Download Lecture 11

Energy: Part 3
Physics 1010: Dr. Eleanor Hodby
Lecture 11:
- Human energy and power
- KE
Reminders:
HW5 online
Don’t forget Phys 1010 D2L discussion forum
Lectures can be rewatched online
Reading quiz in just a second
Power
Power = Energy/Time.
Units: 1 watt = 1J/s.
 100 watt lightbulb means 100 Joules electrical energy/sec.
Inactive human eats 2500 Calories per day (and burns it up, not to fat)
So how many watts does he use just sitting there?
Burns 2500 Cal/(24x 60 x 60) s = 0.29 Cal/s
= 0.29 Cal/s x 4184 J/Cal
= 121J/s
= 121 W
100+ W of heat per person by just sitting here!
No wonder lecture theatres, concert halls etc get hot and stuffy when full!
How much power is 1Watt??
How much useful power (work/second) can a
human output over a 15 second interval?
a.
b.
c.
d.
e.
5W
50W
500W
5000W
50,000W
Human energy – Calories and Joules.
(or how long must I spend on the stairmaster to burn off my chocolate bar?
What the heck is a Joule??
1J (work or energy) = 1N (force) x 1m (distance)
How much work do I do benchpressing a 40kg (90lb) barbell 0.5m?
W = F ×d
= mgh
= (40) (9.8) (0.5)
F
= 196 J
But how does that compare to a chocolate bar?
Calories are just another unit for measuring energy
1 food calorie = 1kcal = 1Cal = 4184 J.
Decent chocolate bar has 400 kcal or 1673600J
So it has the same energy required for 8539 Benchpresses!
mg
How much of our food energy goes into useful work?
- Tour de France rider: 400 W for ~1 hour, [~1/2 horsepower]
- Athletic man: ~150 W on bike for 10 hour day
So if I go to the gym and pedal at 150W output, I could
a) Power the ac for the entire building
b) Power a space heater
c) Power a lightbulb
d) Power not enough to run anything of interest
How much of our food energy goes into useful work?
Athletic man outputs 150 W of mechanical power on bike for
10 hour day
How much mechanical work does he do (expressed as Cal)
during 10 hour ride?
(1 Cal = 4184J)
a. 2140 Cal, b. 1290 Cal, c. 150 Cal d. 12000 Cal
But he eats ~ 5800 Cal/day
Where does the rest of the energy (5800-1291=4500 Cal) go?
a. chemical, b. sweating, c. light, d. heat, e. odor
So back to our human powered gym idea……
Can we generate useful amount of power while getting fit?
• Pedaling on the exercise bike at the gym (connected to generator) I
produce 150W of useful electrical power
• And 4×150W = 600W of body heat
• The ac unit in the gym uses at least 150W of electrical power to remove
the heat I generate from the room and keep the temperature constant
• So at the gym
- I produce 150W of electrical power by pedalling
- I consume more than 150W of electrical power keeping cool
- I have a net electrical power CONSUMPTION at gym………….
- Ignores energy used for lights, car ride there, warm shower……..
• You’d be ‘greener’ (consume less power) just going for a regular
bike ride outside (Power consumption = 0)
• Or better yet ditching the car and doing your errands on a bike
Summary
• Energy and work so far:
– GPE
– Work done by friction (heat)
– Work done by applied forces (by me)
Wext - Wfriction = DPE + DKE
– Power
• This time
– Kinetic energy
– Water distribution (energy of running water)
New form of energy to think about.
Motional or kinetic energy.
KE = ½ mass x (velocity)2
KE = ½ mv2
Notice that this has the right units to be an energy:
KE = kg×m2/s2
Energy = N×m
= kg×(m/s2)×m
= kg×m2/s2
Conservation of energy questions
1
2
Two identical cars with really good bearings and solid tires roll on a
very smooth, hard track (without friction). They start from rest at the
same height and coast downhill, ending at the same height. How do
their speeds compare at the end?
a. 1 is going much faster than 2
b. 1 is going a little faster than 2
c. 1 is going the same speed as 2
d. 1 is going a little slower than 2
e. 1 is going much slower than 2
Conservation of energy questions
1
2
h
How do their speeds compare at the end?
Conservation of energy questions
1
2
h
h = 15cm
What is the speed of the cart at the end of the tracks?
a. 0 m/s
b. 0.6 m/s
c. 1.7 m/s
d. 17 m/s
e. 170 m/s
Conservation of energy questions
1
h
2
h2
A
h2 = 25cm
What is the speed of the cart at A?
a. Faster than final speed
b. Slower than final speed
c. Same as final speed
Push a 0.5 kg cart up 0.10 m (no friction).
How much gravitational potential energy (GPE) does it gain?
0.1 m
If we let it roll back down, how fast will it be going when it is back
to where it started from?
a. 9.8 m/s , b. 1.4 m/s, c. 2 m/s, d. 1 m/s, e. 0.2 m/s
Conservation of energy questions
Push a 1 kg cart up 0.10 m.
How much gravitational potential energy gained?
(Recall : the 0.5 kg cart gained 0.5J)
GPE = mgh, so 1 J
0.1 m
Push the 1 kg cart up 0.10 m. How fast will it be going after it rolls
back down?
a. same as the 0.5 kg cart, b. twice as fast, c. ½ as fast,
d. sqrt(2) x faster, e. sqrt(1/2) slower.
How high do balls go if you toss them?
(Conservation of energy - The easy method)
KE = 0
GPE = mgh
h?
Wext - Wfriction = DPE + DKE
KE lost = GPE gained
Consider the changes between start and
top of flight:
KE lost
½ mv02
h
v0 KE = 1/2mv02
GPE = 0
= GPE gained
=
mgh
=
v02/2g
Example of “expert” approach:
Realize same physics principle applies to any
situation where you’re just trading between
gravitational and kinetic energy
(No friction/external forces)
e.g. Cars on ramps, Balls in air Look different but SAME physics, SAME maths
How high do balls go if you toss them?
Consider 2 balls of different sizes, different masses tossed up
with same initial velocity.
Compare the maximum heights that they reach:
a) Heavier ball goes higher
b) Same height
c) Lighter ball goes higher
v0
v0
Dropping cannonballs onto a board.
What is going to happen to the board?
What forms of energy are involved?
a. Gravitational potential energy
b. Gravitational potential energy and Kinetic energy
c. Kinetic energy and Thermal energy
d. Chemical energy, Gravitational Potential energy, and
Thermal energy
e. Gravitational Potential energy, Kinetic energy, and
Thermal energy
Dropping cannonballs onto board.
Now drop the ball from twice the height.
What will the measured temperature rise be?
a. same, b. somewhat hotter, c. not as hot,
d. 10 times hotter.
Conservation of energy summary
- Often your best route for answering mechanics problems
(especially when time is not involved)
- Wext - Wfriction = DPE + DKE
- Conservation of energy has been checked in thousands of
experiments.
- This principle always works.
- There is no such thing as energy for free, or a perpetual
motion machine!
When tackling a new situation/problem to get a solution or to make a
prediction about behavior, usually the first thing a physicist does is figure
out the different forms of energy, how much there is of each, and how it is
being converted between various forms.