Derive equation for truck slides before stopping

In summary, a truck and car, both traveling at the same speed, suddenly apply their brakes and slide along a road with a coefficient of kinetic friction uk. The car, with a mass of m, stops after sliding a distance d. Assuming uk is the same for both vehicles, the distance D the truck slides before stopping can be determined by relating it to the stopping distance d for the car, which can be found in terms of its mass, initial speed, and uk. The only known factor is the work done.
  • #1
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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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  • #2
What is the stopping distance d for the car in terms of its mass and initial speed and the coefficient of kinetic friction?
 

Related to Derive equation for truck slides before stopping

1. What is the equation for calculating the distance a truck slides before stopping?

The equation for calculating the distance a truck slides before stopping is d = (v2)/(2μg), where d is the distance, v is the initial velocity of the truck, μ is the coefficient of friction between the tires and the road surface, and g is the acceleration due to gravity.

2. How is the coefficient of friction determined for a truck?

The coefficient of friction for a truck can be determined through experiments on a test track, where the truck is driven at different speeds and the distance it takes to stop is recorded. The coefficient of friction can then be calculated using the above equation and the known values of distance, velocity, and acceleration due to gravity.

3. Are there any other factors that can affect the distance a truck slides before stopping?

Yes, there are other factors that can affect the distance a truck slides before stopping. These include the weight of the truck, the condition of the tires, the road surface (e.g. wet vs dry), and the incline of the road.

4. Can this equation be applied to all trucks?

No, this equation may not be applicable to all trucks as it assumes a constant coefficient of friction and does not take into account other factors such as braking systems and variations in tire design. It is important to consider these factors when using this equation for a specific truck.

5. How accurate is this equation for determining the distance a truck slides before stopping?

This equation provides a reasonable estimate for the distance a truck slides before stopping, but it is important to note that it is based on idealized conditions and may not reflect real-world scenarios accurately. Other factors such as human error and external forces can also affect the accuracy of this equation. It is always best to conduct real-world tests to determine the actual stopping distance of a truck.

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