What is the Minimum Speed of a Pendulum Released from a Height of 0.400 m?

AI Thread Summary
A pendulum with a 2.0 kg bob released from a height of 0.400 m can be analyzed using energy conservation principles. The kinetic energy at the lowest point equals the gravitational potential energy at the height, leading to the equation mgh = 1/2 mv^2. The correct calculation for maximum speed yields v = sqrt(2gh), resulting in approximately 7.84 m/s before taking the square root, which is 2.8 m/s. The minimum speed of the pendulum occurs at the highest point of the swing, where it is effectively zero. Therefore, the minimum speed is indeed zero when the pendulum is released from rest.
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A pendulum, with a 2.0 kg bob, is released from a height of 0.400 m and allowed to swing freely. Determine its minimum speed.
I got:
E_grav = E_kin
--> mgh = 1/2 mv^2
--> v = sqrt (2gh)
--> v = sqrt (2*9.8*.4)
--> v = 7.84 m/s
Is that right? It seems weird; so please tell me if I'm right or wrong. If wrong, please show me what I did wrong. Thanks a lot!
 
Last edited:
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Your method is correct, but you forgot to take the square root. (I assume you were asked to find the maximum speed, not the minimum.)
 
Doc Al said:
Your method is correct, but you forgot to take the square root. (I assume you were asked to find the maximum speed, not the minimum.)
Ohh, I forgot that. sqrt (7.84) = 2.8
--> Isn't that the minimum speed?
if that's not the minimum speed, then...Hmm, how to find minimum speed..? Could the minimum speed of the pendulum be "0"? Or should we determine the minimum speed at exactly the highest point, when it gets its best gravitational energy?
 
Last edited:
IB said:
Could the minimum speed of the pendulum be "0"?
Of course.
Or should we determine the minimum speed at exactly the highest point, when it gets its best gravitational energy?
Assuming that its being "released" means that it starts at that point with zero speed, that's as high as it will get.
 
Ahh, I see now. Thanks a lot, Doc Al. :)
 

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