What Is the Maximum Speed a Truck Can Take a Curve Without Losing Its Cargo?

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SUMMARY

The maximum speed at which a truck can negotiate a curve without losing its cargo, specifically a crate of eggs, is determined by the radius of the curve and the coefficient of static friction. Given a curve radius of 35 meters and a static friction coefficient of 0.66, the maximum speed is calculated using the formula v^2/r = a(c). The resulting maximum speed is 15 m/s, ensuring the crate remains secure during cornering.

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  • Understanding of centripetal acceleration and its formula.
  • Knowledge of static friction and its role in motion.
  • Familiarity with basic physics equations involving forces and motion.
  • Ability to manipulate algebraic equations to solve for unknowns.
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  • Study the principles of centripetal force and its applications in vehicle dynamics.
  • Learn about the effects of different coefficients of friction on vehicle stability.
  • Explore real-world applications of static friction in transportation safety.
  • Investigate how weight distribution in vehicles affects cargo security during turns.
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Homework Statement


A crate of eggs is located in the
middle of the flatbed of a pickup
truck. The truck is negotiating a curve in the road that may be considered as an
arc of a circle of radius 35 m. If the coefficient of static friction between the
flatbed and the crate is 0.66, with what maximum speed the truck can negotiate
the curve if the crate is not to slide out during cornering?


Homework Equations





The Attempt at a Solution



Can someone please confirm this answer.

a(c) = v^2/r = v^2/35

You want to find the maximum 'acceleration' your friction can give you, and set it equal to that centripetal acceleration to find the corresponding velocity.

Mu=Friction Force/Normal Force
Mu*Fn=Ff
Mu*m*g=m*a(friction)
.66*g=a(friction)

Now back to original.

v^2/35=.66*g
v=15 m/s
 
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Seems OK.
 

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