DEFINITION OF KINETIC ENERGY Kinetic energy is the energy of motion Kinetic energy depends on an objects speed and mass.
DEFINITION OF KINETIC ENERGY The kinetic energy KE of and object with mass m and speed v is given by Scalar quantity SI Unit for Kinetic Energy is the Joule
Kinetic Energy What are the SI units for KE? kg•m2/s2 or N•m or J Ask students to determine the units from the equation before showing this on the slide. Have them see that, since N are kg•m/s2, the units of N•m are equivalent to kg•m2/s2.
Work and Kinetic Energy KE is the work an object can do if the speed changes. Wnet is positive if the speed increases. Discuss the many examples of moving objects doing work on other objects. For example, a moving baseball bat does work on a ball as it exerts a force on the ball, and the ball moves a distance in the direction of the force. Conversely, the ball does work on the bat as it exerts a force opposite to the direction the bat is moving. Work has a negative value in this case. A change in speed for an object allows it to do work on its environment.
5.2 Energy Question #8 Calculate the kinetic energy of an 8.0X104kg airliner flying at 600.0 km/h. 1.1X109 J
5.2 Energy Question #9 Two bullets have masses of 3.0g and 6.0g, respectively. Both are fired with a speed of 40.0 m/s. Which bullet has more kinetic energy? What is the ratio of their kinetic energies? The bullet with the greater mass 2 to 1
5.2 Energy Question #10 Two 3.0g bullets are fired with velocities of 40.0 m/s and 80.0m/s respectively. What are their kinetic energies? Which bullet has more kinetic energy? What is the ratio of their kinetic energies? 2.4 J The bullet with the more speed 4 to 1
5.2 Energy Question #11 A running student has half the kinetic energy that his younger brother has. The student speeds up by 1.3 m/s, at which point he has the same kinetic energy as his brother. If the student’s mass is twice as large as his brother’s mass, what were the original speeds of both the students and his brother? 3.2 m/s 6.4 m/s
5.2 Gravitational Potential Energy DEFINITION OF POTENTIAL ENERGY ~Stored Energy ~Gravitational potential energy depends on the height from a zero level
5.2 Gravitational Potential Energy DEFINITION OF POTENTIAL ENERGY The potential energy (PE) is defined by the mass and height of the object above an arbitrary zero level.
5.2 Gravitational Potential Energy
Potential Energy Energy associated with an object’s potential to move due to an interaction with its environment 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 Hold a book above the desk. The book has the potential to move due to an interaction with Earth (gravity). Stretch a rubber band with a wad of paper held in it like a sling shot. The paper has the potential to move due to an interaction with its environment (the rubber band).
Gravitational Potential Energy What are the SI units? kg•m2/s2 or N•m or J The height (h) depends on the “zero level” chosen where PEg = 0. This equation comes from W = Fd = (ma)d = mgh, so PEg is simply the work done in lifting an object. To help students understand the fact that the zero level is arbitrary, hold a book over the desk and ask them what they would use for h in order to calculate the PE. Then, maintaining the book at the same height, move it over the floor and ask the students once again what value they would use for h. Point out that, in general, our primary concern in physics involves changes in PE, not the actual amount of PE. The change in PE is always the same regardless of what zero level is assigned. Generally, the zero level is assigned to the lowest point the object will reach. For example, the desk if the book is held over the desk, and the floor if the book is held over the floor.
5.2 Gravitational Potential Energy Example A Gymnast on a Trampoline The gymnast leaves the trampoline at an initial height of 1.20 m and reaches a maximum height of 4.80 m before falling back down. What was the initial speed of the gymnast?
5.2 Gravitational Potential Energy
5.2 Elastic Potential Energy DEFINITION OF ELASTIC POTENTIAL ENERGY The energy stored in a spring that is compressed or stretched K = Spring Constant X= Distance the spring is compressed or stretched
Elastic Potential Energy The energy available for use in deformed elastic objects Rubber bands, springs in trampolines, pole-vault poles, muscles For springs, the distance compressed or stretched = x Point out that x in the diagram is the “Distance compressed.” This will be used in the equation for elastic potential energy (slide 10). Discuss the transfer of the elastic potential energy to the block when the deformed spring returns to its original configuration.
5.2 Elastic Potential Energy DEFINITION OF ELASTIC POTENTIAL ENERGY Increasing the spring constant indicates a stiffer spring K = Spring Constant SI unit = N · m
5.2 Elastic Potential Energy Question #12 Staples inside a stapler are kept in place by a spring with a relaxed length of 0.115m. If the spring constant is 51.0 N/m, how much elastic potential energy is stored in the spring when its length is 0.150 m? 3.1 X 10-2 J
5.2 Elastic Potential Energy Question #13 A spring with a force constant of 5.2 N/m has a relaxed length of 2.45m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57m. Calculate the elastic potential energy stored in the spring. 3.3 J
5.2 Elastic Potential Energy Question #14 A 40.0kg child is in a swing that is attached to ropes 2.00m long. Find the gravitational potential energy associated with the child relative to the child’s lowest position under the following conditions: When the ropes are horizontal. 785 J
5.2 Elastic Potential Energy Question #15 A 40.0kg child is in a swing that is attached to ropes 2.00m long. Find the gravitational potential energy associated with the child relative to the child’s lowest position under the following conditions: When the ropes make a 30.0° angle with the vertical. 105 J
DEFINITION OF MECHANICAL ENERGY The mechanical energy is the sum of potential energy and kinetic energy.
Mechanical Energy (ME) ME = KE + PEg + PEelastic Does not 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 Discuss ME as a useful tool for studying motion. Do not tell students yet that ME is conserved. They will determine this from the coming slides and calculations. As an example. toss a ball in the air and talk about the potential energy and kinetic energy as it rises and falls. As another example. show students a pendulum and talk about the PE and the KE changing as it swings.
5.2 Mechanical Energy Question #16 What forms of energy are involved in the following situations: A bicycle coasting along a level road Kinetic Throwing a football Kinetic and gravitational potential Winding a hairspring of a clock Elastic potential
5.2 Mechanical Energy Question #17 A pinball bangs against a bumper, giving the ball a speed of 42 cm/s. If the ball has a mass of 50.0g, what is the ball’s kinetic energy in joules? 4.4 X 10-3 J
5.2 Mechanical Energy Question #18 A spoon is raised 21.0 cm above a table. If the spoon and its contents have a mass of 30.0g, what is the gravitational potential energy associated with the spoon at the height relative to the surface of the table? 6.18 X 10-2 J
5.2 Mechanical Energy Question #19 A 65kg diver is poised at the edge of a 10.0m high platform. Calculate the gravitational potential energy associated with the position of the diver. Assume the zero level is at the surface of the pool? 6.4 X 103 J
5.2 Mechanical Energy Question #20 What is the kinetic energy of a 1250kg car moving at 45.0 km/h? 9.77 X 104 J
5.2 Mechanical Energy Question #21 The force constant of a spring in a child’s toy car is 550 N/m. How much elastic potential energy is stored in the spring if the spring is compressed a distance of 1.2 cm? 4.0 X 10-2 J
5.2 Mechanical Energy Question #22 A 25.0 kg falling object strikes the ground with a speed of 12.5 m/s. If the kinetic energy of the object when it hits the ground is equal to the gravitational potential energy at some height above the ground, what is the height ? 7.96 m
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 Students should use PE = mgh to get the PE at each point. To calculate the KE they need to first find the velocity. The easiest way to get v2 is using vf2 = 2gy. (Note that the initial velocity is zero, so it was eliminated from the equation). After getting the velocity, use the equation KE = 1/2 mv2. After making these calculations, show students the chart on the next slide.