Transcript m/s Calculations with KE= ½ mv 2

Monday January 11
Tuesday January 12
Unit Question
What is energy?
Guiding Question /
Learning Target
Identify and calculate kinetic and potential energy.
Warm-up
What type of energy is responsible for this?
Agenda
1. Energy Math Notes & practice
2. Newton’s Cradle & Conservation of Energy
Quiz Friday
Homework
Rest of Semester:
Monday
Tuesday
Wednesday
Thursday
Friday
11
12
13
14
15
18 NO SCHOOL
19
20
21 COCOA AND
CRAM 6–8:30 IN GH
(EXTRA CREDIT)
22 LAST DAY FOR
MISSING WORK
25
26
2 & 6 FINAL
27
1 & 5 FINAL
28 HALF DAY
3 & 4 FINAL
29 NO SCHOOL
There will be no A.T. the first few weeks of second semester,
same as there was no A.T. the first few weeks of first semester.
You WILL have a final
• Study guide next week
• Open note
Newton’s POE
The Law of Conservation of Energy
Energy cannot be created or destroyed;
it can only change forms.
How does the picture describe the Law of
Conservation of Energy?
Will the girl swing forever? Why or why not?
Following Energy’s Trail
• If energy is conserved, why do objects that are
moving eventually stop (seem to lose energy)?
• The energy is converted to other forms
• This is why perpetual motion is impossible
Calculating GPE and Motion energy
• The unit for all energy is Joules (J)
Kinetic Energy
• The kinetic (motion) energy of any moving object
depends on both its mass and velocity.
• Velocity = distance(in meters) ÷ time(in seconds)
If you know an
object’s mass and
velocity, you can
calculate its kinetic
energy.
Calculations with KE= ½ mv2
• m = mass in kilograms
• v = velocity in m/s
Calculations with KE= ½ mv2
•
•
•
•
PEMDAS!
Start by squaring the velocity
Divide your mass by 2
Multiply the answers
KE= ½ mv 2
Steps for ½
2
mv
• What is the kinetic energy of a 1500kg car moving at a speed of 29
m/s?
1. Find your velocity
29*29 = 841
2. Square it
3. Find your mass
1500/2 = 750
4. Divide it by 2
5. Multiply your two answers
841*750 = 630750 J
Unit!
Kinetic Energy (KE)
• An object has a lot of KE for two reasons
• It has a lot of mass (a lot of weight)
• And/or it has lots of velocity (speed)
**Note: if you double the mass, it doubles the KE. If you double the velocity, it
will QUADRUPLE the KE
KE= ½ mv
2
Practice Problems
• Calculate the kinetic energy in joules of a 1500kg car moving at the
following speeds:
i. 29m/s
ii. 18m/s
iii. 42km/s
Answers
• Calculate the kinetic energy in joules of a 1500kg car moving at
the following speeds:
• i. 29m/s
KE=1/2mv2=(1/2)(1500kg)(29m/s)2=
630000 J
• ii. 18m/s
KE=(1/2)(1500kg)(18m/s)2=
240000 J
• iii. 42m/s
KE=(1/2)(1500kg)(42m/s)2=
1323000 J
Potential Energy of Position
(gravitational potential)
• GPE depends on an objects mass (kg), height (m), and
the acceleration due to gravity.
PE= mgh
More height
= more
potential
energy.
More mass =
more
potential
energy.
If you know an
object’s height and
mass, you can
calculate its
potential energy.
Calculations with PE= mgh
• m = mass in kilograms
• g = acceleration due to gravity 9.8 m/s2
• h = height in meters
PGE=weight x height
• Weight = mass * gravity
• The units for weight in the metric system are Newton
(N)
• A Newton is a kg-m/s2
Which Equation to use?
• Look at your UNITS!
• If the mass is given, the unit is kg.
• Use mgh
• If the weight is given the unit is N.
• Use weight x height
Practice Problems
• Calculate the gravitational potential energy in the following
systems:
• A car with a mass of 120 kg at the top of a 42 m hill
• A 637N climber on top of Mt Everest (8800 m high)
• A 0.52 kg bird flying at an altitude of 550 m
A car with a mass of 1200 kg at the top of a 42 m hill
Which equation? mgh or weight*height
PE=mgh=(1200kg)(9.8m/s2)(42m)=
493,920 Joules
A 673 N climber on top of Mount Everest (8800m high)
Which equation? mgh or weight*height
PE=weight x height (673)(8800m)=
5,922,400 J
A 0.52kg bird flying at an altitude of 550m
Which equation? mgh or weight*height
PE=(0.52kg)(9.8m/s2)(550m)=
2802.8 J
Example