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.
Direction!
Velocity is a vector quantity and speed is a scalar quantity. Vector quantities includes both magnitude and direction, while scalar quantities only have magnitude. :)
Heat energy and thermal energy are the same because heat energy is thermal energy. Also thermal energy and temperature are the same because temperature is measuring heat in degrees Celsius or degrees Fahrenheit. Hope this helps!
Answer:
relates the electric field at points on a closed surface to the net charge enclosed by that surface.
Explanation:
Gauss Law states that overall electric flux of a closed surface is equivalent right to charge enclosed which is divided by the permittivity. In other words Gauss Law stress that
net electric flux that pass through an hypothetical closed surface is equivalent to overall electric charge present within that closed surface.
The Gauss law can be expressed mathematically as
ϕ = (Q/ϵ0)
Q = total charge within the surface,
ε0 = the electric constant
Answer:
Explanation:
From the question we are told that:
Initial Speed 
Time 
Angle 
Generally the Newton's equation for motion is mathematically given by
