What is the Relationship Between Energy and Friction on an Inclined Plane?

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Homework Help Overview

The discussion revolves around the relationship between energy and friction on an inclined plane, specifically analyzing a scenario involving a car coasting up a slope. The problem involves calculating the average force of friction given the mass of the car, its initial speed, the angle of the incline, and the height gained.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the conservation of energy principles, considering both scenarios with and without friction. Some participants express uncertainty about the initial setup and calculations, while others attempt to derive relationships between kinetic energy, potential energy, and frictional forces.

Discussion Status

Several participants have shared their attempts at understanding the problem, with some providing insights into the energy transformations involved. There is a mix of approaches being explored, and while some have articulated their reasoning, there is no explicit consensus on the method to solve for the friction force.

Contextual Notes

Participants note the requirement to post their attempts, which may influence the depth of their contributions. There is also mention of the need to consider energy lost to friction in the context of the incline's geometry.

slaw155
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Homework Statement


EDIT: I have solved it entirely myself.

Homework Equations


The Attempt at a Solution

 
Last edited:
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slaw155 said:

Homework Statement


A 750kg mass car with initial speed 110km/h coasts up a slope inclined at 2.5degrees to the horizontal to a height of 22m above its starting point. What is the average force of friction?


Homework Equations



No real clue about this one

The Attempt at a Solution



As above, I don't really have an idea on how to do this. I've drawn a force vector diagram and considered energy but can't seem to work it out.
Even so, you are required to post your attempt, so far as it goes.
 
haruspex said:
Even so, you are required to post your attempt, so far as it goes.

I have worked it out entirely using my own self-determined methods.
 
Last edited:
Without friction the initial KE should equal the final PE.
 
With friction, final PE should equal initial KE minus energy lost to friction- the friction force times the distance traveled.
 
So :

The initial KE - the final PE = the energy lost to friction
= ( ½ * m * v ² ) - ( m * g * h )
( Joules )

Over the length of the incline, the energy lost to friction = ( constant ) friction force * distance travelled
( the length of the incline = 22.0 / ( sine 2.5 ° ) )

So, then, the friction force must equal ( ( initial KE ) - ( final PE ) ) / distance travelled

Comments please.
 

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