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What similarity is there between each picture?

What similarity is there between each picture?. Uniform Circular Motion –. BIG IDEAS. EQUATIONS. Centripetal Force ( F c ) = Tension (T)

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What similarity is there between each picture?

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  1. What similarity is there between each picture?

  2. Uniform Circular Motion – BIG IDEAS EQUATIONS

  3. Centripetal Force (Fc) = Tension (T) One person will twirl a rubber stopper in a circular path with a radius given by the teacher. Another student will keep track of how many revolutions the stopper makes in 30s. Determine the Period (T) of the stopper. Calculate the magnitude of the velocity of the stopper. What is the centripetal acceleration? Use a scale to find the mass of the stopper. What is the tension in the string? Draw and label the vectors representing the variables v, ac , and fc at the points shown above. What would the tension be if you twirled the stopper twice as fast as you did previously? If the tensile strength of the string is 100N, how fast could you twirl the stopper before the string snapped? r = m =

  4. Algebraic Relationships – understanding the mathematical relationships amongst variable leads to a greater understanding to the dynamics of circular motion. What happens if… 2v = ac 5) 4ac = Fc 2) 3r = ac 6) 1/2v = Fc 3) 2m = ac 7) 2r = Fc 3v, 1/2r = ac 8) 1/4m = Fc Activity: Using a Newton meter, calculate the velocity of the rubber stopper if the radius is .5m.

  5. Centripetal Force (Fc) = Tension (T) Example: Holding a ball vs bowling a ball.. A 16lb bowling ball has a mass of 7.3kg… a) What force is required to hold the ball off of the ground? b) What centripetal force is required to move a 7.3kg object around in a circular path of .75m radius at 9m/s? c) What is the tension in the bowlers arm? d) If the length of the lane is 60ft (18.28m), how long does it take to get there from the time the ball is released? e) What would be the centripetal force required if the ball has mass of 2m? r =

  6. Centripetal Force (Fc) = Friction (Ff) A 50kg go cart makes a sharp left turn around a corner in a circular path with a 20m radius. If the centripetal acceleration of the car is 8m/s2, how fast is the go cart moving? What centripetal force is required to allow the car to make the turn? If the go cart’s rubber tires keep turning while in contact with dry concrete, will the car be able make the turn? Prove. What is the maximum speed the go cart will be able to attain under these conditions? In terms of Fc how much friction would need to be present if the car traveled at 2v? If the go cart hit a patch of ice at the location shown the right,draw a vector representing the motion of the go cart.

  7. Centripetal Force (Fc) = Friction (Ff) Digging Deeper… Would a more massive vehicle have to go slower around the same turn? Example: What would be the coefficient friction between the tires of a race car and a track if the car is able to make a 40m/s turn around a circular part of the track having a radius of 110m? Vs. r r

  8. Centripetal Force (Fc) = Force of Gravity (Fg) The force of gravity is the centripetal force that is responsible for the circular orbits we see throughout the universe. In fact, the laws that explain circular orbits also explains how an apple falls straight down from a tree…. Example: The Sun & Earth What is the orbital period of the Earth around the sun? Given that Earth’s orbit is nearly circular, how fast does the Earth move around the sun? What is the force of gravity that the Sun pulls on the Earth with? What force does the Earth pull on the sun with? d) What is the centripetal acceleration of the Earth orbiting the sun? Newtonian Mountain

  9. Centripetal Force (Fc) = Force of Gravity (Fg) Orbital velocity is the velocity needed to achieve balance between gravity's pull on the satellite and the inertia of the satellite's motion -- the satellite's tendency to keep going. Without gravity, the satellite's inertia would carry it off into space. Even with gravity, if the intended satellite goes too fast, it will eventually fly away. On the other hand, if the satellite goes too slowly, gravity will pull it back to Earth. At the correct orbital velocity, gravity exactly balances the satellite's inertia, pulling down toward Earth's center just enough to keep the path of the satellite curving like Earth's curved surface, rather than flying off in a straight line Does the mass of a satellite need to be taken into account when determining what its orbital velocity needs to be at a given altitude? Example: Earth’s Satellites What is the acceleration due to gravity at a point where a 300kg communications satellite weighs 2772N? b) What orbital velocity would be necessary if the satellite had an altitude of 200km above Earth’s surface? c) What conditions would have to change if the same satellite was set at a lower altitude and higher one?

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