Energy Model

The Hyper Slide

As part of Yas Islands continued pursuit to surpass Dubai as the entertainment capital of the UAE, it is introducing The Hyper Slide, in conjunction with Elon Musk and Tesla Motors.

During his first trip in the magnetically-levitated capsule through the vacuum tube (as friction free as possible), Lary reached the half way point (0.5 E.M.'s in height) and became philosophical.

Question #1:

Being the dutiful physics student that he is he was wondering how much time he had left in his ride. He had been in accelerating down the Hyper Slide for 60 seconds.

Conceptually, would he continue to accelerate for (a) less than 60s (b) an additional 60s (c) more than 60s. Justify your decision.

Question #2:

He was also wondering how fast he would be traveling at the bottom of the acceleration zone. The speedometer currently read that he was traveling at 200 km/hr.

At the bottom of the ride will he be traveling:

< 400 km/hr.
= 400 km/hr.
>400 km/hr.

From the PIVOT Interactives site, you will be using the experiment: Height vs Velocity for a Puck on a Ramp

There are 11 different heights and 2 masses to experiment with. You will taking data from 5 different settings and adding your data to the class info.

Graph Interpretation and Linearization

To linearize a square root relationship, you can work with either axis:

x-axis changes: find the square root of the x-values, this will 'shorten' the x-axis creating a linear graph.
y-axis changes: Square the values on the y-axis, this will 'stretch' the axis 'pulling' it into a linear function.

We can see from the data that the relationship is a 'root 2' relationship or a power series x^0.5 (sqrt). We can also see from the data that the mass has no impact on the final velocity of the object as it reaches the bottom of the ramp.

Therefore we can derive the relationship in the second graph:

Furthermore, we can see that the slope of the data in the second graph has a unit of ms^-2. Which has a unit of acceleration. Giving us the final relationship of: