GGRC33H3 Final: FInals Essay Question #2, 5

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7 Jul 2011

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The present-day physical landscape of the toronto region is a direct reflection and composite of many years of intense planning policies, initiatives and debates (sewell, 1993; sewell, 2009; Initiatives for improving and or producing a better city in the early twentieth century, marked the beginning and launch of planning in the toronto region (sewell, 1993, p. 4). Regional planning first appeared in toronto during the ww2, but there were thoughts of planning dating back to ww1 (white, 2007). Without question the major event of the 1950s and 1960s was the 1953 establishment of the municipality of metropolitan. Toronto (metro) a regional government which encompassed thirteen municipalities (most of the then urbanized territory plus ambient rural lands (filion, 2000). The focus of this analytical response will centre of investigating many different dimensions of the creation of metro (1953) by answering (1) why was it established and (2) in what ways was it thought to be successful.

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Introduction. Telescope time is a valuablecommodity in astronomy, so astronomers plan their observationscarefully. One of the first steps is to choose what type ofobservation to make. Recall that three basic types of astronomicalobservation are imaging (taking a photograph of anobject), spectroscopy (spreading an object's light into aspectrum), and timing (measuring how an object's lightvaries with time).

Part A: Sort each of the astronomical questionsbelow into the appropriate bin based on the type of observation youwould need to perform to answer it.

Three Categories: Imagine, Spectroscopy andTiming

The Questions:

1. "What are the major surface features of Mars?"

2. "What is the temperature of Jupiter's atmosphere?"

3. "Does the star Mira vary in brightness?"

4. "How large is the Andromeda Galaxy?"

5. "What is the chemical composition of the Crab Nebula?"

6. "Is the X-ray emission fro the galactic center steady orchanging?"

7. "Is the star Vega moving toward us or away from us?"

8. "Are stars in the Orion Nebula surrounded by dusty disks ofgas?"

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Introduction: Different telescopes areoptimized for observing different wavelengths of light, so anotherconsideration in planning an observation is deciding what type oftelescope to use.

Part B: Each of the following statementsdescribes an astronomical measurement. Place each measurement intothe appropriate bin based on the type of telescope you would use tomake it.

Three Categories: Infrared Telescope, VisibleLight Telescope and X-Ray Telescope

The Statements:

1. Study a dense cloud of cold gas in space.

2. Measure the brightness of a star that is similar to ourSun.

3. Observe the hot (1-million K) gas in the Sun's corona.

4. Obtain a spectrum of sunlight reflected by Mars.

5. Determine the surface temperature of Venus.

6. Look for high-energy radiation from a supernova.

Thank you so much to whoever helps!

How fast can a racecar travel through a circular tum without skidding and hitting the wall? The answer could depend on several factors:

The weight of the car;
The friction between the tires and the road;
The radius of the circle;
The “steepness” of the turn.

In this project, we investigate this question for NASCAR racecars at the Bristol Motor Speedway in Tennessee. Before considering this track in particular, we use vector functions to develop the mathematics and physics necessary for answering questions such as this.

A car of mass m moves with constant angular speed to around a circular curve of radius R (Figure 3.20). The curve is banked at an angle . If the height of the car off the ground is h, then the position of the car at time t is given by the function

As the car moves around the curve, three forces act on it: gravity, the force exerted by the road (this force is perpendicular to the ground), and the friction force (Figure 3.21). Because describing the frictional force generated by the tires and the road is complex, we use a standard approximation for the frictional force. Assume that for some positive constant . The constant is called the coefficient of friction.

Let denote the maximum speed the car can attain through the curve without skidding. In other words, is the fastest speed at which the car can navigate the turn. When the car is navigate at this speed, the magnitude of the centripetal force is

The next three questions deal with developing a formula that relates the speed to the banking angle .

Now that we have a formula relating the maximum speed of the car and the banking angle, we are in a position to answer the questions like the one posed at the beginning of the project.

The Bristol Motor Speedway is a NASCAR short track in Bristol, Tennessee. The track has the approximate shape shown in Figure 3.22. Each end of the track is approximately semicircular, so when cars make turns they are traveling along an approximately circular curve. If a car takes the inside track and speeds along the bottom of turn 1, the car travels along a semicircle of radius approximately with a banking angle of . If the car decides to take the outside track and speeds along the top of turn 1, then the car travels along a semicircle with a banking angle of . (The track has variable angle banking.)

The coefficient of friction for a normal fire in Elly conditions is approximately . Therefore, we assume the coefficient for a NASCAR tire in dry conditions is approximately .

Before answering the following questions, note that it is easier to do computations in terms of feet and seconds, and then convert the answers to miles per hour as a final step.

11. Suppose the measured speed of a car going along the outside edge of the turn is . Estimate the coefficient of friction for the car’s tires.

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GGRC33H3 Final: FInals Essay Question #2, 5

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