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The Bateleur
The Bateleur
The bateleur (/ˌbætəˈlɜːr, ˈbætəlɜːr/;[2] Terathopius ecaudatus), also known as the bateleur eagle, is a medium-sized eagle in the family Accipitridae. It is often considered a relative of the snake eagles and, like them, it is classified within the subfamily Circaetinae.[3] It is the only member of the genus Terathopius and may be the origin of the "Zimbabwe Bird", the national emblem of Zimbabwe.[4] Adult bateleurs are generally black in colour with a chestnut colour on the mantle as well as also on the rump and tail. - Wikipedia
The year is 2030, a new roller coaster is being designed for Yas Island. The current ‘record holder’, the Albatross is a nearly frictionless coaster, so much so that it can be ignored, that has a top speed of 162 km/h (45 m/s) attained by a drop height of h=101.25m tall drop tower. The new coaster, the Bateleur, hopes to attain a speed of 67.5 m/s or an astounding 243 km/h. A team of engineers is tasked with determining the new drop height to achieve this new record. The team hypothesized that to create the desired speed outcome, the height will need to be 1.5 times the height of the Albatross.
Design an experiment to test the engineer’s hypothesis. The engineers have the materials available in the PIVOTInteractives Height v. Velocity for a Puck on a Ramp.
Complete the table below to answer the following:
What quantities should be measured?
What symbol would be used to describe each measurement?
What equipment would be used to make the measurements?
Describe a brief procedure to be used to test the engineer’s hypothesis. Give enough detail that other engineers could replicate the experiment.
Describe how you would represent the data in a table or graph. Explain how that representation would be used to determine whether the data are consistent with the engineer's hypothesis.
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.
Before deriving an equation for a quantity such as vfinal , it can be useful to come up with an equation that is intuitively expected to be true. That way, the derivation can be checked later to see if it makes sense physically. The engineers come up with the following equation for the coaster’s maximum speed:
vfinal=2gh, where g is the acceleration of gravity and h is the height of the drop tower.
To test the equation, the engineers roll a cart down the track from various heights and measure the speed of the cart at the bottom of the track. The engineers vary the height (h) of the drop with each trial but keep everything else the same. The graph shown below is the engineer’s plot of the data for vfinal as a function of h.
Are these data consistent with the engineer’s equations?
_____ Yes _____ No
Briefly explain your reasoning.
Based upon the engineer’s initial equation, propose a change to the equation so that it fits the data collected. Briefly explain your reasoning.
vfinal = 2 g h
Based on the data collected by the engineers and your new equation, determine the new height necessary for The Bateleur.
Graph Interpretation and Linearization
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:
Which can be found in the IB Physics Data Booklet as:
Or in the AP Physics 1 Data Page as:
Some Additional Resources
Some Additional Resources
Graph Based
Algebra Based
Calculus Based
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