Car going up a hill. Find the Angle of the hill.

pmd28

1. The problem statement, all variables and given/known data
A 1550-kg car experiences a combined force of air resistance and friction that has the same magnitude whether the car goes up or down a hill at 21 m/s. Going up a hill, the car's engine produces 44 hp more power to sustain the constant velocity than it does going down the same hill. At what angle is the hill inclined above the horizontal?

2. Relevant equations
P=W/t=FvCosθ
W=fΔx

3. The attempt at a solution
I drew out my free body diagram and I have the Normal force, friction, and the components of the weight force (mgCosθ in the y-direction and mgSinθ in the x-direction)
I figured I need to find out the F in P=FvCosθ. I'm just not sure what F it is I have to find.

Related Introductory Physics Homework News on Phys.org

TSny

Homework Helper
Gold Member
There's another force you need to include. What force "propels" the car up the hill?

pmd28

i thought wheels generated friction which caused a recipriocal force on the car by the road, which caused a car to move.

TSny

Homework Helper
Gold Member
Exactly. I'm not sure that the "friction" mentioned in the problem is the same as the friction generated by the wheels to drive the car up the hill. I think they might have been talking about internal friction that acts along with the air resistance. But, anyway, I think we're clear on the forces.

Think of the force generated by the wheels as ultimately coming from the engine. So, if you are going to set up an expression for the power that the engine produces, you are going to need the force generated by the engine (i.e., the friction force generated by the wheels.) Can you think of a way to get an expression for that force?

pmd28

Well I'm given power and I'm velocity. Would it be right to use a rearrangement of P=Fv, F=P/v?

TSny

Homework Helper
Gold Member
OK, but note they only give you the change in power when switching between going up and coming back down.

Can you bring in something else that would let you relate F to the angle of the slope?

pmd28

The components of the Weight force?

TSny

Homework Helper
Gold Member
I was thinking more along the lines of a principle or law that you could apply. Note that they tell you the velocity is constant.

pmd28

Well if velocity is constant it cant be newton's 2nd Law. I'm stumped.

Homework Helper
Gold Member
Oh yes it can :)

pmd28

Well if it's at a constant velocity wouldn't that make F=0 due to the lack of acceleration?

TSny

Homework Helper
Gold Member
But what does F represent in the 2nd law?

Net Force?

TSny

Homework Helper
Gold Member
Sure. That's important. F is always the sum of all of the forces acting on the object when setting up the 2nd law. Or, if you're working with components, it says that the sum of all the components of the forces in a certain direction equals the mass times the component of the acceleration in that direction.

pmd28

So do I use the component(s) of the Weight force to relate F and theta?

TSny

Homework Helper
Gold Member
Let's pick a specific symbol for each force: f for the air resistance, mg for the weight, Fw for the force from the wheels, and Fn for the normal force. How would you write an expression for the net force acting upward along the slope?

ƩF=Fw-f-mgcosθ

TSny

Homework Helper
Gold Member
Good. Can you use the 2nd law to express Fw in terms of the other forces? [Oops: You didn't quite get that right. Think again about the component of the weight.]

Last edited:

pmd28

Yes, because ƩF=0, (because I know that the car is moving at a constant v), Fw = f + mgCosθ

TSny

Homework Helper
Gold Member
Yes, but you'll need to correct the mgCos(theta) term.

pmd28

What do you mean?

TSny

Homework Helper
Gold Member
mgCos(theta) is not the correct expression for the component of the weight that acts down the slope.

pmd28

oh, mgsin(theta). Yea I was reading my Free-Body Diagram wrong.

TSny

Homework Helper
Gold Member
That's it. What would the result for Fw be for coming back down the slope.? (Drawing another diagram would be a good idea.)

pmd28

I'm not sure I understand that question.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving