What is the Velocity at the Bottom of a Roller Coaster with Given Parameters?

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To determine the velocity at the bottom of a roller coaster with a radius of 19.6 meters and an initial velocity of 14 m/s at the top, the relationship between centripetal force and gravitational force is crucial. At the top, the apparent weight is zero, indicating that the gravitational force equals the centripetal force. The discussion suggests using energy conservation principles, where potential energy at the top converts to kinetic energy at the bottom. The user is seeking clarification on how to incorporate mass into their calculations and whether they are using the correct equations. Understanding the dynamics of forces and energy transformations is essential for solving the problem accurately.
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Homework Statement


A roller coaster with radius of 19.6 and at the top of the roller coaster the veloctiy is 14 m/s and the apparent weight is 0. Calculate the veloctiy at the bottom of the roller coast?

Homework Equations





The Attempt at a Solution


I can see that Mv^2/r=mg at the top but i don't get how to solve for the veloctiy at the bottom of the equation of mv^2/r = Fn-mg. Am I looking in the right direction? I've done the force body diagram but the only way i can see to get out the velocity is with mass, am I missing an equation?
 
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Think about potential and kinetic energy.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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