# [SOLVED] how to trajectory and angle for a pendulum?

how to trajectory and angle for a pendulum?

A pendulum is made by tying a 550g ball to a 46 -long string. The pendulum is pulled 21 degrees to one side, then released.

What is the ball's speed at the lowest point of its trajectory?

To what angle does the pendulum swing on the other side?

I have a problem in determing what formula to use.

Any help is appreciated!

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## The Best Answer for how to trajectory and angle for a pendulum?

Energy's conservation:

Uo + Eko = U1 + Ek1

Uo = m g L(1 - cos21°)

Eko = 0

U1 = 0

Ek1 = (1/2) m V^2

Solving:

V = sqr(2 g L(1-cos21°))

L = 46 what ?

On the other side let Ek = 0 and U = Uo ---> @ = 21°

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This is the correct answer for how to trajectory and angle for a pendulum?

owh, its easy girl

u just need to use perpetual law of energy

in the highest point is

Ep = mgh

in the lowest point is

Ek = mv.v/2

in any position

E = mgh + mv.v/2

in the highest position the potential energy is

Ep = m . g . (delta)h

Ep = m . g . (h - h')

Ep = m . g . (h - hcos(x)) x = angle of pendulum pulled at

Epmax=Ekmax

Ep = Ek

m . g . h(1 - cos(x)) = m . v^2/2

g . h (1-cos(x)) = v^2/2

2 . g . h(1 - cos(x)) = v^2

v = sqrt [2 . g . h (1 - cos(x))]

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angular velocity = (max angle).cos(sqrt(g/L)t)

max velocity will be when the cos term = 1

so angular velocity = max angle (in radians)

max linear velocity = (max angle).L

where L=length of string

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+1 vote