1) Two satellites, A and B, are in different circular orbits about the earth. Th

Question

1) Two satellites, A and B, are in different circular orbits about the earth. The orbital speed of satellite A is forty-six times that of satellite B. Find the ratio (TA/TB) of the periods of the satellites. 2) For the normal force in the figure to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points. Suppose, for example, that the track has a radius of 2.6 m and that the driver goes past point 1 at the bottom with a speed of 18 m/s. What speed must she have at point 3, so that the normal force at the top has the same magnitude as it did at the bottom? 3) In an automatic clothes dryer, a hollow cylinder moves the clothes on a vertical circle (radius r = 0.34 m), as the drawing shows. The appliance is designed so that the clothes tumble gently as they dry. This means that when a piece of clothing reaches an angle of ? above the horizontal, it loses contact with the wall of the cylinder and falls onto the clothes below. How many revolutions per second should the cylinder make in order that the clothes lose contact with the wall when ? = 69.0

Explanation / Answer

PerKepler's law, period T is proportional to r^(3/2). Velocity v is proportional to r/T and thus to T^(2/3)/T = T^(-1/3). Thus Ta/Tb = (va/vb)^(-1/3) = 3^(-1/3) = 0.69336.

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