A 59.0-kg ice skater is moving at 4.07 m/s when she grabs the loose end of a rope, the opposite end of which is tied to a pole. She then moves in a circle of radius 0.790 m around the pole. (a) Determine the magnitude of the force exerted by the horizontal rope on her arms. kN (b) Compare this force with her weight. Frope = W
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- A roller-coaster car of mass 309 kg (including passengers) travels around a horizontal curve of radius 35.2 m. Its speed is 21.3 m/s. a. What is the magnitude of the total force exerted on the car by the track? answer in N b. What is the direction of the total force exerted on the car by the track? Enter a positive angle if the direction is above horizontal and a negative answer if the direction is below horizontal. answer in degrees c. If the track is frictionless, then what banking angle would ensure that the car does not slide off of the track? (The banking angle is the angle between the direction normal to the track and the vertical.) answer in degreesA jet airplane is in level flight. The mass of the airplane is ?=8990 kg.m=8990 kg. The airplane travels at a constant speed around a circular path of radius ?=9.33 miR=9.33 mi and makes one revolution every ?=0.123 h.T=0.123 h. Given that the lift force acts perpendicularly upward from the plane defined by the wings, what is the magnitude of the lift force acting on the airplane?A pilot of mass 75 kg takes her plane into a dive, pulling out of it along a circular arc as she nears the ground, If the plane is flying at 1.5 × 107 km/h along the arc, what is its radius such that the pilot feels four times heavier than normal? Provide an appropriate free-body diagram.
- Which of these equations would you use to calculate the very least speed with which you could swing a bucket of water of mass m in a vertical circle of radius r and still keep the water in the bucket? A) v = √(rg) B) v = √(rg tan θ) C) v = √(mrg) D) v = mgh E) v = mg/rAn owner of a speedboat loves high speed but doesn't want to go anywhere. So he tethers the speedboat to a fixed buoy by a strong cable of length 40.0 m40.0 m, which supplies all the centripetal force to run the boat in circles around the buoy. When the tension in the cable is steady at 13500 N13500 N, with what force is the boat's engine pushing the boat? Assume that the mass of the speedboat (including the driver) is 645 kg645 kg. Take the water's drag force to be (450 kg/m)×v2(450 kg/m)×v2, where vv denotes the boat's speed. Ignore any drag force on the cable. Be sure to include the free-body diagram for the boat.In the figure, a stuntman drives a car (without negative lift) over the top of a hill, the cross section of which can be approximated by a circle of radius R = 284 m. What is the greatest speed at which he can drive without the car leaving the road at the top of the hill?
- A curve in a road forms part of a horizontal circle. As a car goes around it at constant speed 14.0 m/s, the total horizontal force on the driver has magnitude 130 N. What is the total horizontal force on the driver if the speed on the same curve is 18.0 m/s instead?A car weighing 10.7 kN and traveling at 13.4 m/s without negative lift attempts to round an unbanked curve with a radius of 61.0 m. (a) What magnitude of the frictional force on the tires is required to keep the car on its circular path? (b) If the coefficient of static friction between the tires and the road is 0.350, is the attempt at taking the curve successful?A car is driving along a circular track with diameter d = 0.59km at a constant speed of v = 21.2 m/s. Write an expression and find the value for the minimum coefficient of friction between the cars tires and road required in order to keep the car going in a circle in terms of the given parameters.
- A pickup truck has a box sitting loose in its bed. The box has a mass of 2.5 kg and the coefficient of static friction between the box and the pickup bed is 0.8. The mass of the truck is 3150 kg and its tires have a coefficient of static friction with the road of 0.9. The truck is currently going through a roundabout with a radius of 30m. How fast can the truck go and not have the box slide on the truck bed? Please answer in m/s.An engineer wants to design a circular racetrack of radius r such that cars of mass m can go around the track at speed V without the aid of friction or other forces other than the perpendicular contact force from the track surface. Find an expression for the required banking angle θ of the track, measured from the horizontal. Express the answer in terms of m, r, V, and g. Suppose the race cars actually round the track at a speed w>V. What additional radial force Fr is required to keep the cars on the track at this speed? Express the answer in terms of m, r, V, w, and g.A stunt pilot in an air show performs a loop-the-loop in a vertical circle of radius 2.87 X 103 m. During this performance the pilot whose weight is 821N, maintains a constant speed of 2.10 x 102 m/s. (a) When the pilot is at the highest point of the loop determine his apparent weight. N (b) At what speed will the pilot experience weightlessness? m/s (c) When the pilot is at the lowest point of the loop determine his apparent weight. N