Calculating Power Output to Climb a 7.0 Degree Hill

In summary, the conversation is discussing the power output required for a cyclist to climb a 7.0 degree hill at a steady speed of 5.0 m/s. The total mass of the cyclist and bike is 75kg. The initial answer given is 450W, but the correct answer is actually 900W. The discrepancy is due to the fact that in addition to gravity, friction is also doing work on the cyclist. To account for this, the power output needs to be doubled in order to maintain kinetic energy and recover potential energy lost while coasting down the hill. The conversation also mentions additional information and resources for cycling and biking.
  • #1
FossilFew
15
0
A bicyclist coasts down a 7.0 degree hill at a steady speed of 5.0 m/s. Assuming a total mass of 75kg (bicycle plus rider), what must be the cyclist's power output to climb the same hill at the same speed?



I get 90N * 5.0 m/s = 450W



The book says 9.0 * 10^2 W

It looks like I'm at half the value of the correct answer. Any help is greatly appreciated!
 
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  • #2
Just glancing at it, I got the same answer as you. Here we are using P=F*v, and that there is no net force on the bike. Maybe someone else can point out the problem here.
 
  • #3
I think I have it. It's 450W *2 due to Frictional Force AND Force in the X direction. Thanks for your help.
 
  • #4
please could you explain how to do this problem?
 
  • #5
ammu said:
please could you explain how to do this problem?

In addition to gravity, friction is doing work on the bicyclist. You need to account for the friction when determining the power necessary for him to climb the slope.
 
  • #6
thanks for the reply,
actually i got the answer as 450 W but the right answer is 900W. i don't know why i can't get this answer! please help
 
  • #7
The amount of work in order to get the bike to go up the hill is equal to the amount of gravitational potential energy in addition to the kinetic energy needed to move at the same speed. that is why you get double the answer you've been getting: the change from potential energy to kinetic energy when coasting "down" the hill gives your velocity. you have to double it in order to maintain your kinetic energy as well as recover your potential energy that you lost from coasting down the hill.
 
  • #8
Sorry, i don't know anything about it.

___________________
Huge information existing about cycling and biking. Observe all that information that you need to know regarding bikes and http://bikes-bicycle-parts.com/cycling-apparels/bicycle-helmets/ [Broken].
 
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1. How do you calculate power output for climbing a 7.0 degree hill?

The formula for calculating power output is Power = (Weight x Gravity x Distance x Slope) / Time. To climb a 7.0 degree hill, you will need to know the weight of the object or person climbing, the acceleration due to gravity (9.8 m/s^2), the distance of the hill, the slope (in degrees or as a decimal), and the time it takes to climb the hill.

2. What is the significance of calculating power output for climbing a 7.0 degree hill?

Calculating power output helps to determine the amount of energy required for an object or person to climb a hill. This information can be useful in designing efficient transportation systems or in training for physical activities such as cycling or hiking.

3. How does the weight of the object or person affect power output when climbing a 7.0 degree hill?

The weight of the object or person directly affects the power output needed to climb a hill. Heavier objects or people will require more power to overcome the force of gravity and ascend the hill.

4. Can the slope of the hill affect the power output needed to climb a 7.0 degree hill?

Yes, the steeper the slope of the hill, the more power output is required to climb it. This is because a steeper slope means there is a greater uphill force to overcome.

5. Is power output the only factor in successfully climbing a 7.0 degree hill?

No, power output is just one factor in successfully climbing a hill. Other factors such as technique, endurance, and equipment can also play a role in the ability to climb a hill. Power output is simply a measure of the amount of energy required to overcome the physical forces of gravity and friction while climbing a hill.

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