Answer:
Acceleration(a) = 0.75 m/s²
Explanation:
Given:
Force(F) = 3 N
Mass of object(m) = 4 kg
Find:
Acceleration(a)
Computation:
Force(F) = ma
3 = (4)(a)
Acceleration(a) = 3/4
Acceleration(a) = 0.75 m/s²
Referencing the diagram below, we can deduce from the geometry that x = 2.5 - 0.55 = 1.95 m, leading to cos θ = 1.95/2.5 = 0.78. Therefore, θ = cos⁻¹ 0.78 = 38.74°. According to the free body diagram, the tension in the chain measures 450 N. Here, F denotes the centripetal force and W signifies Dee's weight. The tension's components are as follows: Horizontal component = 450 sin(38.74°) = 281.6 N, directed to the left, and Vertical component = 450 cos(38.74°) = 351.0 N, directed upward. Answers: Horizontal: 281.6, directed left. Vertical: 351.0 N, directed upward.
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
Answer:
All three pendulums will have the same angular frequencies.
Explanation:
For a simple pendulum, the time period using the approximation 
is expressed as:
The angular frequency 
is defined as
Since the angular frequency remains unaffected by the initial angle (valid strictly for small angle approximations), we deduce that the angular frequencies of the three pendulums are identical.
Displacement stabilizes over time. It is known that exponentials raised to infinity approach zero, hence the system model will yield as time approaches infinity, resulting in 4x'' + e−0.1tx = 0. As time approaches infinity, we deduce that 4x'' equals zero. Consequently, upon integrating, we derive 4x' = c, and further integration leads to the conclusion 4x = cx + d.
