cause an object to move, the relationship between the energy and speed of the object is NOT linear. The speed of the object increases as it stores more energy… But, as the object stores more energy, the change in speed that results is not proportional. The increase in speed does not keep up with the increase in energy that is stored.

11. E k = kinetic energy (J) m = mass (kg) v = speed (m/s) 11 To get a linear relationship, the graph has to be manipulated by squaring the x-axis. The energy is directly proportional to the square of the speed. This energy that is associated with an object’s speed called kinetic energy. Bottom line…if an object moves, it stores energy kinetically.

12. 1.What is the change in the ball’s kinetic energy? 2.What caused the ball’s kinetic energy to decrease? 3.Where does that energy go? A baseball (m = 140 g) traveling 32 m/s moves a fielder’s glove backward 2.5 cm before coming to rest. -71.7 J 12

13. 13 A compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its kinetic energy when it is moving at 30 mi/hr. 80 000 J

14. Law of Conservation of Energy The total energy in a closed system never changes but… Energy can me transferred from one storage mechanism to another inside the system Ex: kinetic energy to potential energy in the cart/earth system 14 In this trampoline/jumper/earth system, the total energy is constant even though it is stored differently in each position. This demonstrates the Law of Conservation of Energy.

15. A pendulum demonstrates energy conservation effectively: At beginning, all energy is potential At bottom, all potential is changed to kinetic At top, all kinetic is changed back to potential The storage mechanism changes, but the total amount stays constant. 15 As it falls, potential is changed to kinetic As it rises, kinetic is changed to potential

16. 16 When energy simply moves being stored kinetically to being stored potentially, the system demonstrates the Principle of Conservation of Mechanical Energy. E k1 + E g1 + E s1 = E k2 + E g2 + E s2 Problem is…this is a theoretical concept that has no basis in reality. In real life…the pendulum would not swing as high In real life, sound would be created and the tracks would heat up. Both of these phenomena demonstrate a “loss” of mechanical energy.

17. 17 If we want to maintain a closed system, we account for this lost energy by calling it “dissipated” energy. Dissipated energy – energy in a system that is no longer mechanically useful. It can be stored in many different nonmechanical ways…light, heat, sound. In some ways, it is a “catch all” for the energy in a closed system that is no longer stored kinetically, elastically, or gravitationally.

18. 18 A 1000-kg roller coaster sits at the top of a 45-m hill at rest. It descends to the bottom of the hill and then through a loop. The loop is at ground level and measures 10 m in diameter. 1. Determine its speed at the top of a 10-m high loop. 2. Determine its speed at the same position if its mass is 500 kg. 26.2 m/s

19. 19 A 17 m long rope swing hangs vertically from a tree branch in the middle of a 10 m wide river. A person runs up, hoping to grab the rope, swing over the hole, and drop vertically off the rope to land on the other side. At what minimum speed must he be running? 3.84 m/s

20. Work When an object outside the system interacts with the system, there is often a transfer of energy either in or out of the system. This process always results in a change in movement because that external object is an agent which exerts a force on the system. The process is called a “working” process and the amount of energy that either enters or leaves the system is called “work”. The general formula for work is: W = Work (Joule) F = force (N) d = distance (m) 20 In the “arrow” system, the bow string is an external agent that gives energy to the arrow. This is a “working” process

21. W = Work (Joule) F = force (N) d = distance (m) Θ = angle between the force and distance 21 W = Fdcosθ When the force being applied is at an angle, it needs to be broken into components. The only component that contributes to the work is the one that is parallel to the movement of the box. This man is not doing work on the bag by holding it because his force on the bag is perpendicular to motion. (cos 90° = 0)

22. Work is a scalar quantity – it has a magnitude but it does not have a vector direction. A working energy process can either introduce or remove energy from your system In the “nail” energy system, the external hammer introduces working energy to the nail system Force and distance traveled are in same direction (+W) Nail experiences a momentary increase in speed In the “hammer” energy system, the external nail removes working energy from the hammer system Force and distance traveled are in opposite directions (-W) Nail experiences a momentary decrease in speed 22

23. A person pulls a stationary 50-kg crate 40 m along a horizontal floor with a constant force of 100 N at an angle of 37°. The floor is rough and exerts a friction force of 50 N. Determine the work done by each force acting on the crate and the net work being done on the crate. How fast is the crate moving after traveling a distance of 40 m? W g = 0 W n = 0 W p = 3195 J W f = -2000 J 23 43.7 m/s

24. Conservative force a force whose work done is stored as potential energy which can be used again Ex:force of gravity force of spring Nonconservative force a force that does no work or whose work done is NOT stored as potential energy but converted to dissipated energy (heat, light, etc) Ex: normal force frictional force 24 Conservative/Nonconservative Forces

25. Suppose our system is a box that gets tossed upward. When F g acts on the box, working energy leaves the “box” system because the force acts downward while the box moves upward. This results in the box slowing down and the E k decreasing (no E g because no earth in system). Because F g is a conservative force, when the box falls it reclaims the working energy that left the system. The force, F g, still acts downward and the box moves downward. This results in the box speeding up the E k increasing. Therefore, the net work done on the system is zero in the closed path. 25

26. If our same “box” system was on the ground and being pushed around, F f would be doing working energy on the box removing energy from the system. Because F f is a nonconservative force, regardless of the direction that the box moves, working energy would be removed from the system. That force can never do work to reclaim the energy. Therefore, the net work on the system is always negative. 26

27. E k1 + E g1 + E s1 = E k2 + E g2 + E s2 + W NC The work done by nonconservative forces (to produce heat, light, etc.) is equal to the combined change in kinetic energy and the change in potential energy. W NC = (E k1 – E k2 ) + (E g1 – E g2 ) + (E s1 – E s2 ) W NC = ∆ E k + ∆ E g + ∆ E s When nonconservative forces are present, the working energy leaving the system changes the amount of mechanical energy. 27

28. A dart of mass 0.100 kg is pressed against the spring of a toy dart gun. The spring (k = 250 N/m) is compressed 6.0 cm and released. If the dart detaches from the spring when the spring reaches its natural length, what speed does the dart attain? 3.0 m/s 28

29. A 21.7-kg child descends a slide 3.5 m high and 5.5 m in length. She reaches the bottom with a speed of 2.2 m/s. How much thermal energy (heat) is generated from friction? What is the force of friction acting on the child? 692 J 29 126 N

30. Power When you lift weights, you apply a force to the bar. If the bar is your system, there is working energy that is entering the system while you lift the bar. When you do faster repetitions, you are doing the same work in less time. 30 Same thing with faster pull ups…Your rate of doing work is greater. Your body is experiencing an energy change in a shorter amount of time.

31. 31 Since working energy always changes the amount of energy in a system, power can be thought of as the rate at which an object’s energy changes. You could express this equation as…

32. P = W / t P = (Fdcosθ) / t P = Fcosθ (d / t) P = power (W) F = force (N) v = constant or average speed (m/s) Θ = angle between force and direction of speed Another useful formula for power is derived from the definition of power (P = W/t) and the definition of speed (v = d/t) 32 P = Fvcosθ

33. A pump is to lift 18.0 kg of water per minute to a height of 3.60 m. Assuming the pump moves the water at a constant speed, what power rating (watts) should the pump motor have? 10.6 W 33

34. A car is traveling up a 10°incline at a constant speed of 80 km/h. The car has a mass of 1400 kg and the frictional force of the road on the car is 700 N. How much horsepower does the motor need in order to move at that speed? (1 Horsepower = 550 ft lb/s = 746 W) 91.2 hp 34