The Physics
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Opus in profectus

# Kinetic Energy

## Problems

### practice

1. Read the following excerpt of an interview with amateur naturalist Timothy Treadwell.

Now, the bears I live with average, the males, eight to twelve hundred pounds [360 to 540 kg]. They're the largest bears in the world…. They've been clocked at 41 [mph] and they've run a hundred meter dash in 5.85 seconds, which a human on steroids doesn't even approach.

1. Compute the speed of a grizzly bear using Mr. Treadwell's hundred meter statement.
2. Compute the kinetic energy of a grizzly bear using the speed you calculated in part a. and the average mass stated by Mr. Treadwell.
3. How fast would a 250 lb man have to run to have the same kinetic energy you calculated in part b? (Do not use a calculator to compute your answer.)
4. How fast would a 4000 lb car have to drive to have the same kinetic energy you calculated in part b? (Do not use a calculator to compute your answer.)
2. NASA uses a combination of metric and British-American units in its publications. Be prepared to do conversions.

The Space Shuttle Columbia disintegrated during reentry on the morning of 1 February 2003. The cause of the accident was determined months later. A review of video footage taken during the launch 16 days earlier showed a large piece of foam insulation falling off the external fuel tank shortly after liftoff then striking the leading edge of the orbiter's left wing. This compromised the thermal protection system at the point of impact and allowed the superheated gases generated on reentry to melt the aluminum frame there. The left wing snapped off first, the orbiter tumbled and broke apart, scattering pieces across eastern Texas. All seven crew onboard were killed

Eighty-two seconds into STS 107 [the mission number], a sizeable piece of debris struck the left wing of the Columbia. Visual evidence and other sensor data established that the debris came from the bipod ramp area and impacted the wing on the wing leading edge. At this time Columbia was traveling at a speed of about 2,300 feet/second (fps) through an altitude of about 65,900 feet. Based on a combination of image analysis and advanced computational methods, the Board determined that a foam projectile with a total weight of 1.67 lb and impact velocity of 775 fps would best represent the debris strike….

Just prior to separating from the External Tank (ET), the foam was traveling with the orbiter at about 2,300 fps. The visual evidence shows that the debris impacted the wing approximately 0.161 seconds after separating from the ET. In that time, the debris slowed down from 2,300 fps to about 1,500 fps, so it hit the orbiter with a relative velocity of about 800 fps. In essence, the debris slowed down and the Orbiter did not, so that the Orbiter ran into the debris.

Columbia Accident Investigation Board, 2003

Show that a piece of rigid foam insulation like the one that struck the Space Shuttle Columbia possesses a considerable amount of kinetic energy despite being "just a piece of foam".

1. Determine the kinetic energy of the foam debris that struck Columbia in 2003.
2. How fast would a 10 lb sledge hammer have to travel in order to have the same kinetic energy as the foam? State your answer in miles per hour or kilometers per hour as you prefer.
3. How massive would a defensive tackle of American or Canadian football have to be if he ran as fast as a world class sprinter and had the same kinetic energy as the foam debris? State your answer in pounds or kilograms as you prefer.
3. Write something different.
4. Write something completely different.

### conceptual

1. Is it possible for a motorcycle to have more kinetic energy than a truck?

### numerical

1. Verify Robinson's first law of space combat (originally known as Robinson's first law of science fiction).

An object impacting at 3 km/s delivers kinetic energy equal to its mass in TNT.

Ken Burnside, 2003

2. The English scientist Thomas Young (1773–1829) was the first person to use the word energy in the modern sense. His definition is nearly the same as the one we use for kinetic energy today.

The term energy may be applied, with great propriety, to the product of the mass or weight of a body, into the square of the number expressing its velocity. Thus, if a weight of one ounce moves with the velocity of a foot in a second, we may call its energy 1; if a second body of two ounces have a velocity of three feet in a second, its energy will be twice the square of three, or 18.

Thomas Young, 1807

Young would not receive full credit on an exam were he a student today. He provided units for the quantitites used in his calculations, but he neglected to include them in his solutions. Let young be the name of the unit that is missing from the passage above.

1. How many youngs are in a joule (the unit of energy in the International System)?
2. How many youngs are in a foot-pound (the unit of energy in the British Engineering System)?
3. How many ergs (the unit of energy in the Gaussian System) are in a young?
3. The asteroid 2007 VK184 is classified as a near Earth object (NEO). It has an orbit that brings it close enough to Earth, often enough that we need to be concerned. When first detected, there was a concern that 2007 VK184 might collide with the Earth in the year 2048. Better measurements have shown that not to be the case. 2007 VK184 will get close, but not close enough to impact the Earth or Moon.
2007 VK184 one month before its closest approach to Earth
Asteroid 2007 VK184's near miss Source: JPL Earth Impact Risk Summary and Small-Body Database Lookup
measurement value
date and time 2 June 2048 3:15 UTC
distance from Earth 1,965,000 km
impact speed 16.02 km/s
diameter 0.130 km
mass 3.3 × 109 kg
Determine the kinetic energy of 2007 VK184 were it to strike the Earth at the time of its closest approach. State your answer in…
1. joules
2. tons of TNT (For comparison, the largest nuclear weapon ever tested had a yield of 50 million tons of TNT.)
4. The Enhanced Fujita scale is a system implemented by the National Weather Service in the US to rank the intensity of tornadoes. EF Scale values are assigned based on three second wind gust speeds. These speeds are estimated (not measured) from observed damage. EF Scale numbers are often reported by the media.
Operational enhanced Fujita scale
three second gust
scale (mph) (m/s) typical damage
EF0 065–085 029–038 Light:
Some damage to chimneys; branches broken off trees; shallow-rooted trees pushed over; sign boards damaged.
EF1 086–109 038–049 Moderate:
Peels surface off roofs; mobile homes pushed off foundations or overturned; moving autos blown off roads.
EF2 110–137 049–061 Considerable:
Roofs torn off frame houses; mobile homes demolished; boxcars overturned; large trees snapped or uprooted; light object missiles generated; cars lifted off ground.
EF3 138–167 062–075 Severe:
Roofs and some walls torn off well-constructed houses; trains overturned; most trees in forest uprooted; heavy cars lifted off the ground and thrown.
EF4 168–199 075–089 Devastating:
Well-constructed houses leveled; structures with weak foundations blown away some distance; cars thrown and large missiles generated.
EF5 200–234 089–105 Incredible:
Strong frame houses leveled off foundations and swept away; automobile-sized missiles fly through the air in excess of 100 meters; trees debarked; incredible phenomena will occur.

Assuming that intensity is based on the kinetic energy of a "piece" of moving air, how many times more intense is…

1. an EF2 than an EF1 tornado,
2. an EF5 than an EF4 tornado,
3. an EF5 than an EF1 tornado?

### investigative

1. Which requires more work: stopping the fastest pitched baseball or stoppping the fastest served tennis ball. To answer this question, complete a table like the one below. Provide the source of your info as well as its value. Use whatever units you find for mass and speed, but please report the work in joules.
quantity baseball tennis ball
mass
(source)

speed
(source)

work
(show work)

2. What's the kinetic energy of… ? ☞ All data must be sourced. Bonus points for using primary sources. ☞ Show all work for any calculations including an equation and substitution with appropriate units.
event m
(kg)
v
(m/s)
K
(J)
1. swimmer, female, fastest 100 m freestyle
2. swimmer, male, fastest 100 m freestyle
3. sprinter, female, fastest 100 m dash
4. sprinter, male, fastest 100 m dash
5. softball, female, fastest pitch
6. Frisbee, fastest throw
7. baseball, male, fastest pitch
8. tennisball, fastest serve