Conservation of mechanical energy: Cyclist up a hill

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Homework Help Overview

The discussion revolves around a cyclist's effort to ascend an 8.00-degree hill with a vertical height of 115 meters. The problem involves calculating the work done against gravity and the average force exerted on the pedals, given the cyclist's mass and pedal mechanics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the calculation of work done against gravity using the formula W = F*d and discuss the potential energy increase related to the cyclist's ascent.
  • Some participants express uncertainty about the second part of the problem, questioning how to relate pedal revolutions to work done.
  • There is a suggestion to consider the potential energy gained per pedal revolution as a way to approach the second question.

Discussion Status

The discussion includes attempts to clarify units and the relationship between work and energy. Some participants have provided calculations, while others are still grappling with the concepts and how to apply them correctly. There is no explicit consensus on the approach to the second part of the problem, but several lines of reasoning are being explored.

Contextual Notes

Participants have noted the importance of units in calculations and the need to understand the relationship between potential energy and the work done in this context. There is also a mention of neglecting friction and other losses in the calculations.

Triad
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Homework Statement



A cyclist intends to cycle up a 8.00 hill whose vertical height is 115 . The pedals turn in a circle of diameter 36.0 .

1:Assuming the mass of bicycle plus person is 80.0 , calculate how much work must be done against gravity.

2: If each complete revolution of the pedals moves the bike 5.90 along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses.


Homework Equations


1: W = F*d

2: I don't know. Somehow I am sure it involves 1/2mv^2 + mgy


The Attempt at a Solution



1: W= (80kg*9.8m/s)*115m = 90160 N*m = 9.02*10^4 J (this one I solved)

2: shrug
 
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Triad said:

Homework Statement



A cyclist intends to cycle up a 8.00 hill whose vertical height is 115 . The pedals turn in a circle of diameter 36.0 .

1:Assuming the mass of bicycle plus person is 80.0 , calculate how much work must be done against gravity.

2: If each complete revolution of the pedals moves the bike 5.90 along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses.


Homework Equations


1: W = F*d

2: I don't know. Somehow I am sure it involves 1/2mv^2 + mgy


The Attempt at a Solution



1: W= (80kg*9.8m/s)*115m = 90160 N*m = 9.02*10^4 J (this one I solved)

2: shrug

Welcome to PF.

So what are your units?
You can't get the right answer without the right units.
 
Ack!. The first attempt to post I had all the units. I hurridly relaid it out.

8.00 Degrees
115m
36.0 cm Breaks down into .36 m with a radii of .16 m
80.0 kg
5.90 m


and the onyl equation I can assume for 2 is 1/2 mv^2+mgy
 
Perhaps you can approach 2) by identifying how much increase in Potential Energy for each revolution. Then knowing that amount of work to do that and the distance over which you had to do it ...
 
W = (80kg*9.8m/s)*(5.90m/2pi.16) = 1160 J ??

I am not understanding at all. I can believe I am being stumped by this when I could get the complete total for #1
 
Triad said:
W = (80kg*9.8m/s)*(5.90m/2pi.16) = 1160 J ??

I am not understanding at all. I can believe I am being stumped by this when I could get the complete total for #1

Well what's a joule? A N-m

And the increase in Y is what determines your increase in PE.

So doesn't that mean that your increase in PE/5.9 = Favg ?
 

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