a bicycle chain is wrapped around a rear sprocket (r=.039m) and a frond sprocket (r=0.10m) the chain moves with a speed of 1.4 m/s around the sprockets while the bike moves at a constant velocit find the madnitude of the acceleration of a chain link that is in contact with (a) the rear sprocket (b) neither sprocket and (c) the front sprocket
5025
To find the magnitude of the acceleration of a chain link in contact with different parts of the bicycle, we can use the centripetal acceleration formula:
a = (v^2) / r
where "a" is the acceleration, "v" is the speed, and "r" is the radius of the circular path. Let's calculate the acceleration for each case:
(a) Chain link in contact with the rear sprocket:
The radius of the rear sprocket is r = 0.039m.
The speed of the chain is v = 1.4 m/s.
Substituting the values in the formula:
a = (1.4^2) / 0.039
= 1.96 / 0.039
= 50.26 m/s^2
So, the magnitude of the acceleration of the chain link in contact with the rear sprocket is 50.26 m/s^2.
(b) Chain link in contact with neither sprocket:
If the chain link is in the portion between the sprockets, it moves in a straight line without following any circular path. Therefore, there is no centripetal acceleration since there is no circular motion. The magnitude of the acceleration in this case would be zero.
(c) Chain link in contact with the front sprocket:
The radius of the front sprocket is r = 0.10m.
The speed of the chain is v = 1.4 m/s.
Using the formula:
a = (1.4^2) / 0.10
= 1.96 / 0.10
= 19.6 m/s^2
So, the magnitude of the acceleration of the chain link in contact with the front sprocket is 19.6 m/s^2.