practice
- A typical adult in the United States consumes something like 2000 dietetic calories
of food per day. Determine the average power generated by such an adult (assuming
he or she is not gaining or losing weight).
- Determine the cost of operating a 7000 Btu, room-sized air conditioner in
New York City for the duration of the summer. Assume that electricity costs 14¢
per kilowatt·hour and that the air conditioner will run about 10 hours
a day for 80 days.
- Write something calculus based if possible.
- The athlete in this video clip [mov]
is performing a weightlifting maneuver known as the snatch. In this maneuver,
the barbell must be lifted from the platform to a point above the head, with
the
arms and legs fully extended, in a single movement. The barbell must then be
held motionless until the referees give the signal and then returned to the
platform.
In this particular video …
- the mass of the barbell is 77.5 kg (for comparison, the mass of athlete is 58 kg),
- the disks on the barbell have a diameter of 450 mm, and
- the video advances at 25 frames per second (with 71 frames total).
Determine the following quantities for the barbell this athlete is lifting as
functions of time …
- height
- velocity
- acceleration
- applied force
- work
- power
Most of this question is a review of mechanical concepts discussed in previous
sections in this book. Only the last part deals with power. To begin this problem,
you will need some sort of screen measuring tool. Many basic image editing applications
have this function built into them. If your doesn't, you might like to try Wadruler
[exe] for Windows or Freeruler
[external link] for Mac OS X.
numerical
- A 64 kg student travels from the first floor to the fourth floor of a school (a height
of 15 m).
- What total work did she do climbing the stairs?
- How long would this trip last if the student produced 480 W of power?
- A motorized winch is rated at 10.0 kW.
At what maximum speed can this winch raise a mass of 27,500 kg?
- A pedaling cyclist turns a 17.5 cm crank arm at 200 rpm.
(The crank arm distance is measured from one pedal to the axle.) Calculate
the average force exerted on the pedals if the cyclist does work at the rate
of 600 W.
- How fast must a cyclist climb a 12° hill to maintain a power output of
190 W? Ignore friction and assume the mass of the cyclist plus bicycle
is 85 kg?
- The graph below shows the power output vs. time for an elevator motor in operation.
- What does the area under this curve represent?
- Calculate it.
- The world's most powerful laser (the Petawatt) went online at Lawrence Livermore
National Laboratory (LLNL) in May of 1996. This laser produced a peak power of
1.25 petawatts (1.25 × 1015 W), ten times
more power than the previous record holding laser (which was also built at LLNL)
and 1200 times more powerful than the entire electrical generating capacity of
the United States. Although it is incredibly powerful, the Petawatt is not particularly
energetic. Pulses from the Petawatt typically last less than half a picosecond
(10−12 s). How long could an ordinary 60 W light bulb
run on the energy delivered in one pulse of the Petawatt?
- A problem for Americans only: Show that one horsepower is equivalent to one pound
of thrust at 375 mph.
- A document based question. Read the following excerpt from the 14 June 2005
New York Times.
Lance Armstrong's strength and endurance sometimes seem too extraordinary
to be believed.
Armstrong, a six-time winner of the Tour de France bicycle race who next month
will try for his seventh straight victory, can cover 32 miles [51.5 km]
in one hour of riding. In contrast, the average cyclist covers 16 miles [25.7 km];
a top marathon runner can cover 21 miles [33.8 km] on a bike.
Armstrong can ride up the mountains in France generating about 500 watts of
power for 20 minutes, something a typical 25-year-old could do for only 30
seconds. A professional hockey player might last three minutes - and then throw
up….
Armstrong showed subsequent improvements until his career was stopped short
in 1996 with a diagnosis of testicular cancer. Eight months after his treatment
ended, he was back in the Austin laboratory.
"He wanted to know if anything was permanently wrong," Dr. Coyle
said.
They took measurements and found nothing to stop him, except his own willingness
to compete.
Armstrong did compete. "In the next two years his heart got even better,
his lactic acid dropped further and, amazingly, his efficiency increased to
23 percent," Dr. Coyle said.
Lance Armstrong has a mass of about 70 kg and competes on a 7.5 kg
bike. How many meters could he climb after 20 minutes of cycling?
investigative
- Ringworld
is the title of a classic science fiction novel written by Larry Niven in 1970.
Set in the year 2850, it is the story of four adventurers (two human and two
alien) who are chosen to explore an engineered world encircling a sun-like star.
The Ringworld is an enormous cylindrical band with a radius roughly equal to
that of the earth's orbit and a width about the same as the diameter of the sun.
It was constructed by some unspecified form of matter transmutation using the
planets and minor bodies that once orbited the Ringworld's sun as raw material.
The flat, inner surface is covered with a natural-looking, earth-like terrain
and it spins at a speed fast enough to provide its inhabitants with the sensation
of earth gravity. Thousand mile high walls along the edges keep the Ringworld's
atmosphere from spilling out into space. The Ringworld is the home of hundreds
of hominid species, but they are mostly non-technological. The sufficiently advanced
civilization that engineered the Ringworld collapsed centuries ago and the adventurers
find only its remains.
- Fill the following table with the data you will need to solve the remaining
problems.
| ringworld parameter |
terrestrial equivalent |
value |
unit |
| radius |
earth-sun distance |
|
m |
| width |
diameter of the sun |
|
m |
| mass |
mass of jupiter |
|
kg |
| " |
mass of saturn |
|
kg |
| " |
mass of uranus |
|
kg |
| " |
mass of neptune |
|
kg |
| " |
total mass |
|
kg |
| available power |
luminosity of the sun |
|
W |
| n/a |
radius of the earth |
|
m |
- Determine the surface area of …
- Ringworld
- the earth
- a sphere with radius equal to the earth-sun distance
- How fast does Ringworld spin to provide its inhabitants with the sensation
of normal earth gravity? State your answer in …
- meters per second
- earth days per rotation
- rotations per earth year
- Determine the …
- kinetic energy of Ringworld due to its rotation and
- number of days it would take to accelerate a newly constructed Ringworld
from rest up to its final rotational speed if all the solar energy that
landed on its surface was converted to kinetic energy.
