AP50a Fall 2013
Estimation Activity
Th Oct 24
Instructions: Estimate (not Guess or Google!) the quantities below to the nearest order of magnitude. Report all
your answers as an order of magnitude (using the indicated units). Spend the first five minutes thinking individually
about a strategy, then go at it with your team. You have 30 minutes exactly, so think fast!
When your team has completed all five questions, check your answers with a teaching staff member.
Important: Start from what you know; do not look up any values. Pretend you are being asked these questions at a
job interview. Or you want to surprise people at a dinner party.
1. Estimate the angular velocity of a formula one race car wheel. Units: [degrees/s]
Formula one car moves at about 200mph (90 m/s)
The wheel radius is approximately 1 ft, therefore the circumference is approximately 6ft (2m)
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AP50a Fall 2013
2. Estimate the speed of a human being at midnight on Earth’s equator with respect to an observer viewing earth
from the sun. Units: [m/s].
From an observer above the North Pole, the earth orbits the sun counterclockwise, and also rotates about its axis
counterclockwise. Therefore at midnight (when you are opposite the sun, you are moving in the direction of the
orbit.
Part I: Determine linear speed of earth in orbit.
Assume the distance from earth to sun is 100,000,000 miles (160,000,000 km)
Assume the length of a year is 365 days
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Part II: Determine the linear speed of a human on earth’s surface.
Assume the earth’s radius is about 6,000km.
Assume the earth rotates once every 24 hours.
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which is negligible compared to the speed of earth’s orbit.
3. Estimate the number of postal delivery trucks in the United States. Units: [postal trucks]
Assume one postal truck makes a single stop every minute on average
Assume that each person receives on average 1 piece of mail per day
Assume that each stop services on average 5 people
Assume there are 300,000,000 people in the US
Assume the trucks are on duty from 9am to 6pm (9 hour day)
AP50a Fall 2013
4. Estimate the torque applied to the back wheel of a bicycle tire when the rider is pedaling to maintain full speed.
Units: [Nm]
Assume top speed of 10m/s
Assume that from top speed on a flat road, frictional force slows the bike to a stop in 200m
Assume it takes about 30 seconds to come to a complete stop
Assume that the mass of bike and person is 100kg
Assume the radius of the bike tire is approximately 0.6m
Acceleration due to friction:
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Force of friction:
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Force of friction is the force that must be exerted by the wheel on the road:
AP50a Fall 2013
5. Estimate the angular momentum of a Ferris wheel. Units: [Nms]
Assume the Ferris wheel has a radius of 20m
Assume there are about 20 carriages
Assume each carriage weighs about 2000kg with people inside
Assume that the support beam holding each carriage is approximately 4000kg
Assume the angular velocity is 1 revolution per minute
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6. Estimate the change in angular velocity of the earth if the entire human population simultaneously faced west
and took one step forward. Units: [rad/s]
Assume there are 6 billion people on earth.
Assume the average mass of a human is 50kg.
Assume the radius of the earth is about 6000km.
Assume each person moves at approximately 1 m/s during one step
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Assume the mass of the earth is 10 kg
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We can get the change in linear velocity of a point on the earth’s equator from ΔL
From the equation for angular velocity
Substitution of change in earth’s linear velocity
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