Answer:
v = 12.52 [m/s]
Explanation:
To solve this problem we must use the energy conservation theorem. Which tells us that potential energy is transformed into kinetic energy or vice versa. This is more clearly as the potential energy decreases the kinetic energy increases.
Ep = Ek
where:
Ep = potential energy [J] (units of joules]
Ek = kinetic energy [J]
Ep = m*g*h
where:
m = mass of the rock = 45 [g] = 0.045 [kg]
g = gravity acceleration = 9.81 [m/s²]
h = elevation = (20 - 12) = 8 [m]
Ek = 0.5*m*v²
where:
v = velocity [m/s]
The reference level of potential energy is taken as the ground level, at this level the potential energy is zero, i.e. all potential energy has been transformed into kinetic energy. In such a way that when the Rock has fallen 12 [m] it is located 8 [m] from the ground level.
m*g*h = 0.5*m*v²
v² = (g*h)/0.5
v = √(9.81*8)/0.5
v = 12.52 [m/s]
Solution
x(t) = 8 cos t, x(5π/6)= 8 cos(<span>5π/6)
</span>cos(5π/6)=cos(3π/6 + 2π/6 )=cos(π/3 +π/2)= - sin π/3 (cos (x+<span>π/2)= -sinx)
</span>x(t) = -8sin <span>π/3 = - 4 .sqrt3
</span>v(t) = -8sint = -8sin (π/3 +<span>π/2)= -8 cosπ/3 </span>(sin (x+π/2)= cosx)
v(t) =<span> -8 cosπ/3 = -8/2= - 4
</span>a(5π/6) = - 8cost = -(- sin π/3)= 4 .<span>sqrt3
</span>a(5π/6) = 4 .<span>sqrt3</span>
Answer:
(A) the angular acceleration of the blades is 13.33 m/s.
Explanation:
Given;
moment of inertia of a blade, I = 0.2 kgm²
net torque exerted on fan blades, ∑τ = 8Nm
Torque is given as product of moment of inertia and angular acceleration;
τ = Iα
where;
α is the angular acceleration
Since there are three blades of the ceiling fan, the net torque is given as;
∑τ = (3I)α
∑τ = 3Iα
α = ∑τ / 3I
α = (8) / (3 x 0.2)
α = 13.33 m/s
Therefore, the angular acceleration of the blades is 13.33 m/s.
Answer:
f=171.43Hz
Explanation:
Wave frequency is the number of waves that pass a fixed point in a given amount of time.
The frequency formula is: f=v÷λ, where <em>v</em> is the velocity and <em>λ</em> is the wavelength.
Then replacing with the data of the problem,
f=
f=171.43
f=171.43 Hz (because 
, 1 hertz equals 1 wave passing a fixed point in 1 second).
