Finding the initial height of a roller-coaster [HELP]

[Scooter I]

Homework Statement

Homework Equations

PE = mgh
KE = [itex]\frac{1}{2}[/itex]mv[itex]^{2}[/itex]
W = ΔKE
W = Fd

The Attempt at a Solution

g = 9.80m/s[itex]^{2}[/itex]
hi = ?
hf = 20.0m

PEi + KEi = PEf + KEf

mghi = mghf

Would you then cancel the masses out? If you did, the initial height would be 20.0m. Am I right? Thanks in advance to anyone who helps.

 

[Poley]

In order to clear the loop, the roller coaster needs to be moving with some speed at the top, and thus have kinetic energy, otherwise it will fall down. Try to find the minimum speed necessary to have a nonzero normal force at the top of the loop. Hope this helps!

 

[Scooter I]

In order to clear the loop, the roller coaster needs to be moving with some speed at the top, and thus have kinetic energy, otherwise it will fall down. Try to find the minimum speed necessary to have a nonzero normal force at the top of the loop. Hope this helps!

How would I find the initial speed, since I'm only given a diameter of 20.0m?

 

[Poley]

At the top of the loop, the centripetal force is the sum of the gravitational force and the normal force (both are directed radially inward). At the minimum possible speed necessary, the normal force at the very top of the loop will be zero. Therefore, the only component of the centripetal force is the gravitational force. Now, using the given diameter, you should be able to find the minimum speed necessary at the top of the loop, and then use conservation of energy to find the minimum initial height. Let me know if this makes sense.

 

[asteriatic]

As a scientist, it is important to approach problem-solving in a systematic and logical manner. In this case, you have correctly identified the relevant equations and variables, and have set up an equation to solve for the initial height of the roller-coaster. However, it is important to consider the physical significance of the equation and the values you are using. In this case, you have assumed that the potential energy and kinetic energy of the roller-coaster are equal at both the initial and final points, which may not necessarily be the case. It is also not clear what the value of 'd' is in the W = Fd equation. Therefore, it would be helpful to provide more information or data in order to accurately calculate the initial height of the roller-coaster. Additionally, it is always good practice to double-check your calculations and units to ensure accuracy.