Circular motion , the loop the loop

AI Thread Summary
To safely complete a loop-the-loop with a radius of 18m, the minimum speed required at the bottom is 30 m/s, contrary to an initial calculation of 13.2 m/s. The correct approach involves equating centripetal force and gravitational force to determine this speed. For part (b), the speed at the top of the loop can be calculated using energy conservation principles, factoring in kinetic and potential energy. The discussion highlights confusion over the interpretation of the problem, emphasizing the need to clarify which speed is being asked for in each part. Understanding the physics of centripetal motion and energy conservation is crucial for solving these types of problems.
NihalRi
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Homework Statement


The loop-the-loop machine has radius R of 18m
(a) What is the minimum speed at which a cart must travel so that it will safety loop the loop
(b) what will the speed at the top be in this case

Homework Equations


Centipetal force = m*v^2/r
Kinetic and potential energies = (1/2) m*v^2 and mgh respectively

The Attempt at a Solution


(a) equating weight and centripetal force and then solving for v I got an answer for velocity of 13.2 but the actual answer is 30
(b) based on (a) calculate the velocity using energy equations
(1/2)m×v^2 = mgh + (1/2) m×v^2
 
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NihalRi said:
(a) equating weight and centripetal force and then solving for v I got an answer for velocity of 13.2 but the actual answer is 30
I believe (a) is asking for the speed at the bottom. (Solve (b) first.)
 
Doc Al said:
I believe (a) is asking for the speed at the bottom. (Solve (b) first.)
I get what it's asking just not how to get the answer
 
You solved part (b).
 
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