What Speed Does the Roller Coaster Need to Maintain at the Top of a 14m Loop?

AI Thread Summary
To determine the speed of a roller coaster at the top of a 14m loop where the normal force is half the weight of the car, the equation Fc = Fg + Fn is used. The centripetal force (Fc) is expressed as mv²/r, where r is the radius of the loop. Given that the normal force (Fn) is 0.5 times the gravitational force (Fg), the equation simplifies to mv²/r = mg + 0.5(mg). After calculations, the speed at the top of the loop is found to be approximately 10.1 m/s. This solution highlights the importance of understanding forces acting on objects in circular motion.
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Homework Statement


A roller coaster is moving past the top of a loop of diameter 14m. The Normal force (directed downwards) provided by the track at the top of the loop is equal to one-half the weight of the car. What is the speed of the coaster car at this point?

Homework Equations



Only the diameter is given.

The Attempt at a Solution


Fc = Fg+Fn
→ mv2/r = mg + .5(mg)

and then minimum speed to go in a circle is sqrt(gr) but that won't work cause in order for that to happen Fn has to be 0 but here is half Fg. i believe the answer is 10.12m/s
 
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Your math is off a bit, and round it off to 10.1m/s
 
thanks soo much
 
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