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

AI Thread Summary
The discussion centers on a physics problem involving a 300 kg roller coaster car navigating a vertical loop with a diameter of 24 m. It enters the loop at a speed of 20 m/s, and the key question is about its speed at the top of the loop. The conservation of energy principle is applied, equating the kinetic energy at the bottom with the sum of the kinetic and gravitational potential energy at the top. A participant encounters a negative value under the square root while solving, indicating that the car does not have sufficient kinetic energy to reach the top of the loop. The conversation emphasizes the importance of assessing whether the car's initial energy is adequate for this ascent.
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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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