Answer:
a) Check Explanation
b) α = - 0.32 rad/s²
Step-by-step explanation:
a) The first drop rises higher than the second drop because the speed of the tire has reduced from what it was during the first turn to a lower value during the second turn. This will most likely be due to how bicycle tires are set up, plenty frictional elements to tamper and reduce the speed of the bike until it is pedalled again.
Note that the speed with which the drops of water rise are both equal to the corresponding tangential speeds of the tire at those points in time. And since the tangential speed of the tire reduces in between turns, the height travelled by the drops too, reduces.
b) To calculate the angular acceleration for the two cases.
The kinetic energy of the drops of water while on the tire is converted to the energy used to attain the respective heights that they attain.
(1/2)mv² = mgh
v = √(2gh)
For the first drop
h₁ = 54.0 cm = 0.54 m
r = 0.381 m
v₁ = √(2gh₁)
v₁ = √(2×9.8×0.54) = 3.253 m/s
w₁ = (v₁/r)
w₁ = (3.253/0.381) = 8.538 rad/s
For the second drop
h₂ = 51.0 cm = 0.51 m
r = 0.381 m
v₂ = √(2gh₂)
v₂ = √(2×9.8×0.51) = 3.162 m/s
w₂ = (v₂/r)
w₂ = (3.162/0.381) = 8.300 rad/s
Using the equations of angular motion,
w₂² = w₁² + 2αθ
θ = 2π
8.3² = 8.538² + 4π (α)
α = -0.32 rad/s²
Negative because it is angular deceleration
Hope this Helps!!!
