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:
When an object is balanced, about a pivot, the total clockwise moment must be equal to the total anticlockwise moment about that pivot.
Hope that helps.
Answer:
the charge per unit area on the plastic sheet is - 3.23 x 10⁻⁷ C/m²
Explanation:
given information:
styrofoam mass, m = 16 g = 0.016 kg
net charge, q = - 8.6 μC
to calculate the charge per unit area on the plastic sheet, we can use the following equation:
where
the force between the electric field
m = mass
g = gravitational force
where
q = charge
E = electric field
and
E = σ/2ε₀
where
ε₀ = permitivity
thus
mg = qσ/2ε₀
σ = (2mg ε₀)/q
= 2 (0.016) (9.8) (8.85 x 10⁻¹²)/( - 8.6 x 10⁻⁶)
= - 3.23 x 10⁻⁷ C/m²
Explanation:
Sound travels faster In solids than liquid than gases
Speed of sound is highest in solids, and higher in liquids and slower in gases. Example- Sound travels in air with the speed of 330 m/s, In steel it travels with a speed of 5920 m/s, In liquids it travels with a speed of 5000 m/s.
Hope this helps you
a)You throw a stone horizontally at a speed of 5.0 m/s from the top of a cliff that is 78.4 m high.
from above statement we got
height = 78.4 m
since the ball is thrown, so its vertical velocity would be zero
u = 0
taking g = 9.8m/s^2
now, using the equation of motion
h = ut + gt^2/2
now putting all the values in it
we got ,
78.4 = 9.8 * t^2/ 2
by solving we got,
t = 4 sec
b) now, since along the horizontal , no force acting and accelaration is zero so
R = ut , R is RANGE
R = 5 * 4
range = 20 m
c) vertical components of the stone’s velocity just before it hits the ground = v sin θ =
horizontal components of the stone’s velocity just before it hits the ground = v cos θ
To know more about velocity visit :
brainly.com/question/18084516
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