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How do you calculate the kinetic energy of pendulum when it makes an angle of 0 and 30 degree with the vertical which was earlier held horizontally and whose mass and length are 100 g and 1 m?
Wiki User
∙ 16y ago
Assuming the simplest conditions (ie (1) the pendulum pivot is frictionless, (2) no air resistance for the bob's travel, etc...):
This is a problem best solved by considering the situation from an ENERGY standpoint (and not from, say, a velocity and force standpoint).
Under energy conservation (the assumption of "simplest conditions" above gives us this), the total energy (TE) remains constant. The two components contributing to the total energy in this situation are: (1) the kinetic energy (KE) and (2) the potential energy (PE).
So, TE = KE + PE
We know (hopefully) that the (simple) formula for the PE of a mass in earth's gravity is:
PE = mgh where m is the mass, g is the force of earth's gravity and h is the height above SOME (any) reference point.
We also know that the pendulum's KE at the top of its swing (in this problem, the top of the swing is when it's horizontal) is zero.
For simplicity, we'll set the reference point for all height measurements at the bottom of the pendulum's swing (ie one meter below the pendulum's point of attachment to the stand/ceiling/support whatever).
Putting all the info. above together:
At the START, TE = PE + KE = PE = mgh = 0.1 kilograms * 9.8 m/s^2 * 1 meter
= 0.98 Joules
Now at the BOTTOM of its swing, TE = PE + KE,
BUT PE is zero at the bottom of the swing (because h is zero)
AND we just computed TE above as 0.98 Joules
SO, at the swing bottom, KE = TE = 0.98 Joules
At the 30 degree from vertical mark,
Trigonometry tells us that the height, h, at 30 degrees is 1 meter - cos(30)*1 meter
= (1 - 0.8660) meters = 0.1340 meters
SO here the PE is: PE = mgh = 0.1 kilograms * 9.8 m/s^2 * 0.1340 meters
= 0.1313 Joules
AND going back to find the KE, TE = KE + PE gives us 0.98 = KE + 0.1313,
implying that KE = 0.8487 Joules
Wiki User
∙ 16y ago
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