Circular Motion - Horizontal Outcome(s): explain and apply the concepts of centripetal acceleration and centripetal force, as applied to uniform horizontal circular motion. A bucket being swung around someone's head can have its speed determined by: What is the difference between "t" and "T"? What is the direction of the following vectors during circular motion? average velocity: instantaneous velocity: acceleration: centripetal force: Centripetal force is just another name for the net force required to maintain circular motion. There may be several forces acting on an object but only when added together is the final result the centripetal force. What provides the centripetal force (F c ) for the following objects to move in a circular path? 1. when a moon is orbiting around a planet? 2. when a bucket of water is swung in a vertical circle? 3. when a bike is ridden in a circle? 4. when we go through a loop on a roller coaster ride? Example Problem(s):
While zooming around in your future car, you navigate a 20 m wide round about at 60 km h -1. What centripetal force is required to hold your 50 kg friend in their seat? A car travels around circular road with a radius of 85 m. A banked curve at angle of 23 o provides the required centripetal force. What speed does the car have? Circular Motion - Vertical Outcome(s): Apply the concepts of centripetal force to describe circular motion in a vertical plane Explain how gravity influences circular motion in a vertical plane Use formula to determine unknowns during circular motion in a vertical plane The same analysis can be used for vertical circular motion as for horizontal. The only exception is that these formula can only be applied at the top and bottom of the circular path. Vertical Circular Motion Problem Types: 1) At the bottom of a loop 2) At the top of a loop
3) At the bottom of a hill 4) At the top of a hill Example Problem(s): What velocity is required at the bottom of a 10 m radius roller coaster loop for a 100 kg cart to stick to the track at the top of the loop? What speed is required for a rally car driver to feel weightlessness when driving over a hill with a radius of curvature equal to 24.5 m? Questions 1) a) A 25 g stopper is swung at the end of a piece of fishing line in a circle such that the fishing line makes an angle of 20 0 to the horizontal. Sketch the scenario and show the two forces acting on the stopper. b) What is the vertical component of the tension equal to? c) What is the size of the centripetal force acting on the stopper?
2) a) An experimental roller coaster ride consists of a special track and a coaster with wheels above and below the track. The roller coaster reaches the top of a 6.0 m radius loop with a velocity of 8.0 ms -1. Calculate the size of the reaction force experienced by a 70 kg passenger at the top of the loop and indicate its direction. b) At what speed would the coaster need to travel at the top of the loop for the passenger to feel weightless? c) If the roller coaster were allowed to speed up under the influence of gravity how fast would it be going at the bottom of the loop. d) When the coaster is half way down the loop in which direction is the centripetal force acting? 3) When you are a passenger in a motor car why are you thrown to one side when the car turns a sharp corner? 4) After travelling along a soft wet gravel road, a truck has lumps of mud stuck on the tyres. These lumps of mud fly off when the truck gathers speed along a smooth bitumen road. a) Why does this happen? b) What is the direction of motion of the lumps of mud relative to the tyres? 5) Explain how there can be an acceleration during circular motion when there is no change in speed. 6) A pilot flies his plane in a vertical circle at a radius of 600 m at such a speed that at the top of the path he feels weightless. ie there is no reaction force between him and the seat or his seat belt a) At what speed is the plane flying at the top of its path? b) The pilot has a mass of 75 kg and the speed of the plane at the bottom of the path is 120 ms -1. What is the reaction between the pilot and his seat at the lowest point? 7) A hammer thrower at an athletic competition swings around a heavy weight attached to a steel cable in a horizontal circle. Explain, with the aid of a diagram, at what point of the circular motion should a hammer thrower release the cable to achieve the desired direction of motion. 8) A body of mass 0.50 kg is hanging from a string 1.25 m long and swung around in a horizontal circle of radius 75 cm. Find the tension in the string and the period of revolution of this conical pendulum. 9) At what angle should a circular bicycle track be banked in order that the horizontal component of the reaction force accelerates the bicycle towards the centre of the 25 m radius track when it is travelling at 8.0 ms -1, while the vertical component of the reaction forces exactly balances the weight? 10) A 500 kg roller coaster begins its decent from 30.0m up, reaches the floor and then performs a loop de loop. If 5% of its initial energy is lost through friction; a) what is the reaction force between the roller coaster and the track if the top of the loop is 15 m off the ground? b) what is the reaction force between the roller coaster and the track at the bottom of the loop, assuming no more loss occurs.
ANSWERS 1. a) 20 0 b) 0.025 N up c)6.73 N towards centre T mg 2. a) 60.7 N towards centre b) 7.67 ms -1 c) 17.3 ms -1 d) 3. A change in velocity, even if only changing direction, requires an unbalanced force to cause an acceleration. Due to inertia, your body continues moving in a straight line until an unbalanced force changes your direction of travel. 4. a) The frictional force between the mud and tyres is not strong enough to create the required centripetal force to maintain a circular motion. b)the mud flies of at a tangent to the circumference of the wheel. 5. Acceleration is the rate of change in velocity. Velocity is a vector with both magnitude and direction. During circular motion the direction of travel changes, therefore there must be an acceleration. 6. a) 76.7 ms -1 b) 2.54 x 10 3 N up 7. v Desired Direction The hammer thrower needs to release the cable when the hammer has a velocity in the desired direction. This will occur when the hammer cable is at a 90 0 angle to the desired direction. This is because once the cable is released, there is no force acting on the hammer (other than gravity) to cause a change in the direction of the velocity. 8. Tension is 6.14 N along string. Period is 2 s. 9. 14.6 0 10. a) 1.37 x 10 4 N down b)4.32 x 10 4 N up