Transcript Energy Math
Energy Math Speed, McQueen - http://www.youtube.com/watch?v=Zb9KnXNYCiQ Potential and Kinetic Energy • Potential Energy = Mass x Gravity x Height (PE = mgh) g = 9.8 m/s2 • Kinetic Energy = ½ Mass x Velocity2 (KE = ½mv2) • • • • • Energy = joules Weight = newtons Height = meters Mass = kilograms Velocity = m/s Pg. 29 Speed • Speed = distance/time (d/t) • Example – If a bicyclist covers 20 kilometers in 1 hour, her speed is 20 km/h. – What if she runs 6 meters in 1 second? • In science, the preferred unit of speed is meters per second (m/s) Table Tennis - http://espn.go.com/video/clip?id=8180705 Bolt - http://www.livescience.com/22082-olympic-speed-usain-bolt.html Megatron - http://espn.go.com/video/clip?id=7126233 Pg. 15 Average Speed • Average Speed = Total Distance covered Total travel time • What is the average speed of a cheetah that sprints 100m in 4 seconds, stops for 10 seconds, and then sprints 200m in 10 seconds? Average Speed • If you drove a car for 4 hours at 80 km/hr, then stopped at the loo for 1 hour, what is your average speed? 16 Velocity • Velocity = distance/time (d/t) in a specific direction • For example, if a vehicle travels at 60km/h, do we know the velocity? • How about if we say it moves at 60km/h to the north – do we know the velocity? Determine if the following statements are speed or velocity… • A cruise ship traveling at 60 knots south. – Velocity • A cyclist going 10 mph. – Speed • A downhill skier going 40 mph. – Speed • A person walking 4 mph on a treadmill. – Speed • A jet traveling 600 mph taking-off headed northeast. – Velocity Acceleration • a = v f – vi t a = acceleration vf = final velocity vi = initial velocity t = time Pg. 17 • Acceleration is ANY change in motion. – When you are in a car and you step on the “accelerator” the car accelerates. – When the brakes are applied, the car accelerates. (called deceleration or negative acceleration) Example • A car steadily increases speed. Suppose that in 1 second, the velocity increases from 30 km/h to 35 km/h. In the next second, you go from 35 km/h to 40 km/h, and so on. • The velocity changes by 5 kilometers per hour each second. change of velocity 5km/h Acceleration = change in time = 1 s = 5km/h.s Example 1 • A skater goes from a standstill to a speed of 6.7 m/s in 12 seconds. What is the acceleration of the skater? change of velocity 6.7m/s - 0 Acceleration = time = 12 s a = 0.56 m/s2 Example 2 • During a race, a sprinter increases from 5.0 m/s to 7.5 m/s over a period of 1.25s. What is the sprinter’s average acceleration during this period? change of velocity 7.5 m/s – 5.0 m/s Acceleration = time = 1.25 s a = 2.0 m/s2 Gravity and Acceleration • Acceleration of a free falling object is 9.8 m/s2 • For every second an object free falls, the velocity will increase by 9.8 m/s2 • Example: An object is dropped for 3 seconds 9.8m/s2 = vf – 0 3 sec vf = 29.4 m/sec Force • • • • Force = Mass x Acceleration F=ma Force is measured in Newtons (N) You push a friend sitting on a swing. She has a mass of 50 kg and accelerates at a rate of 4 m/s2. Find the force you exerted. F = 50kg x 4 m/s2 = F = 200 N Force Videos • FSN Force - http://www.youtube.com/watch?v=A_wnt84iyMk • NFL Impact - http://www.wired.com/wiredscience/2010/11/espn-sport-science-oncollisions-video-break-down Work • Work = Force x Distance • W= F x d • Work is measured in Joules (J) Is the person doing work? ___ When pushing a 1000 N car 20 meters? ___ When lifting a rock off the ground? ___ When holding a book in their hands? ___ When pushing hard against a brick wall? ___ When walking up the stairs? Work 2 • • • • • • More, Less, or the Same amount of Work? ___ You use more force to move an object. ___ You lift a 20 N object faster. ___ You raise an object a shorter height. ___ You move a lighter object. ___ You move an object farther. Work Example • When a weightlifter lifts a barbell, he does work on the barbell • When he is holding the barbell over his head, he does no work Power • Which are you more tired… • Walking a box up a flight of stairs or running a box up a flight of stairs? • You are doing the same amount of work, so why are you more tired? • POWER • Power is the measure of how fast work is done Power • • • • Power = Work/Time P = W/t Power is measured in Watts (Joule per second) One Watt (W) of power is used when one joule of work is done in one second • Power is also the rate at which energy is changed from one form to another Power • • • • More or Less Power? ___ An engine can lift an object faster. ___ Someone takes more time to push a car. ___ You take the same amount of time to do more work. • ___ Same distance; same time; more force.