What Is the Resistive Force Acting on a Car Coasting at Constant Speed?

[mlazos]

Homework Statement

Along a certain section of road a car (m=1600) will coast in neutral at a constant speed of 72km/h if there is no wind.Examination of a topological map shows that for this section of the road the elevation decreases by 200m for each 6000m of road.What is the resistive force that acts on the car when it is traveling at 72km/h?

2. The attempt at a solution
I applied the conservation of energy and i said. For every 6000m the car is falling by 200m so is losing gravitational potential energy equal with $$U=mgh=1600 \cdot 10 \cdot 200 =3.2 10^6$$
We know the car has constant speed so this energy didnt become kinetic thus has to be equal with the work of the resistive force which is $$W=F s$$ and $$s=6000m$$

So we get the equation $$U=W \rightarrow mgh=F s \rightarrow F=\frac{mgh}{s}$$

So $$F=\frac{3.2 \cdot 10^6}{6 \cdot 10^3} \rightarrow F=533 N$$Could you please someone tell me if i did something wrong and where? I didnt use at all the speed of the car since i didnt use the kinetic energy. Thank you

 

[Doc Al]

Could you please someone tell me if i did something wrong and where? I didnt use at all the speed of the car since i didnt use the kinetic energy.

What you did is fine (assuming you're using g = 10 m/s^2--9.8 m/s^2 might be more accurate). The KE doesn't change so it's irrelevant.

Another way to view things is to just view the forces acting on the car directly. Since it's on a decline, there's a gravitational force acting on it equal to $mg \sin\theta = mgh/s$. Since the car's not accelerating, the resistive force must equal that gravitational force.