To find the magnitude of the acceleration of a chain link, we can use the following equation:
a = r * α
where a is the acceleration, r is the radius of the sprocket, and α is the angular acceleration.
To find α, we can use the equation:
α = ω^2 / r
where ω is the angular velocity.
Given that the chain moves with a speed of 1.4 m/s around the sprockets and the bike moves at a constant velocity, we can say that the angular velocity is constant.
Therefore, the angular acceleration is zero for both the rear and front sprockets.
Let's calculate the magnitude of the acceleration for each case:
(a) Rear Sprocket:
Since the angular acceleration is zero, we can conclude that the magnitude of the acceleration of the chain link in contact with the rear sprocket is zero.
(b) Neither Sprocket:
Since the chain is not in contact with either sprocket, there is no force or acceleration acting on it. Therefore, the magnitude of the acceleration of the chain link is zero.
(c) Front Sprocket:
Similar to the rear sprocket, the angular acceleration is zero. Thus, the magnitude of the acceleration of the chain link in contact with the front sprocket is zero.
In summary:
(a) The magnitude of the acceleration of a chain link in contact with the rear sprocket is 0 m/s^2.
(b) The magnitude of the acceleration of a chain link not in contact with either sprocket is 0 m/s^2.
(c) The magnitude of the acceleration of a chain link in contact with the front sprocket is 0 m/s^2.