Astronaut A can cover 10 meters per minute walking with the heavy shovel. What does
1 answer:
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Answer:
Explanation:
a )
Each blade resembles a rod with its axis positioned near one end.
The moment of inertia for one blade is:
= 1/3 x m l²
where m stands for the mass of the blade
l represents the length of each blade.
Total moment of inertia for 3 blades is:
= 3 x x m l²
ml²
2 )
Details provided include:
m = 5500 kg
l = 45 m
Substituting these values produces:
moment of inertia of one blade:
= 1/3 x 5500 x 45 x 45
= 37.125 x 10⁵ kg.m²
Moment of inertia for 3 blades:
= 3 x 37.125 x 10⁵ kg.m²
= 111.375 x 10⁵ kg.m²
c )
Angular momentum
= I x ω
I denotes the moment of inertia of the turbine
ω symbolizes angular velocity
ω = 2π f
f indicates the rotational frequency of the blades
d )
We have I = 111.375 x 10⁵ kg.m² (Calculated)
f = 11 rpm (revolutions per minute)
= 11 / 60 revolutions per second
ω = 2π f
= 2π x 11 / 60 rad / s
Calculating angular momentum yields
= I x ω
111.375 x 10⁵ kg.m² x 2π x 11 / 60 rad / s
= 128.23 x 10⁵ kgm² s⁻¹.
Answer:
a) τ = i ^ (y - z
) + j ^ (z Fₓ - x
) + k ^ (x
- y Fₓ)
b) τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m
c) α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²
Explanation:
a) The torque can be expressed as
τ = r x F
To tackle this equation, using the determinant approach is the most straightforward method
The resulting expression is
τ = i ^ (y - z
) + j ^ (z Fₓ - x
) + k ^ (x
- y Fₓ)
b) Now let's compute
τ = i ^ (0.075 1.4 -0.035 8.4) + j ^ (0.035 2.8 - 4.07 1.4) + k ^ (4.07 8.4 - 0.075 2.8)
τ = i ^ (- 0.189) + j ^ (-5.6) + k ^ (33,978)
τ = (-0.189i ^ -5.6 j ^ + 33.978k ^) N m
c) To find angular acceleration, we use
τ = I α
α = τ / I
The moment of inertia being a scalar means that only the magnitude of each component changes, orientation remains constant.
α = (-0.189i^ -5.6 j^ + 33.978k^) / 241
α = (-7.8 10⁻⁴ i ^ - 2.3 10⁻² j ^ + 1.4 10⁻¹ k ^) rad / s²