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)
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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
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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
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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
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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
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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.