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session.masteringphysics.com Pre-Lab10 Sign in I MyMathTest Course Home Chegg Study | Guided S 7 How Does The Syl NEIUport Central nbox KChapter 5 Problem 5.12 3 of 10 Part A A jet pilot takes his aircraft in a vertical loop, as shown in the figure(Figure 1) If the jet is moving at a speed of 1140 km/h at the lowest point of the loop, determine the minimum radius of the circle so that the centripetal acceleration at the lowest point does not exceed 6.0 g's Express your answer to two significant figures and include the appropriate units. 3.70 N Submit Submit X Incorrect, Try Again: 5 attempts remaining Part B Figure 1 of 1 Calculate the 75-kg pilot's eflective weight (the force with which the seat pushes up on him) at the bottom of the circle, and at the top of the circle (assume the same speed) Express your answers using two significant figures separated by a comma. Submit Incorrect: Try Again; 5 attempts remaining

Explanation / Answer

part(A)

centripetal acceleration a = v^2/r

given v = 1140 km/h = 1140*(5/18) m/s = 316.7 m/s

acceleration a = 6 g = 6*9.8 m/s^2 = 58.8 m/s^2

radius r = v^2/a

radius r = 316.7^2/58.8 = 1.7*10^3 m

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part B

FN bottom = Mg + M*a

FN bottom = 75*9.8 + 75*58.8 = 5145 N

FNtop = Ma - Mg = 75*58.8 - 75*9.8 = 3675 N

5.1*10^3 , 3.7*10^3 N

mass of earth M = 5.972*10^24 kg

radius of earth R = 6371*10^3 m

height h = 4870 km = 4870*10^3 m

IN the orbit

gravitational force Fg = GMm/(R+h)^2

gravitational force provides necessary centripetal force

Fg = Fc

G*M*m/(R+h)^2 = m*v^2/(R+h)

orbital speed v = sqrt(GM/(R+h))

orbital speed v = sqrt((6.67*10^-11*5.972*10^24)/(6371*10^3+4870*10^3))

orbital speed v = 5.95*10^3 m/s

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