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Transcript
Chasing your tail for science. Moving Stand up. Walk in a perfectly round path to your left. Which way do you have to push with your foot to walk in the circle? Answer : Toward the center of your path. Pushing Using the bowling ball and broom at the front of the room. Make the ball travel counterclockwise around the “space” in the center of the room. Which way do you have to push to get the ball to go around the faucets? Answer : Toward the middle of the space. Circular motion You have just studied circular motion. It has 2 dimensions. Speed can be constant but velocity will always change. Moving in a circle causes velocity to constantly change. But which way? Lets study!!!!!!!!!!!!!!!!!!!!!!!! Vocab First, vocab word. Period – time to complete one revolution along a circular or repeating path. Symbol: T Unit : s Circumference – distance around a circle. Calculate speed To find speed, need to know distance and time. Time for once around is the period, T Distance for once around is circumference. C=2pr So, C 2pr v T T Units of m/s This is when moving at a constant speed. Speed calculation A merry-go-round has a radius of 6.0 m and takes 60 s to complete one revolution. How fast is an ant traveling that is sitting at the outer edge of the merry-go-round? Give : T = 60 s, r = 6.0m C 2pr 2p (6.0m) v T T 60 s v = 0.628 m/s Acceleration? What happens to the velocity vector as you move in a circle? It changes direction. You have zero displacement for each round trip. Changing velocity means, acceleration. circular motion1.IP Which way is it changing? Acceleration Velocity changes toward the center. Acceleration points toward center of circular path. Called Centripetal Acceleration Always toward center of curved path for constant speed. circular motion3.IP Centripetal Acceleration Found by equation : Where : v = speed r = radius Acceleration depends on both speed and radius of path. 2 v ac r Centripetal Acceleration So ac= (0.628 m/s)2/6.0m = 0.066 m/s/s How would ac change if Moved toward center? Acceleration will increase. Moved away from center? Acceleration will decrease. Moved to center? No acceleration. r = 0 True Force When you move in a circle, Which way are you accelerating? Toward the center. Which way is a force acting on you? Toward the center. What force is doing this? Friction. What is the net force? Centripetal Force Net force responsible for circular motion. Always acts toward center of path. There is no outward acting force. THERE IS NO CENTRIFUGAL FORCE EVER. What makes you feel the fake effect? Inertia. Centripetal Force Found by using 2nd Law. F=ma Fc=mac 2 v Fc m r This is the net force which causes circular motion. Example Find the centripetal force acting on you when standing at the edge of the merrygo-round. ac = 0.066m/s/s , m = 50 kg Fc=mac Fc=(50 kg)(0.066 m/s/s) = 3.3 N Which way is this force acting? Toward Center of merry-go-round. Why don’t I fall? Gravitron – centripetal force provides the normal force. Friction between body and wall equals weight and you don’t fall. Rollercoaster loop – at top you do not fall because track accelerates cars toward center at g. Circular Motion – Practical You cannot sense constant velocity, but you can sense acceleration (changing velocity; speed OR direction). Park ride, elevator, bad plane ride The change in velocity (acceleration) is ALWAYS toward the center Proportional the the speed squared Inversely proportional to the radius Proportional As one gets bigger, the other gets bigger Since “v” is squared, that means it doesn’t matter which direction (clockwise or counterclockwise) or whether you are slowing down or speeding up…the bigger the “change”, the bigger the acceleration Inversely proportional As the radius (how far you are away from the center) increases the centripetal acceleration decreases. As the radius gets smaller, the acceleration increases…BUT, at the CENTER…there is NO acceleration…! Why measure the period? The period is easy to measure, the velocity is much harder to measure Period is the time required to travel the same distance as the circumference of a circle. Acceleration and Force How do we know the force is “toward the center”, if we feel like the force is “outward”. Acceleration cannot happen without a force. Force MUST be in the same direction as the acceleration. Why does it travel like a projectile after you release the “string”? Only one force is acting on it…What is it? The moon circles the Earth in an almost perfect circle…what is the force acting upon the moon that causes it to do this? What would happen if the moon were closer? Further away? Problem A 0.013 kg rubber stopper is attached to a 0.93 m length of string. The stopper is swung in a horizontal circle, making one revolution in 1.18 s Find the speed of the stopper. Find the centripetal acceleration Find the force the string exerts on it. What do we know: Mass of stopper 0.013 kg Circle radius, r 0.93 m Period, T = 1.18 What do we need to know? Speed, v Acceleration, ac Force, Fc Equations See handout for these equations Velocity = circumference / T Acceleration = (velocity)2/radius Force, Fc = mass (of stopper, kg)* acceleration The Lab – Centripetal Force Centripetal force can only be measured indirectly! Why don’t we use the mass of the stopper?..easier to use “force downward” . Why does this work? The Lab (cont) Because gravity is exerting an acceleration downward on the washers (which have mass) Weight is a force = m*g (acceleration due to gravity) The weight (force) must = the “tension” that is exerted on the string, since the string is not moving (up and down) Since we are “spinning” the cork and the string is “stationary” (force down = tension centripetal force) .