Respuesta :
Answer:
maximium speed V = 0.32 m / s
Explanation:
The pendulum for small angles is a simple harmonic movement, in which the period is independent of the given angle and is described by the equation
w = R l / g
a) To calculate the velocity write the energy at two points, higher and lowest
E1 = U = mg h
E1= ½ m v²
How energy is conserved
E1 = E2
mgh = 1/2 m v²
V = √2gh
Let's calculate the height by trigonometry
cos θ = CA / H
cos 10 = CA /0.35
CA = 0.35 cos 10
CA = 0.3447 m
The height that has risen Esla total height (0.35 m) minus this side
H = L - CA
H = 0.35 - 0.3447
H = 0.0053 m
Let's calculate the speed
V = √(2 9.8 0.0053)
V = 0.32 m / s
Second part
It is requested to find the time for a certain angle, for this we use the equation of the simple harmonic movement
Y (t) = A cos (wt)
Where A is the amplitude of the pendulum
A = L - L cos T
A = 0.35 (1- cos 10)
A = 0.00532 m
w = √g/L
w = √ (9.8 / 0.35)
w = 5.29 s⁻¹
We write the equation
Y = 0.00532 cos (5.29 t)
To find time, let's use trigonometry to calculate the height of 8º
Cos 8 = CA1 / L
CA1 = L cos 8
CA1 = 0.35 cos 8
CA1 = 0.34659 m
the height raised
Y = L -CA1
Y = 0.35 -0.34659
Y = 0.003406 m
We substitute in the equation of motion and clear time
Y = 0.00532 cos (5.29 t)
0.003406 = 0.00532 cos (5.29 t)
cos (5.29 t) = 0.003406 / 0.00532 = 0.640
5.29 t = cos⁻¹ 0.640
the angle in radians
t =0.876 / 5.29
t = 0.166 s
