Physics, 05.10.2019 03:00 starbae1084

Apendulum of length 0.350 m starts from rest at a maximum displacement of 10o from the equilibrium position…

a)what is the max speed of the pendulum?

b)at what time will the pendulum be located at an angle of displacement of 8o?

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Answer from: lisa123465

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

Answer from: Quest

12000j is work done

Answer from: Quest

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

$x(t)=ax(x-6)$

where $a$ is unknown. because the position is parabolic, there is symmetry about the midpoint at $t=3$ , and we know that

$x(3)=10\implies -9a=10\implies a=-\dfrac{10}9$

so that the position function is

$x(t)=-\dfrac{10}9x(x-6)$

which means the velocity is

$v(t)=\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{20}9x+\dfrac{60}9$

then the total distance traveled is

$\displaystyle\int_{t=0}^{t=6}|v(t)|\,\mathrm dt=\left\{\int_{t-0}^{t=3}-\int_{t=3}^{t=6}\right\}v(t)\,\mathrm dt=20$

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at $x=0$ and ends at $x=0$ , so its displacement is 0.

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