In Week 4, we learned that the Zumanjaro drop was not truly a free fall, if for no other reason than they have to stop the fall (Six Flags’ legal department can be such a buzzkill). This week we’ll break the descent into two parts. From the maximum height of 415 ft (position A), we will assume the gondola drops in a free fall until the instant the braking starts (position B). Once the gondola reaches 90 mph at position B, the braking system quickly decelerates the gondola until it comes to rest on the ground (position C). See the figure below for reference.

Your Initial Post :

n the following, express your answers in terms of the mass (m) of the gondola (plus riders) , the heights above ground level (e.g. xA ), and the velocities of the gondola (e.g.vA ). Be concise by, for example, plugging in zeroes, but don’t plug in other known values.

1. Write an equation for the total mechanical energy of the gondola EA at the instant of the drop.
2. Write an equation for the total mechanical energy of the gondola EB at the instant the braking begins.
3. Write an equation for the total mechanical energy of the gondola EC after it comes to rest at the bottom.
4. Without performing any calculations, predict whether total mechanical energy should be conserved during the drop. In other words, given the conditions as stated, should EA = EB? What about EB=EC? EA=EC?
5. Using the kinematic free-fall equations, determine the height xB at which the gondola reaches 90 mph (express your final answer in units of m).

(Do not provide your answer in an attachment. You can type your answer in a Word document and then copy and paste it into the reply box. It’s not a good idea to type directly into the reply box in case you accidentally delete everything that would require you to start over. You can save a Word document often to avoid this kind of situation.)

Your Reply Post:

( I’ll send my classmate reply later , i can’t see their answers unless i post mine first )

Select a classmate who does not have a reply and do not reply on the same day as your initial post. In your reply to this classmate, correct any misconceptions in their initial post or commend them on an excellent post. Now you will check their work.

Determine, using their expressions, the values of EA, EB, and EC. Use the known values for the different positions and velocities given in the problem (converted to SI units) and your classmate’s value for xB. You may assume the mass of the gondola is m = 500 kg .

Comparing these values of total mechanical energy, do they match your classmate’s predictions from step 4? If not, what went wrong? Were the expressions for total mechanical energy incorrect, or were the predictions incorrect? If they do match, still verify that the expressions and predictions were correct (i.e. make sure it wasn’t just a coincidence).

Finally, why isn’t the total mechanical energy conserved at point C?