Bicycle for investigations

The following worksheets may serve as first steps for investigations. You are invited to add your own proposals for studies.

Authors:   Helmut Kühnelt, Helmuth Mayr and Helga Stadler
                University of Vienna, Physics Education Group at Institute for Theoretical Physics

Remark: Of the many kinds of acceleration – becoming faster, slowing down, going around corners – only slowing down on straight paths will concern us here.

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Remark: You are certainly aware of the fact that in an inertial frme of reference a moving objects continues to move with constant speed in a straight line until a force acts and changes the state of the object’s motion.

1. Consider the steering mechanism of your bike.
1. Look which parts of the bike move and how, when you turn the steering bar? How is cornering achieved? Why is the steering axis not vertical? Why is the fork not straight on most bikes?
2. Compare different handle bars. What might be their advantages and disadvantages?
3. A member of the team should hold the bike such that the front wheel can turn freely. Then let the wheel rotate fast. What do you observe when you turn the handle bar to the left or to the right?
2. How does speed affect the way you ride a bike around a corner? You will certainly notice different angles of tilt of bike and biker.
1. Explain the tilt angle in terms of physical concepts. Give the connection between the relevant physical quantities.
2. Is it possible to go around a corner without tilting the bike? Describe your considerations in detail.
3. Assume that a biker tries to pass a corner on slippery ground with excessive speed so that he skidds.
   – Which type of motion would you observe from a fixed stand point on the street?
   – Can you find an analogy to a hammer thrown on the athletics field?
4. Try to calculate to tilt angle of a biker going on a circular path with a certain radius on a concrete surface.
3. Assume that several racing bikers are riding side by side – remember it is forbidden for ordinary people on the roads – and they are approaching a curve. They want to stay side by side so there will be no advantage after passing the curve. Is there a danger in the situation, how should the bikers behave?
   
4. In curves a biker should always have his/her body axis lie in the plane spanned by the bike’s center of mass and the wheels’ contact points with the street. You may have looked closely how a bike does a right turn, e.g.:
   mostly unconscious the rider turns the front wheel shortly to the left;
   then bike and biker are tilted to the right and also the front wheel is turned to the right,
   the curve is traversed in this position,
   and finally, the sequence of actions is reversed, until the biker travels aupright and straight.
   What is the advantage of such actions?
   Hint: Push a bike holding it only at the saddle und try to let it go in a circular path.
   
5. Racing bikes have slimmer tires than commuting bikes or mountain bikes.
   Investigate the effect of different tires on cornering.
   Look for the influence of the tire pressure.
   
6. Some competitions are performed on tracks with banked turns. If you watch racers on such tracks you may observe that they neglect the advice in 4. and that they bring their body even more inside.
   Investigate the role of the banked turns.
   What advantage do bikers gain by moving the body inside?

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Remark: In the circus you may have wondered how artists may climb freely standing ladders. If you have ever tried to keep your balance when riding a bike at rest, you got an impression ow difficult it is. Why is it so much easier to keep your balance on a moving bike?

Make observations in the following situations and give reasons for the bike’s behaviour:

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Remark: Remember the slightly different usage of terms, as e.g. energy, force, power, in everyday life and in physics.

1. Why do you need to use your forces, why are are becoming tired or even exhausted through riding a bike? What do you mean by that? What might be important factors?
2. Let us assume you want to attain a decent comfortable speed. What would your guess be for that speed, how many meters per second or kilometers per hour would you be going? I what ti9me do you want to reach that speed?
3. With your choices of item 2. determine the force needed to accelerate bike and biker. Which quantities should you know in addition? Can you give estimates if you cannot determine them?
4. How is the required force transmitted from biker to street? Where does it act? Is your estimate of the magnitude of the force realistic? What force can you apply on the pedal? Do your estimates differ significantly?
   Think of ways to justify your estimates and considerations.
5. How could the force be measured which is exerted on the pedal? In which direction is the force acting, when the pedal is horizontal or vertical or in other directions?
6. Immediately after starting the air resistance is unimportant. In Item 2 you have chosen a certain speed and time to accelerate. Calculate the necessary power and check whether you might be able to deliver it.
7. What speed might be attained by a top athlete who can deliver 700 W for a short time and 300 W for long periods? Give reasons why you consider the result unrealistic.
8. Think of ways how you could estimate or measure with appropriate accuracy your short term power output without ergometers.
9. Even going with constant speed on a smooth horizontal surface requires "force". Continue your considerations under 1. Which quantities are relevant for air resistance, which for internal friction (rolling resistance)? Where does internal friction become important?
10. How would you suggest to measure the internal friction – does it play a role in everyday life?
11. Assume the internal friction of your bicycle is 10 N at a velocity of 5 m/s. How much power could you supply in addition if your continous power output would be 150 W?
12. Assume the internal friction is (more or less) increasing linearly with speed. Which speed could YOU obtain on flat solid surfaces? Which inclines could you climb with constant speed of 5 m/s?
13. Biking might be called "Sitting while running". Why is it less exhausting than running at the same speed?
14. Air resistance is the dominant force opposing your motion at higher speed. On what does it depend? Interpret the main dependences.
15. Estimate the power needed to overcome the air resistance at constant speed and then specify it at v = 5 m/s or 10 m/s.
16. Assume a headwind with a speed of 10% of your cruising speed hits you. By what fraction do you have to increase your effort (power) to maintain your speed?
17. Sidewinds are annoying, too. How dou you experience a sidewind which is 50% of your travelling speed and comes just perpendicular to your path?

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