Answer:
a)106.48 x 10⁵ kg.m²
b)144.97 x 10⁵ kgm² s⁻¹
Explanation:
a)Given
m = 5500 kg
l = 44 m
The moment of inertia for one blade
= 1/3 x m l²
where m denotes the mass of the blade
l represents the length of each blade.
Substituting the necessary values, the moment of inertia for one blade is
= 1/3 x 5500 x 44²
= 35.49 x 10⁵ kg.m²
Total moment of inertia for 3 blades
= 3 x 35.49 x 10⁵ kg.m²
= 106.48 x 10⁵ kg.m²
b) The angular momentum 'L' is calculated using
L = x ω
where,
= the moment of inertia of the turbine i.e 106.48 x 10⁵ kg.m²
ω= angular velocity =2π f
f represents the frequency of rotation of the blade i.e 13 rpm
f = 13 rpm=>= 13 / 60 revolutions per second
ω = 2π f => 2π x 13 / 60 rad / s
L= x ω =>106.48 x 10⁵ x 2π x 13 / 60
= 144.97 x 10⁵ kgm² s⁻¹
Let T be the force exerted on the rope by her. This force induces tension in the rope, which exerts an upward force on the crates, while the weight of the crate pulls downward. Thus, the net force acting on the crate can be expressed as mg - T, acting in the downward direction. According to Newton's law, we can set up the equation: mg - T = ma. Given that a = 0 (the speed remains constant), this simplifies our equation to mg - T = 0, which leads to T = mg. Therefore, T = 25 x 9.8 = 245 N, indicating that the force she needs to apply is 245 N.
The question lacks complete details or specifications. Here is the missing information: 1. impossible to establish 2. half of Isaac's 3. identical to Isaac's 4. double Isaac's The angular velocity of Feng will match that of Isaac. Thus, the correct choice is option 3.
