Problems

practice

1. A supertanker doesn't come with brakes. Using engines alone, it takes a loaded supertanker 13 km (8 miles) to stop. A typical vessel of this class has a gross mass of about 150 million kilograms and a cruising speed of 50 kph (30 mph). Determine …
   1. the average stopping force applied to the ship and
   2. the average power dissipated while stopping it.
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.

   Read this passage from the Columbia Accident Investigation Board (CAIB)

   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 2300 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 2300 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 2300 fps to about 1500 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.

   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. 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. There is a small but non-zero probability that 2007 VK184 will collide with the earth in the year 2048.

   Asteroid 2007 VK184
   impact probability	0.033 %
   impact date and time	30 May 2048 22:11 UTC
   impact uncertainty	2 days, 3 hours, 21 minutes
   impact speed	16.94 km/s
   diameter	0.130 km
   mass	3.3 × 109 kg
   Source: JPL Impact Risk and Small-Body Database

   Determine the kinetic energy kinetic energy at impact of 2007 VK184 were it to strike the earth on the predicted date. 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.)
2. 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 dammage. EF Scale numbers are often reported by the media.

   Operational Enhanced Fujita Scale
   	three second gust
   scale	(mph)	(m/s)	typical damage
   EF0	65-85	29-38	Light: Some damage to chimneys; branches broken off trees; shallow-rooted trees pushed over; sign boards damaged.
   EF1	86-110	38-49	Moderate: Peels surface off roofs; mobile homes pushed off foundations or overturned; moving autos blown off roads.
   EF2	111-135	50-60	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	136-165	60-74	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	166-200	75-89	Devastating: Well-constructed houses leveled; structures with weak foundations blown away some distance; cars thrown and large missiles generated.
   EF5	> 200	> 200	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.
   Source: Online Tornado FAQ, Storm Prediction Center, National Weather Service

   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?