Ch 7 - Circular Motion Circular motion: Objects moving in a circular path.
CIRCULAR MOTION - Warren Consolidated Schoolsvirt.wcskids.net/mmstc/staff_websites/mcmillan...
Transcript of CIRCULAR MOTION - Warren Consolidated Schoolsvirt.wcskids.net/mmstc/staff_websites/mcmillan...
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CIRCULAR MOTION
• Centripetal acceleration
• Centripetal Force
• Universal Law of Gravitation
• Keplers Laws
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Uniform Circular Motionmotion in a circle of constant radius & constant speed
Instantaneous Velocity always tangent to path
Change in direction = change in velocity = acceleration
Acceleration is towards center of circle along the radius• Centripetal Acceleration• Radial Acceleration
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Texas Motor Speedway
• Radius of Turns = 775ft = 230m
• Record Qualifying Speed = 233mph
• What is the centripetal Acceleration of the driver?
• How many g’s does the driver feel?
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G-force Threshold Test
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G-Force Simulator• Jet Pilots, Astronauts, Daredevils
• r = 7.0m
• a = 6.1gs
• V=?
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480 rpm (max)
r=0.15m r=0.09m
Record player (rpm)What is the centripetal acceleration at outer edge?
Rpm m/s
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Centripetal ForceFor an object to accelerate, a force must be applied.
𝐹 = 𝑚𝑎 , 𝑎𝑐 =𝑣2
𝑟, 𝐹𝑐 = 𝑚𝑎𝑐 = 𝑚𝑣2
𝑟.
Centripetal Force is a NET resultant Force
It can be provided by:
• Tension
• Gravity (moon)
• Friction (Car, motorcycles)
• Normal Force (Gravitron, Nascar)
Or any combination of these
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Centrifugal Force
• DOES NOT EXIST!!!!
• Natural tendency for a body to move in a straight line (INERTIA)
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• A 300 kg motor cycle and rider rounds a curve (r=60m) with a velocity of 25 m/s.
• What is the force of friction between the tires and the track?
• What is the coefficient of friction between the tires and the track?
FRICTION AS CENTRIPETAL FORCE
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Normal Force as Centripetal Force Wall of Death
• Diameter of bowl = 20m
• M = 0.80
• Minimum Velocity?
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Tension & gravity• m=850lbs =386 kg
• r=60m
• Vmax = 35m/s
• Max force on cable =1000lbs
• Why did the cable break?
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Gravity as centripetal Force • What is the minimum speed at max height to complete the loop with a height of 5.0m?
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Windseeker at Cedar Point
• Maximum Diameter = 110 ft = 33.5 m
• Velocity = 8 rpm
• What is the angle of the swing arm?
Components as Centripetal Force
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Components as Centripetal Force
Horizontal Component of Normal Force is directed toward the center of turn.
Horizontal Component of Normal Force contributes to Centripetal Force
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Components as Centripetal Force
Ted Ligitym=95kgV=15m/sϴ above hz = 20What is the radius of the turn?
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UNIVERSAL LAW OF GRAVITATION• Isaac Newton (1686)• Observed that apple falls towards the center of the earth.
• Moon orbits the earth in nearly circular path.
• Earth orbits sun in nearly circular path.
• Common Centripetal Force that attracts all masses to each other.
• All particles attract every other particle in the universe using a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
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UNIVERSAL LAW OF GRAVITATIONTHE CAVENDISH EXPERIMENT (1797-1798)• Henry Cavendish (Great Britain) Measured the Force between two objects.
• Calculated G (Universal Gravitational Consant).
• Measured the mass of the earth.
•G = 6.67 x 10-11 N*m2/kg2
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UNIVERSAL LAW OF GRAVITATION
• Measure the mass of the earth.
• G = 6.67 x 10-11 N*m2/kg2
• re = 6.38*103 km
𝑚𝑔 =𝐺𝑚1𝑚2
𝑟2
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UNIVERSAL LAW OF GRAVITATION• Calculate the Force between any two masses.
• m1 = 70kg
• m2=50kg
• d = 1.5m
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UNIVERSAL LAW OF GRAVITATIONGravity as Centripetal Force
• What is the velocity of the International Space Station?• Altitude = 370km
• re = 6.38*103 km
• me= 5.98*1024kg
𝑚𝑠𝑣2
𝑟=𝐺𝑚𝑠𝑚𝑒
𝑟2
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UNIVERSAL LAW OF GRAVITATION• Acceleration of Gravity on other Planets
• Mars• Mass = 6.39*1023kg
• Radius = 3.40*106m 𝑚𝑔 =𝐺𝑚1𝑚2
𝑟2
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Keplers Laws of Planetary Motion
• 1st Law: Planets move in ellipses with the Sun at one focus.
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Keplers Laws of Planetary Motion
• 2nd Law: The radius vector describes equal areas in equal times
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Keplers Laws of Planetary Motion
• 3rd Law: The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semi-major axes.
𝑻𝟐
𝑻𝟐=𝒓𝟑
𝒓𝟑
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Sample Problems
Planet Period of Orbit Average
Orbital Radius
Mercury 88 days
Earth 1 year 1 A.U.
Mars 2.125 A.U.
Saturn 29 years
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Sample Problems
• The average radius of the moons orbit around the earth is 384 748 km and has a period of 27.3 days. A Direct TV satellite has a period of exactly one day.
• What is the radius of the satellites orbit?
• How far is the satellite above the Earths surface?