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Using centripetal force, determine the acceleration of gravity 
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#1
Dec711, 08:08 AM

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1. The problem statement, all variables and given/known data
This question relates centripetal acceleration and gravity. The general question is to determine the acceleration of gravity using centripetal force. A coin is tied to a string and swung in a circle over a person’s head. There is also a plastic tube attached to the string. The number of full rotations in a certain amount of time is counted, and the length of the string is measured as well. My question is, how would I go about finding the acceleration of gravity. I know that the centripetal force, (mv^2)/r, is equal to the force of gravity, F(g). I know the radius and the velocity, but what do I do for the mass, and how to I solve the overall problem for gravity? Is the mass just the mass of the coin, or the mass of the tube plus that of the coin? 2. Relevant equations Centripetal force = (mv^2)/r (mv^2)/r = F(c) = F(t) = F(g) Mass of coin  58.1 g Mass of tube  20.1 g 3. The attempt at a solution One line of data Using mass=coin + tube 20 revolutions in 18.91 s at a radius of 1.03 m m = 58.1 + 20.1 = 78.2 g r = 1.03 m v = d/t 2pir = 2pi(1.03)/ 18.91 = 0.342 m/s (78.2*.342^2)/1.03= 8.88 m/s^2 Pretty close to 9.8, but is this the right way to solve it? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


#2
Dec711, 08:19 AM

Mentor
P: 41,465

Instead, examine the forces acting on the object. Draw a free body diagram and apply Newton's 2nd law to both vertical and horizontal directions. Hint: The string isn't horizontal. What angle does it make? 


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