DO ALL SEVEN PROBLEMS. THE VALUE OF EACH PART OF EACH PROBLEM IS MARKED BESIDE T

Question

DO ALL SEVEN PROBLEMS. THE VALUE OF EACH PART OF EACH PROBLEM IS MARKED BESIDE THE ANSWER SLOT. SHOW YOUR WORK FOR PARTIAL CREDIT ALL ANSWERSSHOULD BE IN MKS UNITS UNLESS OTHERWISE INDICATED. Mearh 6.0 x 1024kg: Rearth 6,390 km 1) In all parts of this problem, neglect air resistance. a) How much kinetic energy will an object of 3 kg have if it has a speed of 35 m/s? b) How high will this object go if it is projected straight up with an initial speed of 35 m/s? 1.837.5J 62.5 m c) If you assume that gravity remains constant, how high would this object go if it had an initial speed of 3,500 m/s ? 625,000 m d) If you use real gravity that decreases with height, how high would the object go if it had the initial speed of 3,500 m/s? 693.000 m

Explanation / Answer

1. (A) KE = m v^2 / 2

KE = 3 x 35^2 /2 = 1837.5 J ....Ans

(B) PEi + KEi = PEf + KEf

0 + 1837.5 = (3 x 9.8 x h) + 0

h = 62.5 m

(C) 0 + 3 (3500^2)/2 = (3 x 9.8 x h) + 0

h = 625000 m  

(D) PE = - G M m / r

- G M m / Re + m v0^2 /2 = - G M m / r + 0

- (6.67 x 10^-11 x 6 x 10^24 )/(6390 x 10^3) + (3500^2 / 2) = - (6.67 x 10^-11 x 6 x 10^24)/ r

r = 7082670 m

h = r - Re = (7082670) - (6390000)

h = 692670 m

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