Solving a Car Coasting Downhill Problem: Average Retarding Force

[TeeNaa]

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

 

[rude man]

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?

 

[TeeNaa]

Is there any other way to solve this problem beside KE? I haven't learn that yet. Thanks

 

[rude man]

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.

 

[Nickie]

To solve this problem, we can use the equations of motion and the concept of work and energy. First, we need to find the initial potential energy and final kinetic energy of the car.

Initial potential energy = mgh = (1200 kg)(9.8 m/s^2)(35 m) = 411600 J
Final kinetic energy = (1/2)mv^2 = (1/2)(1200 kg)(20 m/s)^2 = 240000 J

The difference between the initial and final energy is the work done by the retarding force (friction) on the car. Therefore, we can calculate the average retarding force using the equation:

Work done = F(avg) * distance traveled

F(avg) = Work done / distance traveled = (240000 J - 411600 J) / 800 m = -213 N

Since the retarding force is acting against the direction of motion, it is negative in sign. This value represents the average retarding force (friction) encountered by the car while coasting downhill.

To find the coefficient of friction (μ), we can use the equation:

Ff = μN = μmgcosθ

Substituting the known values, we get:

-213 N = μ(1200 kg)(9.8 m/s^2)cosθ

Since we do not have the value of μ, we cannot solve for it unless we know the angle of the grade (θ). If the grade is known, we can use the given information to find the value of μ.

In summary, to solve this problem, we used the equations of motion and the concept of work and energy to find the average retarding force encountered by the car while coasting downhill. The value of the coefficient of friction (μ) can be found if the angle of the grade is known.