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Unformatted text preview: Chapter 5
Circular Motion and Gravitation Centripetal Acceleration (ac) acceleration due to the constantly changing direction of circular motion. Kinematics of Uniform Circular Motion
Always points toward the center of the circle Sometimes called radial acceleration v ac = r 2 Example: What is the acceleration experienced by a car going around a curve with a radius of 15 meters at a constant speed of 20 m/s? Period (T) time for one complete revolution Frequency (f) number of complete revolutions in one second. Kinematics of Uniform Circular Motion Frequency and period are inverses of one another. 1 1 T= , f = f T Example: A ball is whirled around in a circle at the end of a 0.80 m long string, and you count 15 complete rotations in 10 seconds. Find the frequency, period, velocity, and acceleration of the ball. Centripetal Force (Fc) force causing the centripetal acceleration.
Always directed toward the center of the circle. Not a "new" force, anything that causes circular motion. Examples: Tension ball on a string Dynamics of Uniform Circular Motion Friction car rounding a curve Normal "Roundup" ride Gravity satellites and planets Question: Which direction would a ball on a string move if the string is cut? Centripetal Force Dynamics of Uniform Circular Motion
mv 2 Fc = mac , Fc = r Example: A 3 kg mass rests on a record turntable 6.0 cm from its center. If the turntable rotates at 45 rpm, what is the magnitude of the centripetal force? What is actually providing this force? Example: A 0.5 kg ball is whirled in a vertical circle at the end of a string that is 0.9 m long with a speed of 6.5 m/s. What is the tension in the string at the top of the circle and at the bottom of the circle? Example: What is the minimum speed that a 80 kg skateboarder must have in order to complete a looptheloop inside a pipe that has a radius of 2 meters? (video) Problem Solving with Circular Motion Problem Solving with Circular Motion Example: If a 2000 kg car rounds a flat curve with a radius of 25 m at a speed of 15 m/s, what is the minimum coefficient of friction between the road and the tires so that the car doesn't skid off the road? Question: Why are most roadway curves banked? The Centrifugal "Force" No such thing as a Centrifugal "force" It is simply a result of inertia. Universal Gravitation Newton's Law of Universal Gravitation "Every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers." Gm1m2 FG = 2 d G = 6.67 10 -11 N m 2 kg 2 Universal Gravitation Example: What is the gravitational force between two 80 kg people sitting 3 meters apart? Example: What is the force of gravity between the Earth (mE=5.98x1024 kg) and the moon (mM=7.35x1022 kg) if the distance between their centers is 384,000 km? Acceleration due to Gravity for any planet: Universal Gravitation
GmP g= 2 rP Example: What is the acceleration due to gravity at the surface of the Moon (mass =7.35 1022 kg, radius = 1740 km)? Example: A 4 kg bowling ball is taken to a newly discovered planet with a measured radius of 5000 km. It is dropped from a height of 2 meters and hits the ground 0.5 seconds later. What is the mass of the planet? Satellite Motion and "Weightlessness" Are astronauts orbiting in the space shuttle actually weightless and free from gravity? Satellite motion is circular motion with gravity providing the centripetal force. Satellites are in constant freefall. Example: What tangential velocity must a 400 kg satellite have in order to maintain an orbit 400 km above the Earth's surface? Example: A new moon is discovered orbiting the planet Saturn and a probe is launched to study it. Upon arrival the probe is measured to orbit the moon once every 4 hours at a distance of 1500 km from its center. What is the mass of this moon? Satellite Motion and "Weightlessness" ...
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