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1. Air Puck An air puck of mass 0.25 kg is tied to a string and allowed to revolve in a circle of radius 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of 1.0 kg is tied to it. Calculate the constant speed of the puck so that the suspended mass remains in equilibrium. v = 6.26 m/s ◄ 2. Banked Ramp A car enters a circular banked exit ramp with a radius of 60 m at a speed of 90 km/h. Calculate the minimum required static coefficient of friction μs so that the car can safely negotiate the curved road without skidding off of it, if the angle of bank is 10 o Note that you do not need the mass of the car. Include a free body diagram of the car in your solution. μs = 0.744 ◄ 3. Forces on a Model Airplane A model airplane of mass 0.750 kg flies with a speed of 35.0 m/s in a horizontal circle at the end of a 60.0 m long control wire as shown. The forces exerted on the airplane are shown in the free body diagram below. Calculate the tension in the control wire, assuming that θ = 20o. T=11.9N ◄ 4. Key Chain Angle A vehicle enters a circular and level highway exit ramp with a constant speed of v = 70 km/h. At this moment the driver notices that the ignition key chain makes an angle θ with respect to the vertical. Calculate this angle θ if the radius of the ramp is r = 50 m. θ=37.6o ◄ 1 5. Atmospheric Re-Entry A broken satellite is orbiting the Earth at a certain altitude with a speed of 20,000 km/h. In order to let the satellite, fall and burn in the atmosphere, officials must move the satellite from its current orbit to a smaller orbit whose radius is 15 times smaller than its current orbit radius. Calculate the number of times the satellite circles the Earth per hour when it is at the smaller orbit. Assume that both orbits are circular. Note that the mass and the average radius of Earth are M = 5.98 × 1024 kg and R = 6.37 × 106 m respectively and the gravitational constant is G = 6.673 × 10-11 N·m2/kg2 . n=14.3 ◄ constant is G = 6.673 × 10-11 N·m2/kg2 . h = 35,900 km v = 3,076 m/s ◄ 6. Geosynchronous Orbit A geosynchronous orbit is used for communication satellites. It is a circular orbit that is located on the equatorial plane. An object in this orbit remains in the same position at all times with respect to the Earth. In other words, the object completes one revolution around the orbit in 24 hours. Calculate (a) the altitude in [km] and (b) the speed in [m/s] of a satellite circling Earth in a geosynchronous orbit. Note that the mass and the average radius of Earth are M = 5.98 × 1024 kg and R = 6.37 × 106 m respectively and the gravitational 2

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Circular Motion Dynamics
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