Derive equation for truck slides before stopping

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SUMMARY

The discussion focuses on deriving the stopping distance for a truck and a car that are both subjected to the same coefficient of kinetic friction (uk) while braking. The car, with mass m, stops after sliding a distance d, while the truck, with mass M (where M > m), requires a different distance D to stop. The relationship between stopping distance and mass, initial speed, and friction is central to the solution, emphasizing the role of work done in calculating these distances.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with the concept of kinetic friction
  • Basic knowledge of free body diagrams (FBD)
  • Ability to apply work-energy principles
NEXT STEPS
  • Derive the stopping distance formula using the work-energy principle
  • Explore the relationship between mass and stopping distance in frictional scenarios
  • Investigate the effects of varying coefficients of kinetic friction on stopping distances
  • Learn about the dynamics of braking in vehicles and how mass affects stopping performance
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Students studying physics, particularly those focusing on mechanics, as well as engineers and automotive professionals interested in vehicle dynamics and safety analysis.

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Homework Statement



A truck of mass M and a car of mass m are traveling at the same speed. Suppose M>m. Now the drivers of both vehicles suddenly apply their brakes and the vehicles slide along the road, which has coefficient of kinetic friction uk. the car stops after sliding a distance d. assuming uk is the same for both vehicle, what is the distance D the truck slides before stopping?

Homework Equations


The Attempt at a Solution



I have drawn the FBD but i do not know how to relate to the stopping distance. The only thing i could think of is work done.
 
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What is the stopping distance d for the car in terms of its mass and initial speed and the coefficient of kinetic friction?
 

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