5 The highest speed that a car can round a horizontal curve of radius of curvatu

Question

5 The highest speed that a car can round a horizontal curve of radius of curvature R-30m, without skidding off the road, is 24m/s. What is the coefficient of the static friction between the tires of the car and the road? If the driver changes the tires so that the coefficient of the static friction between the new tires and the road is 3.0 then how fast can the car round the same curve without skidding of the road? 6, A satellite is orbiting a planet of mass M, at a distance R- 4x10 m from the planet's center. The speed of the satellite is 2000 m/s. -What is the planet's mass? -A second satellite orbits around the same planet at a distance R'-1.6x10 m from its center. What is the speed of this second satellite? Salell le Pi se cc

Explanation / Answer

the frictional force provides the necessary centripetal force

Fc = fk

mv^2/R = uk*m*g

v^2/R = uk*g

coefficient of friction uk = v^2/(R*g)

uk = 24^2/(30*9.8)

uk = 1.96 <<-----------ANSWER

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for uk = 3

v^2/R = uk*g

v = sqrt(uk*g*R)

maximum speed v = sqrt(uk*g*R)

v = sqrt(3*9.8*30)

v = 30 m/s <<-----------ANSWER

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Q6)

orbital speed of satillite v = sqrt(GM/R)

given v = 2000 m/s

R = 4*10^8 m

mass of planet M = v^2*R/G

M = 2000^2*4*10^8/(6.67*10^-11)

M = 2.4*10^25 Kg <<-----------ANSWER

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speed v' = sqrt(GM/R')

v' = sqrt(6.67*10^-11*2.4*10^25/(1.6*10^7))

v' = 10000 m/s <<<-----------ANSWER

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