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.
Answer: Well first of all, for an Atom to be neutral, it shall have an equal number of the protons and the neutrons. So given that, the protons are able to be positively charged and since the electrons are negatively charged (Protons and Electrons are completely different from each other) then that means the Algebric are aggregated of charges because it equal to zero. So overall, the 'neutral atom' has to be neutral, and how? Protons must equal the number of electrons or else it wouldn't be considered neutral.
Hopefully this helps you very much!! :-) Have a great daayy!
Answer:
F_A = 8 F_B
Explanation:
The force exerted by the planet on each moon is given by the law of universal gravitation
F = 
where M is the mass of the planet, m the mass of the moon and r the distance between its centers
let's apply this equation to our case
Moon A
the distance between the planet and the moon A is r and the mass of the moon is 2m
F_A = G \frac{2m M}{r^{2} }
Moon B
F_B = G \frac{m M}{(2r)^{2} }
F_B = G \frac{m M}{4 r^{2} }
the relationship between these forces is
F_B / F_A = 
= 1/8
F_A = 8 F_B
Answer:
90 meters
Explanation:
Given:
x₀ = 0 m
v₀ = 0 m/s
v = 30 m/s
t = 6 s
Find:
x
x = x₀ + ½ (v + v₀)t
x = 0 + ½ (30 + 0)(6)
x = 90
The car travels 90 meters.
Answer:
v = 1 i ^ m / s, v = 1 m / s
Explanation:
In this problem we show the difference between vectors and scalars.
The average speed is
v = Δx / Δt
The bold are vectors
Δx = 20-10 = 10 i^ m
v = 10/10
v = 1 i ^ m / s
the unit vector indicates that the velocity is on the x-axis
The average speed is
v =Δx / Δt
v = 10/10
v = 1 m / s
in this case we have a scalar
