Conservation of mechanical energy: Cyclist up a hill

In summary: I am not understanding at all. I can believe I am being stumped by this when I could get the complete total for #1Well what's a joule? A N-mAnd the increase in Y is what determines your increase in PE.So doesn't that mean that your increase in PE/5.9 = Favg ?
  • #1
Triad
3
0

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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  • #2
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.
 
  • #3
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
 
  • #4
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 ...
 
  • #5
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
 
  • #6
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 ?
 

1. What is conservation of mechanical energy?

Conservation of mechanical energy is a fundamental principle in physics that states that the total mechanical energy of a system remains constant as long as there are no external forces acting on the system. This means that the sum of the kinetic energy and potential energy of the system remains constant.

2. How does a cyclist's energy change while riding up a hill?

As a cyclist rides up a hill, their potential energy increases while their kinetic energy decreases. This is because the cyclist is gaining height, which results in an increase in potential energy, while their speed decreases, resulting in a decrease in kinetic energy.

3. Is mechanical energy conserved for a cyclist riding up a hill?

Yes, mechanical energy is conserved for a cyclist riding up a hill as long as there are no external forces acting on the cyclist. This means that the total energy of the cyclist, which is the sum of their kinetic and potential energy, will remain constant throughout the ride.

4. How does the mass of the cyclist affect conservation of mechanical energy?

The mass of the cyclist does not affect the conservation of mechanical energy. This is because, according to the law of conservation of energy, the total mechanical energy of a system remains constant regardless of the mass of the objects in the system.

5. What other factors can affect the conservation of mechanical energy for a cyclist riding up a hill?

Other factors that can affect the conservation of mechanical energy for a cyclist riding up a hill include external forces such as friction, air resistance, and the slope of the hill. These forces can cause a decrease in mechanical energy by converting it into other forms of energy, such as heat or sound.

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