Solving a Car Coasting Downhill Problem: Average Retarding Force

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To solve the problem of a 1200 kg car coasting downhill, the average retarding force due to friction can be determined by analyzing the energy balance and forces acting on the car. The car reaches a speed of 20 m/s after descending 35 m over 800 m. The kinetic energy at the bottom can be calculated, and the difference between this and the kinetic energy that would exist without friction indicates the work done against friction. The forces acting on the car include gravity and friction, with the normal force being irrelevant for the calculation of retarding force. Understanding the relationship between acceleration, velocity, and distance is crucial for solving the problem effectively.
TeeNaa
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A 1200 kg car start from rest and coast down a uniform grade, at the bottom of which ti has a speed of 20 m/s. If the car has traveled 800 m along the grade and has descended 35 m, what is the average retarding force(friction) encountered by the car? How would I solve this problem? I know Fx = ma = Ff - mgsintheta Fy = 0 = N - mgcostheta Ff = muN I don't have mu though. Thanks
 
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I would consider energy balance.

What is the kinetic energy at the bottom?
What would be the kinetic energy in the absence of friction?
What happened to the difference?
 
Is there any other way to solve this problem beside KE? I haven't learn that yet. Thanks
 
TeeNaa said:
Is there any other way to solve this problem beside KE? I haven't learn that yet. Thanks

Sum of forces along the ramp = ma
One force is gravity.
Second force is friction.
(Third force is force pushing up against the car. Why is this irrelevant?)

Get a from ramp length s and final velocity v.
Hint: dv/ds = dv/dt dt/ds = a/v.
 
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