Presentation on theme: "Dynamics of Circular Motion"— Presentation transcript:
1Dynamics of Circular Motion Ch. 5 Applications of Newton’s Laws
2Dynamics of Circular Motion The net force is directed towards the center of the circular path; that is,
3Unbanked CurveThe car to the right is going around a circular curve of radius r that is flat; that is, unbanked. The static force of friction is acting towards the center of the circular path.
4Sample ProblemIf the maximum speed of the car is 25 m/s to just maintain a circular path of 50 m, what is the coefficient of static friction?
5Conical PendulumIn examining the conical pendulum, you need to analyze the 2-dimensions of motion.
6Sample ProblemIf the angle is 15o and the length of the rope is 1.2 m, what is the speed of the mass to maintain this circular motion?
7Lab 6: Conical Pendulum When pigs fly… The purpose of this activity is to show that the net force for a conical pendulum is
8Dynamics of Vertical Circles When the roller coaster car and passenger are on top of the vertical circle, the net force isWhen they are at the bottom of the vertical circle, the net force is
9Dynamics of Vertical Circles-continued When the roller coaster car and passenger are on top of the next vertical circle and upside down, the net force is
10Sample ProblemIf the total mass of the roller coaster car and the passenger is 1500 kg and the radius of the top vertical circle is 10 m, what is their speed if the passenger experiences weightlessness as they go over the top?
11Sample ProblemAs the roller coaster car and the passenger pass through the bottom of the next vertical circle, their speed is 15 m/s. Determine the force of the seat on the passenger.
13Sample ProblemDetermine the velocity of the car to maintain its circular motion on the banked curve of 15o at a radius of 100 m.
14Banked Curves with Friction The "ideal" speed, videal, at which the car the car will negotiate the turn - even if it is covered with perfectly-smooth ice. Any other speed, v, will require a friction force between the car's tires and the pavement to keep the car from sliding up or down the embankment:
15Banked Curve with Friction v > videal (right diagram): If the speed of the car, v, is greater than the ideal speed for the turn, videal, the horizontal component of the normal force will be less than the required centripetal force, and the car will "want to" slide up the incline, away from the center of the turn. The friction force will oppose this motion and will act to pull the car down the incline, in the general direction of the center of the turn.Write the equations applying Newton’s Second Law
16Banked Curves with Friciton v < videal (right diagram): If the speed of the car, v, is less than the ideal (no friction) speed for the turn, videal. In this case, the horizontal component of the normal force will be greater than the required centripetal force and the car will "want to" slide down the incline toward the center of the turn. If there is a friction force present between the car's tires and the road it will oppose this relative motion and pull the car up the incline.Write the equations applying Newton’s second law.
17Sample ProblemSuppose you want to negotiate a curve with a radius of 50 meters and a bank angle of 15o. If the coefficient of friction between your tires and the pavement is 0.50, what is the maximum speed that you can safely use?
18Sample ProblemNASCAR race cars actually go through the turns at Talladega Motor Speedway at about 200 mi/hr. If that is the case, what coefficient of friction exists between the car's tires and the pavement? The radius of the turn is 1100 ft.
19Sample ProblemUsing the coefficient of static friction from the previous problem, determine the minimum speed that NASCAR race cars can actually go at through the turns at Talladega Motor Speedway.