Motion and force along a curved path

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SUMMARY

The discussion focuses on calculating the speed of a car navigating a curved exit ramp with a radius of 82 meters, where a 76 kg passenger exerts a force of 220 N to avoid sliding. The relevant equations include F = m*a and a = V²/R, which relate force, mass, acceleration, and velocity. The correct approach involves using the centripetal acceleration formula to derive the car's speed directly from the force applied by the passenger.

PREREQUISITES
  • Understanding of Newton's second law (F = m*a)
  • Knowledge of centripetal acceleration (a = V²/R)
  • Familiarity with basic physics concepts such as mass and force
  • Ability to manipulate algebraic equations to solve for unknowns
NEXT STEPS
  • Calculate centripetal acceleration using the formula a = F/m
  • Derive the car's speed using the equation V = √(a*R)
  • Explore the effects of friction on motion along curved paths
  • Study the impact of banking angles on vehicle dynamics in curves
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and motion, as well as educators seeking to explain concepts of force and acceleration in curved motion.

a18c18
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Homework Statement



A car speeds along the curved exit ramp of a freeway. The radius of the curve is 82 m. A 76 kg passenger holds the arm rest of a car door with a 220 N force to keep from sliding across the front seat of the car. (Assume the exit ramp is not banked and ignore friction with the car seat.) What is the car's speed?

Homework Equations



v=2(3.14)r/t
u(static)=v^2/rg

The Attempt at a Solution



I tried to use the v=2(3.14)r/t formula but I don't know the time. I'm not sure what else to try.
 
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a18c18 said:

Homework Statement



A car speeds along the curved exit ramp of a freeway. The radius of the curve is 82 m. A 76 kg passenger holds the arm rest of a car door with a 220 N force to keep from sliding across the front seat of the car. (Assume the exit ramp is not banked and ignore friction with the car seat.) What is the car's speed?

Homework Equations



v=2(3.14)r/t
u(static)=v^2/rg

The Attempt at a Solution



I tried to use the v=2(3.14)r/t formula but I don't know the time. I'm not sure what else to try.

You would do better to work from the 220N force on the individual.

F=m*a since this is also equal to mV2/R you know that a = V2/R ... Calculate a. Calculate V.
 

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