Answer:
The moment of inertia is
Explanation:
From the question we are told that
The frequency is
The mass of the pendulum is
The location of the pivot from the center is
Generally the period of the simple harmonic motion is mathematically represented as
Where I is the moment of inertia about the pivot point , so making I the subject of the formula it
=>
But the period of this simple harmonic motion can also be represented mathematically as
substituting values
So
Answer:
The acceleration of the body, a = 2193 m/s²
Explanation:
Given,
The mass of the body, m = 0.3 kg
The force acting on the body, F = 657.9 N
The force acting on an object is proportional to the product of mass and acceleration of the body.
F = m x a
Therefore, the acceleration of the body is
a = F / m
= 657.9 N / 0.3 kg
= 2193 m/s²
Hence, the acceleration of the body, a = 2193 m/s²
Actually, the speed of the earth is the same everywhere, taking the angular speed as the valid measure of the speed
Answer:
7.74m/s
Explanation:
Mass = 35.9g = 0.0359kg
A = 39.5cm = 0.395m
K = 18.4N/m
At equilibrium position, there's total conservation of energy.
Total energy = kinetic energy + potential energy
Total Energy = K.E + P.E
½KA² = ½mv² + ½kx²
½KA² = ½(mv² + kx²)
KA² = mv² + kx²
Collect like terms
KA² - Kx² = mv²
K(A² - x²) = mv²
V² = k/m (A² - x²)
V = √(K/m (A² - x²) )
note x = ½A
V = √(k/m (A² - (½A)²)
V = √(k/m (A² - A²/4))
Resolve the fraction between A.
V = √(¾. K/m. A² )
V = √(¾ * (18.4/0.0359)*(0.395)²)
V = √(0.75 * 512.53 * 0.156)
V = √(59.966)
V = 7.74m/s
Answer:
You will hear the note E₆
Explanation:
We know that:
Your speed = 88m/s
Original frequency = 1,046 Hz
Sound speed = 340 m/s
The Doppler effect says that:
Where:
f = original frequency
f' = new frequency
v = velocity of the sound wave
v0 = your velocity
vs = velocity of the source, in this case, the source is the diva, we assume that she does not move, so vs = 0.
Replacing the values that we know in the equation we have:
This frequency is close to the note E₆ (1,318.5 Hz)