You want to design an oval racetrack such that 3200 lb racecars can round the turns...

You want to design an oval racetrack such that 3200 lb racecars can round the turns of radius 1000 ft at 96 mi/h without the aid of friction. You estimate that when elements like downforce and grip in the tires are considered the cars will round the turns at a maximum of 175 mi/h.

a) Find the banking angle ? necessary for the racecars to navigate these turns at 96 mi/h and without the aid of friction.

b) This banking and radius are very close to the actual turn data at Daytona International Speedway where 3200 lb stock cars travel around the turns at about 175 mi/h. What additional radial force is necessary to hold the racecar on the track at 175 mi/h?

Expert Solution

You will see that the mass of the cars doesn't matter.

For the case of no friction, the downslope component of the weight is equal to the upslope component of the centripetal force:
m*g*sin? = m(v²/r)*cos? ? mass m cancels; divide by g*cos?
tan? = v² / g*r ? frictionless case

96mi/h * 22ft/s / 15mi/h = 141 ft/s
so
tan? = (141ft/s)² / 32ft/s²*1000ft = 0.6213
? = 31.85º ? "ideal" banking for this radius and velocity

175mi/h * 22ft/s / 15mi/h = 257 ft/s

At this speed (and any speed greater than 96 mi/h on this track) we need a friction force downslope to hold the car on the curve.

normal force Fn = mgcos? + m(v²/r)sin?
so the friction force
f = µ*Fn = µ(mgcos? + m(v²/r)sin?)

Equilibrium parallel to the slope requires that
mgsin? + f = m(v²/r)cos?
3200lb * sin31.85º + f = (3200lb/32ft/s²)*[(257ft/s)² / 1000ft]*cos31.85º
f = 3922 lb ? friction force

I'm not sure what they mean by "radial" force. To me, that's the component of the friction force that's parallel to the ground, or
3922lb * cos31.85º = 3331 lb

Hope this helps! Please rate the answer.

genius_generous answered 2 years ago

Google tells you the average cat’s weight is 45 lb. You want to test it. 1...

Google tells you the average cat’s weight is 45 lb. You want to test it. 1 What is hypotheses? (in math terms and words) 2 Let alpha level to be 0.01. Conduct a hypothesis test (H0, p value, conclusion). A (cat numbers) 300 B (average weight) 38 C (sample standard deviation) 7 3 If someone tests if average weight > 45 lb. What is the hypotheses and conclusions (on same data)?

For this first Pause-Problem, I want you to design three (brief!) studies (they can all be...

For this first Pause-Problem, I want you to design three (brief!) studies (they can all be variations on the same idea). Make sure to note the independent and dependent variables for all 1). One should use an independent two group design 2). One should use a matched OR natural pair design 3). One should use a repeated measures design

For this Pause-Problem, I want you to design three (brief!) studies (they can all be variations...

For this Pause-Problem, I want you to design three (brief!) studies (they can all be variations on the same idea). ***Make sure to note the independent and dependent variables for all 1). One should use an independent three group design – 2). One should use a matched OR natural set design – 3). One should use a repeated measures design

Chester has a new design for their product City next round that can reduce their material...

Chester has a new design for their product City next round that can reduce their material cost of producing units from $8.14 to $7.32. Chester passes on half of all cost savings by cutting the current price to customers. For simplicity: - Use current labor costs of $4.06 - Assume all period costs as reported on Chester's Income Statement (Annual Rpt Pg 2) will remain the same. Determine how many units (000) of product City would need to be sold...

You want to design a magnetic device to keep cupboard doors closed. What are the design...

You want to design a magnetic device to keep cupboard doors closed. What are the design consideration? Suggest suitable materials that may be used.

Assume that you have a balance of $3200 on your MasterCard and that you make no...

Assume that you have a balance of $3200 on your MasterCard and that you make no more charges. Assume that MasterCard charges 12% APR and that each month you make only the minimum payment of 6% of the balance. What will the balance be after 24 months? (Round your answer to the nearest cent.)

1 design a column that supports 4500 lb if it is 12 feet long

Design and analyse of a circuit which turns a DC motor at a speed which is...

Design and analyse of a circuit which turns a DC motor at a speed which is proportional to how much a temperature is away from a set temperature, and turns: Clockwise when temperature is greater than (say) 25 degrees C. Anticlockwise when the temperature is less than (say) 20 degrees C. Such a circuit might be used to regulate the temperature of a room by turning a ceiling fan to move warm air in/out of that room (using the roof...

If I want to design an experiment related to kinetic friction, can the following proposal meet...

If I want to design an experiment related to kinetic friction, can the following proposal meet the requirement? By varying the weight of an object and measure the stopping distance of that object. Is this related to kinetic friction? If not, how should I change my experiment?

1. You want to design a pendulum for a grandfather clock so that it has a...

1. You want to design a pendulum for a grandfather clock so that it has a period of 2.00 seconds (so that one “tick” plus one “tock” occur during one complete period). The pendulum has a heavy 8.00-kg bob. (Throughout this problem, assume an ideal simple pendulum: the pendulum’s arm has negligible mass, the bob can be approximated as a point-mass, the initial angle of displacement is small, and there is negligible friction.) a.) If you want the clock to...

Question