How much work is done on a bicyclist and her bike when coasting up a hill?

In summary, the problem presents a bicyclist on a bicycle encountering a small hill while coasting at 7.10 m/s. The bicyclist and bicycle have a combined mass of 67.60 kg and the speed at the top of the hill is 6.00 m/s. The attempt at a solution involved using the equation for kinetic energy and finding the difference between the final and initial kinetic energies. However, the final expression was incorrect and the correct answer is -487 J.
  • #1
PhyzicsOfHockey
42
0

Homework Statement



Coasting along at 7.10 m/s, a 60.0 kg bicyclist on a 7.60 kg bicycle encounters a small hill. If the speed of the bicyclist is 6.00 m/s at the top of the hill, how much work was done on the bicyclist and her bike?


Homework Equations



KEf-KEi=W
.5mvi^2-.5mvf^2
kg*m^2*s^-2
m=60kg+7.60kg
v=m/s


The Attempt at a Solution



I tried finding the loss in KE and having that be the work done. I get

.5mVf^2 -.5mVi^2
.5*67.6kg*36 - .5*67.6kg*50.41

I get -487 J and it tells me this is the wrong answer? What did I do wrong?
 
Last edited:
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  • #2
Please write out the whole equations. Include the mass and the units.
 
  • #3
I tried finding the loss in KE and having that be the work done. I get

.5m(Vf-Vi)^2 and I get -487 J and it tells me this is the wrong answer? What did I do wrong?

Your final expression is incorrect mathematically.
 
  • #4
I relized i posted that wrong but the answer comes out to -487 the right way but that's the wrong answer. I edited and wrote everything out.
 

1. How does coasting up a hill on a bicycle work?

Coasting up a hill on a bicycle involves using the momentum and forward motion of the bike to carry you up the hill without pedaling. As the bike moves forward, it builds up kinetic energy, which can be used to propel the bike up the hill. This is similar to how a car can coast up a hill without pressing on the accelerator.

2. Is coasting up a hill more efficient than pedaling?

In most cases, pedaling up a hill will be more efficient than coasting. This is because using your leg muscles to pedal requires less energy than relying on the kinetic energy of the bike. However, if the hill is not too steep and you have enough momentum, coasting can be a more efficient option.

3. How steep of a hill can a bicycle coast up?

The steepest hill that a bicycle can coast up will depend on a variety of factors such as the rider's weight, the weight of the bike, the condition of the road, and the amount of momentum the rider has built up. In general, a bicycle can coast up a hill with a slope of around 3-5% without pedaling.

4. What techniques can help with coasting up a hill on a bicycle?

There are a few techniques that can help with coasting up a hill on a bicycle. One is to shift to a lower gear before starting the climb to build up more momentum. Another is to stay relaxed and avoid tensing up your muscles, as this can slow down your progress. You can also try to find a balance between coasting and pedaling to maintain a steady speed.

5. Can coasting up a hill be dangerous?

Coasting up a hill on a bicycle can be dangerous if the hill is too steep or the rider loses control. It's important to always use caution and be aware of your surroundings when coasting up a hill. Make sure to maintain a safe speed and be prepared to start pedaling if needed. It's also crucial to have well-maintained brakes and a helmet for safety.

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