Respuesta :
Answer:
a. T = 119.68 N.m
b. r = 140 rev
Explanation:
first we know that:
∑T = Iα
where ∑T is the sumatory of the torques, I is the moment of inertia and α is the angular aceleration.
so, if the prop goes from rest to 400 rpm in 14 seconds we can find the α of the system:
1. change the 400 rpm to radians as:
W = 400*2π/60
W = 41.888 rad /s
2. Then, using the next equation, we find the α as:
w = αt
solving for α
α = [tex]\frac{w}{t}[/tex]
note: t is the time, so:
α = [tex]\frac{41.888}{14}[/tex]
α = 2.992 rad/s^2
Now using the first equation, we get:
T = Iα
T = 40(2.992)
T = 119.68 N.m
On the other hand, for know the the number of revolutions turned as the prop achieves operating speed, we use the following equation:
θ = wt +[tex]\frac{1}{2}[/tex]α[tex]t^2[/tex]
Where w = 41.888 rad /s, α = 2.992 rad/s^2, t is the time and θ give as the number of radians that the prop made in the fisrt 14 seconds, so:
θ = (41.888)(14)+[tex]\frac{1}{2}[/tex](2.992)(14[tex])^2[/tex]
θ = 879.648 rad
and that divided by 2π give us the number of revolutions r, so:
r = 140 rev
