Download Lecture 8

9/17/2010
I’ll be in the help room:
• Friday: 1:30-2:30
Today2) conservation of energy- pushing file cabinets, and
blocks of stone across ground and up ramps.
3) Human energy. Work when
exercising, calories burned.
4) motional energy (kinetic energy).
Force is the same if book stationary or moving up
with constant velocity (= weight =mg)
What about the amount of work needed?
Get tired more quickly lifting book (or weight)
up and down or just holding it up?
a. same, b. more tired if lifting.
work = force x distance, only do work on weights
if moving through a distance by lifting.
To lift cart straight up at constant speed, force up needs to
balance force of gravity down.
So force up is mg.
So work is mg x (change in height “h”).
So amount of work to move something up without friction is
always mgh!!
Steeper ramp, bigger force, shorter distance, same work.
To transfer energy to other objects requires work
Confusing Terminology: “WORK”
In “Everyday life language” : we are doing
work if it takes our energy to do it!
In “Physics”:
work = force applied times distance
through “work” transfer energy to the
object it is acting on or the surrounding
world.
I can only push with a force of 10 N, but I want to move
a 3 kg weight up a height of 0.5 m. How steep a ramp
should I make (keeping it as short as possible)?
a. can’t do it, takes 29.4 N to raise a 3 kg mass.
b. a 50% grade (2m forward for 1 m up)
c. 3 m forward and 1 m up?
d. 5 m forward and 1 m up?
e. 5 m forward and .5 m up?
Longer ramp, smaller force, longer distance, same work.
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9/17/2010
I can only push with a force of 10 N, but I want to move
a 3 kg weight up a height of 0.5 m. How steep a ramp
should I make (keeping it as short as possible)?
a. can’t do it, takes 29.4 N to raise a 3 kg mass.
b. a 50% grade (2m forward for 1 m up)
c. 3 m forward and 1 m up?
d. 5 m forward and 1 m up?
ans. c
e. 5 m forward and .5 m up?
What could be a good first step to solve this problem?
a. Ask the professor
b. Remember that the work to push something up a ramp
to 0.5 m is the same as to lift it straight up 0.5 m.
c. Draw a picture with the forces labeled.
d. Remember that W= Fxd so multiply 10N x 0.5m = 5J
e. All of the above
Push weight (file cabinet, stone block) across board.
Weight of “file cabinet” = 19.5 N
Measure force needed. F= weight x ?
measure Ffriction = 5.8 N
= 0.3 x weight
slide it 0.5 m.
(work) Force x distance done =?
a. 5.8 J, b. 19.5 J, C. 2.9 J., d. 11.6 J
answer: C.
0. 5 m
= 5.8 N X 0.5 m
= 2.9 J
Now push it (weight = 19.5 N) up a hill so it goes up 0.25 m in
moving 0.5 m. How much work will it take to push it up?
a. 2.9 J. b. 4.9 J, c. 9.8 J, d. 19.5 J, e. 7.8 J
ans. is e: 7.8 J. Total work =
work against friction nearly the same (= 2.9 J)
+ work to lift it up against gravity
(= mg*change in height = 19.5 N x 0.25 m = 4.9 J
= 7.8 J
.25 m
So now, how much
force is required to
push it up the board?
a. 9.75 N, b. 15.6 N, c. 19.5 N, d. 5.8 N, e. impossible to tell
ans. is b: 15.6 N.
work=force x distance = 7.8 J from above = F x 0.5 m.
so F= 7.8 J/0.5 m = 15.6 N.
I can only push with a force of 10 N, but I want to move
a 3 kg weight up a height of 0.5 m. How steep a ramp
should I make (keeping it as short as possible)? How to start?
a. Ask the professor
b. Remember that the work to push something up a ramp
to height h is the same as to lift it straight up height h.
c. Draw a picture with the forces labeled.
d. Remember that W= Fxd so multiply 10N x 0.5m = 50N
e. All of the above
F hand =
10N
h = 0.5m
F gravity = Weight = 30N
•W straight up= F x d = mgh = 3 kg x 9.8 x 0.5
•W up ramp=10 N x d and W straight up= W up ramp
•so d = 30 x .5/10 = 1.5 m.
•1.5 m long for 0.5 m up is same as 3 m for 1 up.
A note about friction
• Friction force varies with lots of things …
roughness of material, little things sticking up
on surface, etc.
• But we can find an average friction force for a
particular type of surface. Many fairly smooth
surfaces near friction force of 0.3 x weight.
Push it up same hill so it goes up 0.25 m in moving 0.5 m.
Friction force was 0.3 weight. Now add some gritty sand
so friction larger, 0.5 weight. How much is the energy that
turns into heat though friction compared to energy in grav.
potential energy? (heat J)/(grav. energy).
a. They are the same, b. Heat energy greater than grav. pot. energy
c. Grav pot energy greater than heat energy, d. can’t tell which
W grav. = mgh = 19.5 N x 0.25 m = 4.9 J
W frict. = 0.5 mg x dist = 0.5 x 19.5 N x 0.5 m = 4.9 J
They are the same!
.25 m
What about without the gritty sand?
W frict. less than W grav.
Note on homework- bunch of calculations.
“Expert” approach- sees how concepts apply. Actually
same problems over again. Different form but applying same
concepts- easy. “Novice” new form= new problem, start
from scratch each time-hard.
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9/17/2010
1 food calorie = 4184 J.
Human energy.
1. What the heck is a Joule??
= force(N) x distance(m) = 0.75 foot pounds (lift 1 pound up 1ft)
lift 20 pound barbell up 7 feet = 140 foot pounds = 187 Joules.
I jump 0.5 m. How many Joules of energy?
1 food calorie = 4184 J.
power= energy/second. 1 watt = 1J/s. 100 watt lightbulb
means 100 Joules electrical energy/sec.
Human eats 2500 calories per day (and burns it up, not to fat)
means 2500/24x 60 x 60 s = 0.29 cal/sec =
0.29 cal/s x 4184 cal/J = 121watts.
100 watts of heat just sitting here!
How much of food goes into work?
How much force x distance can person do?
easy to measure with stationary bicycle.
elite women bicyclist can produce 300 W power,
typical tour de France rider 400 W of power, [~1/2 horsepower]
and Lance Armstrong can hit 500 W of power.
Athletic man sustain ~150 watts (nonheat!) for 10 hour day
= 150 J/s x 10 x 60 x 60 s = 5,400,000 J of work/day.
How many calories is this?
a. 2140 cal, b. 1290 cal, c. 150 cal d. 12000 cal
b. 5.4E6 J/4184J/cal =1291 cal.
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
d. heat.(80%) 755 cal in 1 hour on stair stepper = 3.6 million J!
=2,237,000 ft pounds. 1 step = 1 ft, F x dist = 170 ft lbs, x 3600 steps
per hour= 1ft x 170 lb x 3600 = 612,000 foot-pounds of F x dist.
2,237,000 ft-lb chem. energy from food.
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