First we reduced the radius to 17 cm and the next

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pointer. First, we reduced the radius to 17 cm and the next time we increased it to 21 cm. At each radius we calculated a static force since a different amount of mass was needed
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to pull the bob out these two distances. We then calculated T by observing how many revolutions the bob makes in a set amount of time. Determining T, we calculated the velocity the bob was spinning with at each radius. Knowing the radius, mass, and velocity we calculated the centripetal force for the formula discussed above. We also compared these calculated values at each radius to the static force at each radius to observe our difference and error in calculations. From these comparisons of values, we were able to verify if the formula F =  (mv^2)/ r is accurate.  Data/Calculations:  The first calculations were done when the radius of the circle the bob spun  around was at 19 cm with no added mass to the bob. We started by calculating the static force  (F ststic  ) since it equal in magnitude to the actual centripetal force. We added 700 g to the pulley  system to pull the bob out directly over the pointer – at 19 cm. The static force (in Newtons) is  equal to the mass added (in kg) multiplied by little g (the acceleration due to gravity - 9.8 m/s).  We divided 700 g by 1000 to convert it into kg: 700g/1000 = 0.700 kg Thus, the static force is: F static  = 0.700 kg * 9.8 m/s = 6.9 N Next, we calculated the centripetal force. The formula is F c  = (mv^2)/ r.  The mass of the bob (in  kg) and the radius (in meters) are known. We had to find the velocity (V) the bob was rotating  with from the formula V = (2*pi*r) / T.  T is the time in seconds it takes for the bob to make one rotation.  We observed that in 60 seconds the bob made 83 rotations. To find the time for one rotation we  set up a proportion:
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83 Rotations/60 seconds = 1 rotation/x seconds 83*x = 60 X = 60 /83 = 0.72  So, in 0.72 seconds the bob made one rotation.  The radius also had to be converted to meters: 19cm * (1 meter/100cm) = 19/100 = 0.19 m  Plugging in the radius and T into the equation V = (2*pi*r) / T: (2*pi*0.19) / 0.72 = 1.66 m/s We weighed the bob on the scale to find its mass. The bob weighed 445.1 g. Converting to kg: 445.1/1000 = 0.4451 kg Now velocity, radius, and mass of bob are known: V = 1.66 m/s Mass of bob = 0.4451 kg Radius = 0.19 m Inserting these numbers into the formula F c  = (mv^2)/ r: (0.4451*1.66^2) / 0.19 = 6.5 N In the next calculations of centripetal force, we changed the mass of the bob twice while keeping  the radius at 19 cm (0.19 m). Then we adjusted the radius twice while keeping the mass of the  bob at 445.1 g.  
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Adjusting for mass of bob: 1) We added 50 g to the bob. The total mass then is 445.1 g + 50 g = 495.1 g Converting to kg: 495.1/1000 = 0.4951 kg
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