A car rounds a banked curve where the radius of curvature of the road is R, the

Question

A car rounds a banked curve where the radius of curvature of the road is R, the banking angle is theta, and the coefficient of static friction is mu. (a) Determine the range of speeds the car can have without slipping up or down the road. (b) What is the range of speeds possible if R = 100 m, theta = 10 degree, and mu = 0.10 (slippery conditions)? The Solar Maximum Mission Satellite was placed in a circular orbit about 150 mi above Earth. Determine (a) the orbital speed of the satellite and (b) the time required for one complete revolution. A 0.400-kg pendulum bob passes through the lowest part of its path at a speed of 3.00 m/s. (a) What is the tension in the pendulum cable at this point if the pendulum is 80.0 cm long?

Explanation / Answer

(A) v = (Rg(u+tan(theta))/(1-u*tan(theta)))^0.5

(b) R =100 m , theta = 10 degrees

u = 0.1

v = (100*9.8*(0.1+tan10)/(1-0.1*tan10))^0.5

v = 16.56 m/s

53) h = 150 mi = 241402 m

mass of earth M = 5.98*!0^24 kg

adius of earth R = 6371 k

(a) V = (GM/(R+h))^0.5

v = (6.67*10^-11*5.98*10^24/(6371000+241402))^0.5

v =7.77 km/s

(b) from Keplers third law

T^2 = 4pi^2(R+h)^3/GM

T^2 = 4*3.14^2*(6371000+241402)^3/(6.67*10^-11*5.98*10^24)

T = 5346 s

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