Problem 8: A bicyclist notes that the pedal sprocket has a radius of 1}, = 8. 3' cm while the wheel sprocket has a radius of m = 5.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R : 62 cm When pedaling the cyclist notes that the pedal rotates at one revolution every t : 1.2 5. When pedaling, the wheel sprocket and the wheel move at the same angular speed. Randomized Variables I 'lhempL't'lluxnm rp : 8.5 cm my: 5.5 cm R = 62 cm 21.25 Part (1)) Calculate the angular speed of the pedal sprocket my, in radians per second. (0,, : Part (c) Calculate the linear speed of the outer edge of the pedal sprocket 1:2, in centimeters per second. vp = Part ((1) Calculate the angular speed of the wheel sprocket cow, in radians per second. co\" = Pai't (e) Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground. 2 Part (D If the cyclist wanted to travel at a speed of v: : 5.5 m/s, how much time, in seconds, should elapse as the pedal makes one complete revolution? :3 = Problem 15: A ball with mass m = 5 g at the end of a massless strand is swinging in a circle of radius R = 1.57m with and angular velocity w = 13 rad/s R Part (d) Calculate the centripetal acceleration of the ball, ac in m/s-. ac = Otheexpert Problem 17: A small child of mass m = 38 kg is swinging on a swing. The length from the top of the swing set to the seat is L = 4.6 m. The girl is attempting to swing all the way around in a full circle. theexpert Part (c) If the velocity at the bottom is the same as the velocity at the top from part (a), what is the girl's apparent weight, in newtons, at the very bottom of the path? Waz = 1/2Problem 20: Part of riding a bicycle involves leaning at the correct angle when making a turn; the rst gure in the image carousel shows a rider leaning the bicycle at an angle 39 from the vertical. To be stable, the net force exerted by the ground where it contacts the tire must be on a line passing through the center of gravity. The forces have been summarized with a 'ee-body diagram, as seen in the second gure in the image carousel. The ground exerts a normal force which is equal in magnitude to the combined weight of the bicycle and the rider. The ground additionally exerts a force due to static friction which is parallel to the ground, causing the bicycle to move in a circle. () Part (a) Enter an equation for the tangent of the angle between the bicycle and the vertical in terms of the speed of the bicycleva, the radius of curvature of the turnLlr, and the acceleration due to gravitngg. Part (D) Calculate 00, in degrees, for a turn taken at ll.62In/sl 1 .62mfs with a radius of curvature 25.8m25.8m.__3