Max Hill Steepness for a Cyclist: Solving the Problem

[ndwiseguy]

Ok now, i know it says that i should show the work I've done on the question. Problem is, I have no idea where to start. So here is the question:

Assume a cyclist of weight w can exert a force on the pedals equal to 0.90w on the average. If the pedals rotate in a circle of radius 18cm, the wheels have radius of 34cm, and the front and back sprockets on which the chain runs have 42 and 19 teeth, respectively, determine the maximum steepness of hill the cyclist can climb. Assume bike mass is 12kg and rider mass is 60 kg. Ignore friction.

If you could tell me where to start that would be great.

 

[NateTG]

What do you think you should do? What have you tried?

If you can figure out the force that the tire exerts on the ground, you're almost there.

You could cheat, and claim that w/o friction the bike can't make it up the hill. ;)

 

[ndwiseguy]

thank you very much

 

[Mr. Robin Parsons]

Bicycles are one of the most efficient machines known to humanity, so you can ignore friction as it amounts to be very little. A really good Bike can be ~95% to ~98% efficient (if I recall that one right) so the remaining 2% - 5 % is the friction part.

P.S. rarely will a back sprocket have an odd number of teeth (I've a friend with an eleven though) like 19, (cause it doesn't divide nicely into 360°) and the wheel radius are the wheel sizes in inches. A racing bike has 27 x 1 1/4 tires, so the wheel, when measured with a tape measure, will have a 27 inch diameter, 13.5 inch radius, and cheese, a "12 Kg" bike, WOW, heavy!