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

[yashi5166]

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

 

[yashi5166]

Help ASAP

 

[PhanthomJay]

Your math is off a bit, and round it off to 10.1m/s

 

[yashi5166]

thanks soo much

 

[asteriatic]

I would first clarify the units being used for the given values, as well as the direction of the forces and the orientation of the loop. I would also double check the given information to ensure that it is physically possible. If the given values are accurate, then the solution provided by the student is correct. To calculate the speed of the coaster car at the top of the loop, we can use the equation Fc = Fg + Fn, where Fc is the centripetal force, Fg is the force of gravity, and Fn is the normal force. Since the normal force is equal to one-half the weight of the car, we can substitute this value into the equation and solve for the speed, v. This would give us v = √(g*r/2), which, when plugged in with the given values, gives us a speed of approximately 10.12 m/s. This speed is necessary for the coaster car to maintain a circular motion at the top of the loop with a diameter of 14m. Additionally, I would also consider any other factors that may affect the speed, such as friction and air resistance. Overall, the provided solution is accurate and meets the requirements of the given information.