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Force moving a pendulum (hanging object)

ÀÛ¼ºÀÚ Uploader : dutyfree ÀÛ¼ºÀÏ Upload Date: 2018-08-10º¯°æÀÏ Update Date: 2018-08-10Á¶È¸¼ö View : 331

When a pendulum is hanging at the angle  ¥è with respect to the horizontal, as shown in figure,
the pulling force -Px is calculated as follows.

With the pendulum/object weight being P,
vertical force Py is equal to P.
The tension force T on the string has the following relationship.
(For convinience, calculate the magnitude first and consider thr direction.)

T*sin¥è = Py, T*cos¥è = Px, T = (Px^2 + Py^2)^(1/2)

Then,

Px = (T^2 - Py^2)^(1/2)
 = {Py^2(1-(sin¥è)^2)/(sin¥è)^2}^(1/2)
 = Py*cos¥è/sin¥è = P*cos¥è/sin¥è

-Px is the force having the same magnitude as Px but in the opposite direction.

*** Âü°í¹®Çå[References] ***

Px = P*cos(¥è)/sin(¥è)
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