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Circular motion practice problems: A tire 2.0 ft in diameter is placed on a balancing machine where it is spun so that its tread is moving at a constant speed of?62?mph. A small stone is stuck in the tread of the tire. What is the acceleration of the stone as the tire is being balanced? (2.36 X 102 m/s2)A race car starts from rest on a circular track?of radius 400 m. The?car's?speed increases at a constant rate of 0.500 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, determine (a) the speed of?the race car, (b) the distance traveled, and (c) the elapsed time. (14.1 m/s, 200 m, 28.2 s)A 2000 kg car rounds a circular turn of radius 20 m. If the road is flat and the coefficient of friction between the tires and the road is 0.70, how fast can the car go without skidding? (v=11.7 m/s)An airplane is flying in a horizontal circle at a speed of 100 m/s. The 80.0 kg pilot does not want her radial acceleration to exceed 7 g. (a) what is the minimum radius of the circular path? (b) at this radius, what is the force causing the centripetal acceleration of the pilot? (146 m, 5.5x 103 N)An engineer wishes to design a curved exit ramp for a toll road in such a way that a car will not have to rely on friction to round the curve without skidding. He does so by banking the road in such a way that the force causing the centripetal acceleration will be supplied by the component of the normal force toward the center of the circular path. (a) Show that, for a given speed v and a radius r, the curve must be banked at the angle θ such that tan θ = v 2 /rg. (b) Find the angle at which the curve should be banked if a typical car rounds it at a 50.0-m radius and a speed of 13.4 m/s. (20.1°)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. The suspended mass remains in equilibrium while the puck on the tabletop revolves. (a) What is the tension in the string? (b) What is the horizontal force acting on the puck? (c) What is the speed of the puck? (T=9.8 N, tension, v=6.26 m/s)Tarzan (m = 85 kg) tries to cross a river by swinging from a hanging vine suspended by a tree limb half way across the river. The vine is 10 m long. His speed at the bottom of the path (almost touching the water) is 8.0 m/s.??The vine will break at 1,000 N.??Does he make it? (T=1380 N—since T could need to be greater than the Tmax, the vine breaks)A 40.0-kg child takes a ride on a Ferris wheel that rotates four times each minute and has a diameter of 18.0 m. (a) what is the centripetal acceleration of the child? (b) What force (magnitude and direction) does the seat exert on the child at the lowest point of the ride? (c) What force does the seat exert on the child at the highest point of the ride? (d) What force does the seat exert on the child when she is halfway between the top and bottom? (a = 1.58 m/s2, Fseat = 455 N, Fseat = 329N)A roller coaster car has a mass of 500 kg when fully loaded with passengers. The car passes over a hill of radius of curvature r (r = 15 m) as shown. At the top of the hill the car has a speed of 8.0 m/s. Calculate the force of the track on the car at the top of the hill. Give magnitude and direction. (Fn = 24,900 N, v = 12.1 m/s)A 0.150kg ball on the end of a 1.10m long cord (of negligible mass) is swung in a vertical circle.A.) determine the minimum speed the ball must have at the top of its arc so that it continues moving in a circle.B.) Calculate the tension in the cord at the bottom of the arc assuming the ball is moving at twice the speed from part A.A 1000-kg car rounds a curve on a flat road of radius 50 m at a speed of 13.9 m/s (50 km/ h). Will the car follow the curve, or will it skid? Assume: (a) the pavement is dry and the coefficient of static friction is ?s = 0.60; (b) the pavement is icy and ?s = 0.20. The answer is it will turn when the. Pavement is icy and the ?s = 0.25?? A car can negotiate an unbanked curve safely at a certain maximum speed when the coefficient of static friction between the tires and the ground is 0.88. at what angle should the same curve be banked for the car to negotiate the curve safely at the same maximum speed without relying on friction ?In a popular amusement park ride, a rotating cylinder of radius 3.00 m is set in rotation. The people on the ride eventually reach a constant speed of 15.0 m/s. The floor then drops away leaving the riders suspended against the wall in a vertical position. What minimum coefficient of friction between a rider’s clothing and the wall is needed to keep the rider from slipping? (?=.131)A race car starts from rest on a circular track?of radius 400 m. The?car's?speed increases at a constant rate of 0.500 m/s2. At the point where the magnitudes of the centripetal and tangential accelerations are equal, determine (a) the speed of?the race car, (b) the distance traveled, and (c) the elapsed time.In civil aviation, a standard turn for level flight of a propeller-driven airplane is one in which the air plane makes a complete circular turn in 2.0 min. If the plane’s speed is 180 m/s, what is the radius of the circle? What is the centripetal acceleration of the plane? (r = 3440 m, ac = 9.42 m/s2) ................
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