Centripetal Acceleration Problem

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SUMMARY

The centripetal acceleration problem involves a student using an accelerometer to measure the speed of her car around an unbanked curve. The accelerometer setup includes a plumb bob that hangs at a 15-degree angle when the car travels at 23 m/s. The calculations reveal that the centripetal acceleration is 2.628 m/s², derived from the force equations involving tension and gravitational force. The key equations used include Tcos(15°) = mg and Tsin(15°) = ma, leading to the final acceleration value through the tangent function.

PREREQUISITES
  • Understanding of centripetal acceleration concepts
  • Knowledge of force equations in physics
  • Familiarity with trigonometric functions and their applications
  • Basic principles of accelerometers and their calibration
NEXT STEPS
  • Study the derivation of centripetal acceleration formulas
  • Learn about the calibration and use of accelerometers in physics experiments
  • Explore the application of trigonometry in solving physics problems
  • Investigate the relationship between speed, radius, and centripetal force
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Students in physics, educators teaching mechanics, and anyone interested in understanding the principles of centripetal acceleration and the use of accelerometers in real-world applications.

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Hello,
I am having the worst time figuring out how to solve this problem:

A student build and calibrates an acclerometer, which she uses to determine the speed of her car around a certain unbanked highway curve. The accelerometer is a plumb bob with a prtractor that she attaches to the roof of her car. A friend riding in the car with her observes that the plumb bob hangs at an angle of 15 degrees from the vertical when the car has a speed of 23m/s. What is the centripetal acceleration of the car?

Ok, I have my force equations:

The sum of the forces in the x=-Tcos75=-(mv^2)/r
The sum of the forces in the y=Tsin75-mg=0
I substituted T for mv^2/r, so mass cancels out, but I can't seem to figure out where to go from there.

Any help would be greatly appreciated!
 
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I didnt use the speed.

resolve Tcos15 = m 9.81
Tsin15 = ma

divide

9.81tan15 = a

a = 2.628ms^-2
 

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