Presentation on theme: "Centripetal Force and Acceleration"— Presentation transcript:
1 Centripetal Force and Acceleration Circular MotionCentripetal Force and Acceleration
2 Tangential Velocity Tangential Velocity (Vt)- object’s speed along an imaginary line that is drawn tangent to the circular pathDepends on distance from the object to the center of the circular pathWhen the tangential speed is constant then the motion is described as uniform circular motion
4 Tangential Velocity r=radius of the circle Vt=2πr/Tr=radius of the circleT=Period (amount of time to complete one circle)
5 ExampleA plane makes a complete circle with a radius of 3622 m in 2.10 min. What is the speed of the plane?180 m/s
6 Centripetal Acceleration When an object is moving in a circular path, the direction changesIf the object has a constant SPEED, Acceleration is due to the direction changingThis is called centripetal acceleration
7 Centripetal Acceleration Centripetal acceleration is always directed towards the center of the circleCentripetal=center seeking
9 Tangential Accleration Centripetal acceleration results from change in directionWhen the speed changes in a circle it is called tangential accelerationConsider a car moving in a circle
10 Centripetal Force Remember! When an object is accelerating there is a net forceIf there is centripetal acceleration, there is a net force- Centripetal ForceThis is not a new forceNet force that accelerates an object towards the center of a circle
11 ExamplesIf a mass is twirled in a circle, at the end of a string, the centripetal force is provided by the tensionWhen a car rounds a corner on a highway, the centripetal force is provided by frictionWhen the moon orbits the Earth, the centripetal force is provided by gravity
12 Centripetal Force Centripetal Force =mass x centripetal acceleration Fc=macSubstitute acFc=m V2/rSubstitute VtFc=m 4π2r/T2
13 Example- StandardA 0.50 kg mass is whirled in a circle of radius m at 2.3 m/s. Calculate the centripetal force acting on the mass13.2 N
14 Example-HonorsA 0.50 kg mass sits on a frictionless table and is attached to hanging weight. The 0.50 kg mass is whirled in a circle of radius 0.20 m at 2.3 m/s. Calculate the centripetal force acting on the mass .Calculate the mass of the hanging weight13.2 NFg=T=Fc=mg =m9.81.35 kg
15 ExampleA car traveling at 14 m/s goes around an unbanked curve in the road that has a radius of 96 m. What is its centripetal acceleration?What is the minimum coefficient of friction between the road and the car’s tires?2.04 m/s2Ff=Fc=mac μmg=mac μg=ac μ9.8= coefficient=.21
16 Clicker QuestionCalculate the centripetal force acting on a 925 kg car as it rounds an unbanked curve with a radius of 75 m at a speed of 22 m/s.
17 Clicker QuestionAn amusement park ride has a radius of 2.8 m. If the time of one revolution of a rider is s, what is the speed of the rider?
18 Clicker QuestionA 2.7x103 kg satellite orbits the Earth at a distance of 1.8x107 m from the Earth’s centre at a speed of 4.7x103 m/s. What force does the Earth exert on the satellite?
19 Clicker Question. An object moves in a circle at a constant speed. Which of the following is not true of the object?A. Its centripetal acceleration is constant.B. Its tangential speed is constant.C. Its velocity is constant.D. A centripetal force acts on the object.
20 Clicker QuestionA car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m.2. What is the centripetal acceleration of the car?A. 2.4 10-2 m/s2B m/s2C. 9.0 m/s2D. zero
21 Centrifugal ForceWhen a driver takes a sharp left turn, the passenger slides to the right of the car and into the door, Why?Centrifugal=center-fleeingApparent force that causes a revolving or rotating object to move in a straight lineHowever-Newton’s first law states- an object in motion will stay in motion until a force acts on itCentrifugal force does not really exist!
22 Describing MotionWhat happens when centripetal force disappears? Where does the object go?A ball that is on the end of a string is whirled in a vertical circular path.If the string breaks at the position shown in (a), the ball will move vertically upward in free fall.If the string breaks at the top of the ball’s path, as in (b), the ball will move along a parabolic path.
23 Vertical Versus Horizontal Draw a free body diagram of a mass moving in a vertical circle, when the object is at the top of the path and the bottom of the pathAs with any object moving in a circle there is a net force acting on it towards the center of the circleThe net force is the centripetal forceAt the top Fnet (Fc)=Ft +FgAt the bottom Fnet (Fc)=Ft-Fg
24 ExampleA 1.7 kg object is swung from the end of a 0.60 m string in a vertical circle. If the time of one revolution is 1.1 s, what is the tension in the stringA) at the top?B) at the bottom?Top- 17NBottom- 50 N
25 Constant VelocityWhen you are trying to find the minimum speed of an object at the top of its circular arc we can use the equationFc=Fg soThe centripetal acceleration equals the acceleration due to gravity (ac=9.8 m/s/s)Sog=Vt2/rV=√(gr)
26 ExampleAn object is swung in a vertical circle with a radius of 0.75 m. What is the minimum speed of the object at the top of the motion for the object to remain in circular motion?2.7 m/s
28 What is Gravity? The force that pulls us to the earth It is much more than thatGravity is the force that attracts two bodies that have mass and energy to each otherNewton discovered that gravity attracts any two objects depending on their masses and their distance apart
29 GravityThe gravitational forces that two masses exert on each other are always equal in magnitude and are opposite in directions.Newton’s Third Law
30 Gravity Is Proportional to the two masses Is inversely proportional to the square of the distance between their center of massSo if two objects are twice as far away from each what happens to the gravitational force by?Fg=Gm1m2r2G=6.67 x N m2/kg2M1= mass of the first objectM2= mass of the second objectr= distance between the two centers of massIt gets reduced by 1/4
31 ExampleCalculate the force of gravity between two 75 kg students if their centers of mass are 0.95 m apart4.2 x N
32 Example 2A satellite weighs 9000 N on Earth’s surface. How much does it weigh if its mass is tripled and its orbital radius is doubled?Fg is the same thing as weightFg= 9000 NMass is on the top of the equation and the mass is proportional to the Fg, so the Fg goes up by a factor of 3The radius is inversely proportional to the square of the distance, so if the radius is doubled then the Fg is reduced by a factor of ¼So Fg X ¾ = 6750 N
33 Clicker Question. Earth (m = 5.97 1024 kg) orbits the sun (m = 1030 kg) at a mean distance of 1.50 1011 m. What is the gravitational force of the sun on Earth? (G = N•m2/kg2)A 1032 NB 1022 NC 10–2 ND 10–8 N
34 Clicker QuestionGravitational force F exists between point objects A and B separated by distance R. If the mass of A is doubled and distance R is tripled, what is the new gravitational force between A and B?A) 9/2 FB) 2/3 FC) 2/9 FD) 3/2 F
35 Common Misconception: Mass Versus Weight Amount of matterConstant everywhereGravitational attraction (Fg)Changes depending on location
36 Clicker Question Which of the following statements is correct? A. Mass and weight both vary with location.B. Mass varies with location, but weight does not.C. Weight varies with location, but mass doesnot.D. Neither mass nor weight varies with location.
37 SatellitesAre constantly “falling” when in orbitThey are in freefall
38 Gravitational FieldGravity is an example of a field force (ie not a contact force)A force that is exerted which has no direct contactA field- an area of influenceThink about a campfireAs you approach itAs you increase the size
39 Gravitational FieldsFields can be described as vectors or scalars, depends on what kindGravitational fields are field forces so..They are vectorsGravitational fields are represented by arrows, magnitude is represented by how many arrows are present
40 Gravitational Field Strength Gravitational field strength=acceleration due to gravityRecall Fg=mgSo…g=Fg/mg=acceleration due to gravity, gravitational field strength,9.80m/s2 near the Earth’s surfaceg varies with distanceg=Gm1r2Measured in N/kg, same as m/s2
41 ExampleWhat is the gravitational field strength on the Earth’s surface of the moon? The mass of the moon is 7.35 x 1022 kg and the radius of the moon is 1.74 x 106 m1.62 m/s2 or N/kg
42 Clicker Question. Which of the following is a correct interpretation of the expression? A. Gravitational field strength changes with an object’s distance from Earth. B. Free-fall acceleration changes with an object’s distance from Earth. C. Free-fall acceleration is independent of the falling object’s mass. D. All of the above are correct interpretation
43 The Period of a Satellite T=√(4π2r3)Gmm refers to the mass of the center of the orbit
44 ExampleA satellite orbits the Earth at a radius of 2.2 x 107 m. What is its orbital period, when the mass of the earth is 5.98 x 1024 kg. What is the speed of the satellite?32500 s4251 m/s