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

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    Angle Car Hill
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Homework Help Overview

The problem involves a 1550-kg car navigating a hill, requiring the determination of the hill's angle based on the forces acting on the car, including air resistance and friction. The car's engine produces additional power when ascending compared to descending the hill, and the task is to find the angle of inclination above the horizontal.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the forces acting on the car, including the normal force, friction, and components of weight. There is an exploration of how to relate power, force, and angle, with some participants questioning the definitions and roles of various forces involved.

Discussion Status

The discussion is active, with participants exploring different interpretations of the forces at play and how they relate to the power produced by the engine. There is a focus on establishing expressions for the forces involved and how they change when the car is going up versus down the hill.

Contextual Notes

Participants note the importance of constant velocity in applying Newton's laws, and there is an ongoing examination of the definitions of forces and their components in relation to the problem's setup.

  • #31
No, Oh is it f=Fw+mgSin(theta)
 
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  • #32
So, Fw is?
 
  • #33
Fw=f-mgSin(theta)
 
  • #34
Good. So, find an expression for the power due to Fw going up and also for coming down. (Don't worry about numbers yet.)
 
  • #35
Up the hill: P=Fw(v) = (f+mgSinθ)v
Down the hill: P=Fw(v) = (f-mgSinθ)v
 
  • #36
Right. How do you now bring in the 44 hp?
 
  • #37
Set the equations equal to each other and add 44 to the "up hill" side
 
  • #38
Do you want to add it to the "up hill" side or the "down hill" side? Also, is hp the SI unit for power?
 
  • #39
o right becasue going uphill is 44 more hp you would add it to the downhill side. and no 1hp=745watt
 
  • #40
Right. (1 hp = 746 W the last I checked, but who's counting?) [OK, just checked, it's 745.699872 W for 1 "mechanical hp" and exactly 746 W for "electrical hp". Trivia for the day.]

http://en.wikipedia.org/wiki/Horsepower
 
Last edited:
  • #41
So just checking my equation:

v(f+mgSinθ)=v(f-mgSinθ) + 32810.8w

Now I can just plug and chug.
 
  • #42
Yep. Good work!
 
  • #43
I got a domain error... [never mind calculator error]
 
  • #44
What?
 
  • #45
I just put my nunmbers in my calculator wrong. No big deal thanks again.
 
  • #46
ok. No problem.
 

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