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Energy of Motion. What is Energy?. Definition: Energy is the ability to do work. Work is done when a force moves an object over a given distance. Engineering Connection:. Engineers need to understand the many different forms of energy in order to design useful products
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What is Energy? Definition: Energyis the ability to do work. Work is done when a force moves an object over a given distance.
Engineering Connection: Engineers need to understand the many different forms of energy in order to design useful products • Mechanical engineers are concerned about the mechanics of energy — how it is generated, stored and moved. • Product design engineers apply the principles of potential and kinetic energy when they design consumer products. For example, a pencil sharpener employs mechanical energy and electrical energy. • When designing a roller coaster, mechanical and civil engineers ensure that there is sufficient potential energy (which is converted to kinetic energy) to move the cars through the entire roller coaster ride.
Introduction • All energy is classified into two broad categories: Potential Energy & Kinetic Energy • Either form of energy can change into the other. • You need energy in order to get things done. For example, you know that your body must use energy if you want to pick up a box and move it across the room.
Potential Energy Potential energy is energy an object has because of its position 0r composition. Potential energy is stored energy. It has the “potential” to do work.
Potential Energy -example • A rock at the edge of a cliff has potential energy due to its position. Gravitational force can pull the rock down to the bottom of the cliff.
Potential Energy -example • Fuel, such as gasoline or coal, also has potential energy. When the fuel burns, the energy stored in its chemical bonds is released.
Calculating Potential Energy Potential energy is measured in Joules (J). • Near Earth, you can calculate an object’s gravitational potential energy (PE) by the following formula: GPE = mass x g x height GPEis the gravitational potential energy mass is the mass in kilograms height is the height in meters g is the acceleration due to gravity At sea level, g = 9.81 meters/sec2or 32.2 feet/sec2. .
Calculating GPE - example • Suppose a rock at the edge of a cliff has a mass of 10 kg, and its height above the ground below is 100 m. • GPE = mgh =10 kg x 9.8meters/sec2 x 100 m = 9800 J
Kinetic Energy • Definition: The energy of motion Kinetic energy is the energy an object has because of its motion and is also measured in Joules (J). Any object that is moving has kinetic energy
Kinetic Energy- Example • An example is a baseball that has been thrown. The kinetic energy depends on both mass and velocity
Calculating Kinetic Energy • Kinetic Energy can be expressed mathematically as follows: • KE stands for kinetic energy. • Mass is in kilograms • V is the speed in meters per second Note that a change in the velocity will have a much greater effect on the amount of kinetic energy because that term is squared. :
Calculating Kinetic Energy • The 1 kg ball is moving at a speed of 20 m/s. • KE = ½ mv2 = 0.5 x 1 kg x (2o m/s)2 = 0.5 x 1 x 400 = 200J
Potential and Kinetic Energy Transformations • Potential energy can change into kinetic energy, and vice versa.
Mechanical Energy • The total amount of mechanical energy in a system is the sum of both potential and kinetic energy, also measured in Joules (J). Total Mechanical Energy = Potential Energy + Kinetic Energy
Total Mechanical Energy = Potential Energy + Kinetic Energy
Law of Conservation of Energy • In the perfect physics world, a pendulum will swing forever. Energy is constantly transferred between potential and kinetic energies.
Law of Conservation of Energy • In the real world, a swinging pendulum eventually stops due to friction. However, the total energy of the pendulum never changes. The energy is transferred from potential energy to kinetic energy. The friction is shown as a form of heat energy which includes air resistance and sound energy.
Potential and Kinetic Energy Transformations • Potential energy can change into kinetic energy, and vice versa. In the perfect physics world, a person can jump from a diving board and hit the water with the same amount of energy as they had before they jumped. Energy is transferred from potential energy to kinetic energy until they hit the water. When the diver hits the water, kinetic energy is transferred into heat and sound energies. The energy of the system is transferred from potential to kinetic to heat.
Swinging Pendulum • This activity demonstrates how potential energy (PE) can be converted to kinetic energy (KE) and back again. Given a pendulum height, students calculate and predict how fast the pendulum will swing by understanding conservation of energy and using the equations for PE and KE. The equations are justified as students experimentally measure the speed of the pendulum and compare theory with reality.
Introduction • Remember that an object's potential energy is due to its position (height) and an object's kinetic energy is due to its motion (velocity). • Potential energy can be converted to kinetic energy by allowing the object to fall (for example, a roller coaster going down a big hill or a book falling off a shelf).
As a pendulum swings, its potential energy converts to kinetic and back to potential. Recall that energy may change its form, but there is no net change to the amount of energy. This is called conservation of energy.
Pre-lab Questions • Where will the pendulum have the greatest potential energy? • Where will it have the greatest kinetic energy? • Will pendulums with higher heights go faster or slower?
Materials • Materials List • 2 stopwatches • Masking tape • 10 feet of string or fishing line • Heavy object or weight • Calculator
Three equations will be used in this activity: PE = m∙g∙h KE = ½ m∙Vt2 Vm = distance ÷ time where m is mass (kg), g is gravity (10 m/s2), h is height (meters), Vt is the calculated velocity (m/s), and Vm is the measure velocity (also m/s). To make the calculations simpler, use the metric system for measurements and calculations. This way, we can approximate gravity as 10 m/s2 and not worry about the English system's wacky units of mass.
Procedure • Work in Groups of 4 • Pick a height at which to release the pendulums. This should range from 15-40 cm (.15-.4 m) from the floor. • Calculate the potential energy. Each team member should do this, as a way to verify the result. • Calculate the theoretical velocity, Vt, at the bottom of the swing. • Remember, KE at the bottom of the swing will equal PE at the top of the swing. • Move to a designated area and tie your weight to the string/line so that it barely misses the ground while hanging. • Place two pieces of tape on the wall on opposite sides of the hanging pendulum and record the distance between the two pieces. The distance should range from 30-50 cm (.3-.5m). Choose a larger distance for a higher height (i.e., h = 40 cm → distance = 50 cm). The pendulum should rest in the middle of the two pieces of tape. • One person pull back the weight until it reaches one of the pieces of tape. • Two team members synchronize two stopwatches, each holding one, and start timing when the pendulum is released. • The first person stops his/her stopwatch when the pendulum passes over the opposite piece of tape and the second person stops his/her watch when it returns back to the initial piece of tape. • Record both times and calculate the difference in time. • Repeat the experiment four times so everyone can exchange roles. • Complete the worksheet. • How close were the values for the theoretical velocity and the measured velocity?
Questions to think about during the lab • What happens to the potential energy as the pendulum swings down? • When the pendulum swings to the other side, what happens to the kinetic energy?
Post Lab Discussion • If engineers can use potential energy (height) of an object to calculate how fast it will travel when falling, can they do the reverse and calculate how high something will rise if they know its kinetic energy (velocity)? • For what might an engineer use this information?
Activity Extensions So far, you have calculated the mechanical energy when it is either completely potential or kinetic energy. What about when the mechanical energy is composed of both? Create a table and/or graph showing the potential and kinetic energies of their pendulum at heights of 0, ¼h, ½h, ¾h, and h. (Hint: You already know the values at heights 0 [purely kinetic] and h [purely potential].)
Engineering Connection • Understanding mechanical energy, or the energy of motion, is at the root of so many engineering applications in our world. Engineers design a wide range of consumer and industry devices — vehicles, appliances, computer hardware, factory equipment and even roller coasters — that use mechanical motion. To do this, they pay close attention to how energy is generated, stored and moved. Whether designing elevators, power plants or race cars, engineers take into consideration the concepts of work and power. Engineers collaborate to design dams that generate electricity from the flow of water. Part of this process involves calculations to determine how much power can be generated. Engineers incorporate what they know about momentum and collisions to design protective "crumple zones" and safety devices into vehicles to absorb most of the energy being transferred during a crash. In sports such as baseball and golf, investigating how the human body and equipment interacts with the ball during impact helps engineers design better and safer sports equipment. To reduce drag force and thus improve gas mileage, engineers design vehicles to be more aerodynamic. Engineers understand friction and use it to help control motion; some engineers design braking systems that prevent skidding. When designing vehicles — everything from push scooters to light rail trains to your car — engineers take into account all of the energy of motion concepts, because in real life, these forces are happening and interacting at the same time.
Key Words energy, motion, mechanical energy, kinetic energy, potential energy, work, power, waterwheel, momentum, conservation of momentum, conservation of energy, collision, elastic, inelastic, heat, friction
Mechanical Energy Definition: Energy that is composed of both potential energy and kinetic energy. Mechanical energy is the form of energy that is easiest to observe on a daily basis. All moving objects have mechanical energy. There are two types of mechanical energy: potential energy and kinetic energy.
Conservation of Energy • energy can change from one form into another. • Due to the principle of conservation of energy, energy can change its form (potential, kinetic, heat/thermal, electrical, light, sound, etc.) but it is never created or destroyed.
