How Fast Will the Roller Coaster Car Be at the Top of the Loop?

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SUMMARY

The discussion centers on the physics of a roller coaster car, specifically a 300 kg car navigating a vertical loop with a diameter of 24 m. It enters the loop at a speed of 20 m/s. The analysis reveals that the car does not have sufficient initial kinetic energy to reach the top of the loop, as indicated by the negative result obtained when calculating the speed at the top using the conservation of energy principle. The key takeaway is that the car's initial kinetic energy must be evaluated against the gravitational potential energy required to ascend to the loop's apex.

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Homework Statement


At one point in a roller-coaster, a single 300 kg car goes around a vertical, circular loop with a diameter of 24 m. It enters the loop at the bottom with a speed of 20 m/s. What will its speed be at the top?

Homework Equations


Kinetic Energy = 1/2mv^2
Gravitational Energy = mgh

The Attempt at a Solution


Initial Energy = Final Energy => Kinetic Energy of the Bottom = Kinetic Energy of the Top + Gravitational Energy at the Top

I set up the equation for this problem and plugged in numbers to solve this, but I have a negative answer under the square root. Am I missing something else here?
 
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You are right, that car will not reach the top.
 
To check - and help you understand your result - ask instead: "does the car have enough initial kinetic energy to get to the top?"
Or, another way, what is the highest the car can reach?
 

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