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- In a race like the Indianapolis 500, a driver circles the track counterclockwise and feels his head pulled toward one shoulder. To relieve his neck muscles from having to hold his head erect, the driver fastens a strap to one wall of the car and the other to his helmet. The length of the strap is adjusted to keep his head vertical. (a) Which shoulder does his head tend to lean toward? (b) What force or forces produce the centripetal acceleration when there is no strap? (c) What force or forces do so when there is a strap?A car moves at speed v across a bridge made in the shape of a circular arc of radius r. (a) Find an expression for the normal force acting on the car when it is at the top of the arc. (b) At what minimum speed will the normal force become zero (causing the occupants of the car to seem weightless) if r = 30.0 m?If a car takes a banked curve at less than the ideal speed, friction is needed to keep It from sliding toward the inside of the curve (a problem on icy mountain roads). (a) Calculate the ideal speed to take a 100.0 m radius curve banked at 15.0. (b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 20.0 km/h?
- (a) What is the radius of a bobsled turn banked at 75.0and taken at 30.0 m/s, assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you?(a) What is the radius of a bobsled turn banked at 75.0° and taken at 30.0 m/s, assuming it is ideally banked? (b) Calculate the centripetal acceleration. (c) Does this acceleration seem large to you?If a car takes a banked curve at less than a given speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). a) calculate the minimum speed, in meters per second, required to take a 92 m radius curve banked at 11 degrees so that you don't slide inwards, assuming there is no friction. b) What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 25 km/h?
- A civil engineer designs a banked road that needs to have a curvature of 38 meters. If the angle is designed to be 18 degrees a) calculate the speed (in m/s and in mph) at which the car must go in order not to skid even on icy conditions. b) If the speed is required to be lower, should the road be banked at higher or lower angle? Explain.If a car takes a banked curve at less than a given speed, friction is needed to keep it from sliding toward the inside of the curve (a real problem on icy mountain roads). a) Calculate the minimum speed, in meters per second, required to take a 84 m radius curve banked at 14° so that you don't slide inwards, assuming there is no friction. b)What is the minimum coefficient of friction needed for a frightened driver to take the same curve at 25 km/h?spin Out is a carnival ride consisting of a large open cylinder. Riders stand inside with their backs against the cylinder wall. a) What is the centripetal force acting on you in the ride if the radius of the cylinder is 3.5 m, your mass is 50 kg, and your are traveling at 5 m/s? b) What force keeps you from sliding downward and how does that force relate to the above spinning speed?
- i) A car of mass m moves at a constant speed v of 30 m/s around a banked circular trackof radius R = 150 m. (It is a normal car, rather than a race car, which means any verticalforce from the passing air is negligible.) Assume that the frictional force from the track isnegligible.a) Draw a free-body diagram of the car. [1]b) What bank angle θ prevents sliding?E8. A Ferris wheel at a carnival has a radius of 10 m and turns so that the speed of the riders is 8 m/s. a. What is the magnitude of the centripetal acceleration of the riders?b. What is the magnitude of the net force required to produce this centripetal acceleration for a rider with a mass of 60 kg?A small ball of mass m swings in a vertical circle at the end of a thin, massless string of length L. When the ball is at the bottom of the circle, the tension in the string is TB. Be sure to draw all appropriate force diagrams. Solve in terms of the provided variables plus other known constants. (a) What are the speed and angular velocity of the ball at that point? (b) Assuming the speed of the ball at the bottom is twice that at the top, find the tension in the string when the ball is at its highest point. (c) What is the minimum speed (measured at the top of the motion) needed to have the ball complete the circle? Based on your equations for the above problem, solve for the tension in the string (in newtons) when the ball is at its highest point. The ball has mass of 0.284 kg, the string as a length of 2.49 m, and the tension at the bottom is 79.1 N. (Enter a number only. No units!)