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PHYS_2014_Homework_4_soln

# PHYS_2014_Homework_4_soln - PHYS2014 Fall 2010 Benton OSU...

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Unformatted text preview: PHYS2014 Fall 2010 Benton OSU Physics Dept. 1 Physics 2014: General Physics I Solutions to Homework Assignment 4 Due: Friday, 1 October 2010 at the beginning of your Recitation session. 1. On July 30, 1958, Lieutenant Carter C. Collins, riding in a human centrifuge at Langley Research Center in Virginia, established to world’s record for highest number of g’s without passing out. The human centrifuge was 30 ft (9.2 m) in diameter and when Lt. Collins (who coincidentally was the father of a good high school friend of mine) broke the record, it was spinning at a frequency of 41.8 revolutions per second. What was the centripetal acceleration in m/s 2 and in g’s, when he broke the record? Solution: In lecture 7, we saw that centripetal acceleration is 2 2 c v a r r ω = = and 2 f ω π = . Then, given that the radius is half the diameter, i.e. r = 4.6 m: ( ) 2 2 2 2 2 2 2 4 rev m 4 1.06 4.6 m 204.0 s s m 204.0 s 20.8 m 9.8 s c c a f r a g π π = = = = 2. My research group at OSU is involved in measuring radiation in space. We’ve been given the opportunity to fly a radiation detector on a polar orbiting satellite (i.e. the satellite’s orbit will pass over both North and South poles and is perpendicular to the equator) in order to measure radiation above the Arctic and Antarctic. The satellite will orbit at an altitude of 800 km where the acceleration due to gravity is about 79% of its average value at the Earth’s surface. How many times a day will we be able to measure the radiation levels above the Antarctic? Solution: The number of times a day the radiation levels can be measured above the Antarctic will be the same as the number of orbits per day, since the satellite passes over the Antarctic once during each orbit. If we can determine the period of one orbit, then we can divide the time in one day by the period, giving us our result. The period is related to angular velocity by: 2 T π ω = We can find the angular velocity by using the equation that relates centripetal acceleration to the acceleration due to gravity. PHYS2014 Fall 2010 Benton OSU Physics Dept. 2 2 2 c v a r r a r ω ω = = = Note that in this case, a = 0.79 × g . Also note that r is equal to the radius if the Earth plus the altitude of the orbit: ( ) 6 6 2 6 m 6.37 10 m + 800 km 1000 7.17 10 m km m 0.79 9.8 s rad 0.001 s 7.17 10 m 2 6047 s = 1.68 hr rad 0.001 s hr 24 day 14.3 times per day 1.68 hr r T ω π = × ⋅ = × ⋅ = = × = = = 3. A 30 kg box of chemistry textbooks is sitting on a loading ramp, which is at an angle, θ , with respect to the horizontal. The coefficient of static friction is μ s = 0.38 and the coefficient of dynamic friction is μ k = 0.22. a) At what angle, θ , will the box start to slip as one end of the loading ramp is slowly raised? b) At this angle, what acceleration will the box have once it starts sliding? c) At this angle, how fast will the box be moving after it has slid a distance of 5.0 m down the ramp?...
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PHYS_2014_Homework_4_soln - PHYS2014 Fall 2010 Benton OSU...

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