Thread: [SOLVED] Need help with pulley problem

Hi, i need help with the following question:

The sprocket assembly for a
0.800 m diameter bike wheel is
shown here. If the rider can
pedal at 50.0 rotations per
minute, what speed will the bike
be traveling? Express your
answer in km/hr. The radius of
the back sprocket is 0.050 m
and the radius of the front
sprocket is 0.150 m.

Here is the picture for reference:
[html]http://img191.imageshack.us/i/33012387.png/[/html]I don't know how to start this question, but i do know that the velocity of the pulley or sprocket is the same.

If the pedal is attached to the larges sprocket, and the wheel to the smaller sprocket, one rotation of pedal of 0,150 m radius will produce 3 rotations of smaller sprocket of radius 0.05 m.So the wheel will also rotate 3 rotations during one rotation of pedal.
Now proceed to find the speed of the bike.

i understand how you got the three rotations but im stuck after that. The answer is suppose to be 22.6 but i can't even get close to it

Originally Posted by ogglock

i understand how you got the three rotations but im stuck after that. The answer is suppose to be 22.6 but i can't even get close to it

In one rotation wheel travels π*D m,where D is the diameter of the wheel. In three rotation it will be moving 3π*D m.
In one minute pedal rotates 50 revolutions.
In one minute wheel rotates .........revolutions.
In one minute wheel travel ........... m.
In one hour wheel travel ........... m = ........km.

Originally Posted by sa-ri-ga-ma

In one rotation wheel travels π*D m,where D is the diameter of the wheel. In three rotation it will be moving 3π*D m.
In one minute pedal rotates 50 revolutions.
In one minute wheel rotates .........revolutions.
In one minute wheel travel ........... m.
In one hour wheel travel ........... m = ........km.

sorry but could you explain what the symbols π and m stand for

Originally Posted by ogglock

sorry but could you explain what the symbols π and m stand for

π is pi ......3.1416... m is meter.

sorry to ask again but can you show me how you did it.

Originally Posted by ogglock

sorry to ask again but can you show me how you did it.

Hi oddlock,
You sure are having trouble here.
pedal rotates 50 revs per min. or 3000 revs per hr
rear sprocket rotates 3x3000 =9000 revs per hr= bike wheel revs per hr
distance traveled in one hr =9000xpi x wheel dia =22,619 m perhr or 22.62 km per hr

bjh

thanks i was able to get it