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 = vf – vi

ta = accelerationvf = final velocityvi = initial velocityt = 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/hAcceleration = 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 - 0Acceleration = 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/sAcceleration = 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 seconds9.8m/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-on-collisions-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.