“ You look so sweet, upon the seat of a bicycle meant for two” So sang the golden oldies ; very easy to sing. But it is not so easy to explain how it goes forward when the pedal is pushed down. When you consider the transmission of force from pedal to the tyre you will realise that the tyre gets pushed back. If so how does it go forward ? Why it is easy to balance on the run? Fig. 1 A bicycle meant for two. courtsey:- design boom.Fig.2 Transfering of the force on pedal to wheel. The figure shows how the push on the pedal pulls the chain and turns the cog wheel of the rare wheel and makes it rotate . When the small cog wheel completes one turn, the rim which is attached to it by the spokes also must do one turn. As the circumference of the tyre is larger than the circumference of the cog wheel the distance a point on the tyre will move will be much higher than the distance a cog will move. This is proportional to the ratio of their diameters. In mechanics in order to gain an advantage of distance there has to be a sacrifice.
The energy given to the pedal is equal to the energy, the cog wheel can use in pulling the chain. Considering this machine taken out of the bike we can see how the force alters. Fig.2 Pedal and wheel
Effort is the force used on the pedal. Let this be E. Load is the force exerted by the cog wheel on the chain. Let this be L. Work done by effort (energy used) is equal to the work done (energy transmitted) by load. Work done by effort = Effort x 2π R.e. ( Work done= Force X Displacement) Work cone by load = Load x 2π R.l. Therefore E x 2π Re. = L x 2πR.l.
effort x 2π R.e Load = ------------------------------- ( 2π Cancels) 2πR.l. Then we get.. Load = Effort x Re ÷ R,l.
Machine 2. Transferring of the force from the large cog wheel to the small cog wheel forms the second machine. This increases the force according to the ratio of their diameters . As there are only a fewer cogs in the second wheel it has to turn a number of rounds for one revolution of the large wheel. Machine 3 This is a wheel and axle machine. In a usual wheel and axle there is a mechanical advantage. Here it is the opposite that happens. As work (energy) is equal to force times distance , here force is lowered to gain distance. The bike is designed not to make travelling easier but to make travelling speedier. The bike as a single machine. If you can determine the ratio of distance effort moves : the distance bike moves we can calculate the highest theoretically possible (ideal) mechanical advantage. This is also called ‘velocity ‘ratio’. There are two methods to do this. Practical method Place the bike against a wall and mark the exact position of the bike. Then turn the pedal one complete round, allowing the bike to move forward.. Measure the distance bike has moved and the distance your had has moved. Your hand would have moved the circumference of the circle where pedal arm is the radius. When you divide the distance hand moved by the distance bike moved will give you the Ideal mechanical advantage or the Velocity Ratio.
The answer will be a fraction as the bike is not designed for a mechanical advantage. Theoretical method Make the following measurements as accurately as possible. Radius of the pedal arm = …………(lets call it R1) Radius of the wheel =…………..(Let it be R2) Number of cogs in the large Cog wheel = …………. ( let it be N1) Number of cogs in the small cog wheel = ……….. (N2)
Distance effort moves = 2 Π x R1 Distance load moves = 2 Π x R2 The ratio N1 : N2 gives the number of rotations of the small wheel for 1 round of the large wheel Therefore the total distance load moves = 2 Π x R2 (N1/N2) Total distance Effort moves = 2 Π x R1
2 Π x R1 Velocity ratio =--------------------------------- 2 Π x R2 (N1/N2)
R1 = -------------------------------------- R2 (N1 / N2)
Real Mechanical advantage This can be obtained by a practical method. The Mechanical Advantage is the ratio of Load : Effort (Load / Effort)
The bike has to be lifted or turned upside down so that the wheel may turn freely. Fig.3. Then hand two pans, one from the pedal where the effort is used and another from the end of the wheel that’s going up. Enter the results in this table.
Illustrate the results using a graph.
Frequently asked questions. Why is it easier to balance while riding?
Fig. A fast cyclist has to encounter molecules of air in the atmosphere.
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