Answer:
0.191 s
Explanation:
The distance from the center of the cube to the upper corner is r = d/√2.
When the cube is rotated an angle θ, the spring is stretched a distance of r sin θ. The new vertical distance from the center to the corner is r cos θ.
Sum of the torques:
∑τ = Iα
Fr cos θ = Iα
(k r sin θ) r cos θ = Iα
kr² sin θ cos θ = Iα
k (d²/2) sin θ cos θ = Iα
For a cube rotating about its center, I = ⅙ md².
k (d²/2) sin θ cos θ = ⅙ md² α
3k sin θ cos θ = mα
3/2 k sin(2θ) = mα
For small values of θ, sin θ ≈ θ.
3/2 k (2θ) = mα
α = (3k/m) θ
d²θ/dt² = (3k/m) θ
For this differential equation, the coefficient is the square of the angular frequency, ω².
ω² = 3k/m
ω = √(3k/m)
The period is:
T = 2π / ω
T = 2π √(m/(3k))
Given m = 2.50 kg and k = 900 N/m:
T = 2π √(2.50 kg / (3 × 900 N/m))
T = 0.191 s
The period is 0.191 seconds.
The distance from the horizontal top surface of the cube to the water level is "6.282 cm".
<h3>What is Archimedes' principle?</h3>
According to Archimedes' principle, the weight of the fluid that the body displaces is equal to the upward buoyant force that is applied to a body submerged in a fluid, whether fully or partially. The Archimedes' principle is a fundamental physical law in fluid mechanics. It was created by Syracuse's Archimedes.
According to Archimedes' principle, a body submerged in a fluid experiences an upward force proportional to the weight of the fluid that has been displaced. One of the prerequisites for equilibrium is this. We believe that the buoyancy force, also known as the centre of buoyancy, is situated in the middle of the submerged hull.
From Archimedes' principle, we get
=11.72cm
So,
The distance from horizontal top to the water level will be:
=18-11.72
=6.282cm
To learn more about Archimedes' principle refer to:
brainly.com/question/1155674
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The significant figures also known as the significant digits or precision of a number written in positional notation are digits that carry meaningful contributions to its measurements
Answer: 45000kgm/s
Explanation:
Given that:
Mass of speed boat = 1500 kg
Velocity of speedboat = 30 m/s
Speed boats Momentum = ?
The Speed boat momentum is the product of its mass and the velocity by which it moves. Momentum is a vector quantity and measured in kgm/s
i.e Momentum = mass x velocity
= 1500 kg x 30 m/s
= 45000kgm/s
Thus, the speed boats momentum is 45000kgm/s
