Presentation on theme: "Horizontal Circular Motion"— Presentation transcript:
1Horizontal Circular Motion Show video: Frames of Reference: 17: :45
2Review If an object travels at a constant velocity a = 0 Fnet = 0 If an object travels with a changing velocity.
3What if?What if you do not speed up or slow down, but change direction?Velocity changes (vector)Acceleration occursFnetAt end of slide, show Mechanical Universe 17: :15
4Centripetal Acceleration Centripetal - center seekingpoints towards the center of the circlesometimes called radial accelerationdependent on v and r
5ExampleA ball at the end of string is revolving in a horizontal circle of radius 0.6 m. The ball makes 2 revolutions in a second. What is the centripetal acceleration?
6ExampleA jet plane traveling at 525 m/sec pulls out of a dive by moving in an arc of radius 6 km. What is the plane’s centripetal acceleration?Change ac to “g” and discuss into g’s.
7Dynamics of Circular Motion If there is an acceleration, Newton’s Second Law requires a net external forceSince the acceleration is centripetal, the net force must also be centripetal
8Centripetal ForceBut that would mean centripetal force is not a real force, but is a net force and caused by something else.Fw, Fn, Ft, Ff
9Okay, that other ForceCentrifugal - an outward force acting on an object moving in a circular pathEveryone has felt itSo, what do you feel? Depends on who “you” are.
10Centrifugal ForceIf there was a centrifugal force acting on the ball, what would happen if you let it go?Play video: Frames of Reference: 17:45 to end of circular discussion
11Sample ProblemA 10 kg mass is attached to a string that has a breaking strength of 200 N. If the mass is whirled in a horizontal circle of radius 0.8 m, what maximum speed can it have?
12Circular Motion A Review In most cases, the string force not only has to provide the force required for circular motion, but also the force required to balance the gravitational force.
13DynamicsSince there is a net force, we need to know which forces are acting ON the object and then solve.A 300 g tetherball is attached to a massless rope 2 m long. If the rope makes an angle of 30o to the vertical, what is the speed of the ball?
14In a version of a “Giant Swing”, the seat is connected to two cables as shown. The seat swings in a horizontal circle at a rate of 32 rpm. If the seat weighs 255 N and a 825 N person is sitting in it, find the tension in each cable.Sample Problem
15Circular Motion and Friction This required force is provided by the friction force between the tires and the road.But remember ….. The friction force has a maximum value, and there is a maximum speed with which you can make the turn.
16Highway CurvesA 1000 kg car rounds a curve on a flat road of radius 50 m at a speed of 15 m/sec. What minimum coefficient of friction is needed for the car to safely navigate the corner?
17SampleA flat puck of mass M is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block of mass m. What is the speed of the flat puck if the radius of the circle is R?
18sampleA 4 kg object is attached to a vertical rod by two strings. The object rotates in a horizontal circle at constant speed 6 m/sec. Find the tension in each of the strings.
20Vertical CirclesMotion in a vertical circle is no different, other than the weight of the object now comes into play.Look at the forces acting on the passenger to keep them in the circular path both at the top and the bottom.
21Ferris WheelA passenger on a Ferris wheel moves in circle of radius 8 m. The passenger’s mass is 60 kg and the wheel completes one revolution in 10 sec at a constant speed. What is the normal force of the seat on the passenger both at the top and the bottom?
22ExampleA bowling ball weighing 70 N is attached to a ceiling by a 4 m long rope. The ball is pulled back until the rope makes an angle of 30o to the vertical. The ball is then released. Determine:the speed of the ball when the rope is vertical.the tension in the rope when the rope is vertical.
23amusement Park Physics What is the minimum speed that a roller coaster must be traveling when upside down at the top of a circle so that the passengers do not fall out? Assume a radius of 7.4 m.
24amusement Park Physics If the riders are at the top with the speed you just found, how fast will they be moving when they get to the bottom?What will the normal force be on the passengers at the bottom assuming they are still moving in a circular path?
25Amusement park physics A roller-coaster car has a mass of 500 kg when fully loaded with passengers.what is the maximum speed the vehicle can have at B and still remain on the track?with that speed at b, what is the normal force of the track on the car at point A?