Calculating Amplitude of Brick Separation from Piston with SHM

In summary, the brick on top of a vertically moving piston with simple harmonic motion of period 1.08 s will fly off when the acceleration exceeds the gravitational acceleration, regardless of whether the piston is moving up or down. To calculate the amplitude at which the brick will separate from the piston, the angular frequency can be found using the period, and then the derivative of the velocity equation can be used to solve for the amplitude. However, care must be taken to set the time and phase properly. This problem is complicated by the lack of consideration for external factors such as air resistance.
  • #1
nazarip
16
0
A brick is resting atop a piston that is moving vertically with simple harmonic motion of period 1.08 s. At what amplitude will the brick separate from the piston?

I came across this question reviewing for my test next Thursday. Anyway, I can calculate the angular frequency using the period, but I am not sure what to do after that. Any help is appreciated.
 
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  • #2
What happens when the downward acceleration exceeds g? :-)
 
  • #3
I would say that the brick would fly off, but I would have guessed that the upward acceleration would have had to exceed g. Can you explain please?
 
  • #4
nazarip said:
I would say that the brick would fly off, but I would have guessed that the upward acceleration would have had to exceed g. Can you explain please?

That depends on how you start the oscillation! In either case, what happens if the acceleration exceeds g? Do you think the answer will be different in those two cases?
 
  • #5
So if the acceleration in the direction of the orcillation exceeds g the brick will fly off...? I tried taking the derivative of the velocity equation -wAsin(wt+phi) but I got a wrong answer. This question is driving me nuts...
 
  • #6
I'm guessing there's a problem with your calculation. Why don't you show what you've done?
 
  • #7
ok here is what I did:

v=-wAsin(wt+phi)
a=dv/dt=-Aw^2cos(wt+phi)

I set phi=0 (maybe went wrong here?) and...wait a second, hmm. Ok, I had to set t=0 also, then I just solve for A. Nothing like solving a problem at 2:02 am. Thanks for the patience Tide.
 
  • #8
A funny thing to note is that in both cases (going up & down) what we're looking for is the _downwards_ acceleration to exceed g. The going upwards case is somewhat less intuitive at first than the going downwards one (were the piston disconnects because it's just 'running away' too fast), but it works like this: the brick will stay with the piston while the piston moves up to the equilibrium (since the piston will be constantly accelerating and 'pushing' the brick with it) and then it'll stay with the piston until the piston's acceleration reaches -g (until it's decelerating at a rate of g), when it'll be the brick running away from the piston, not the other way around.

(:D I'm as always bothered by the absence of the effects of air resistance and such in these problems)
 

FAQ: Calculating Amplitude of Brick Separation from Piston with SHM

What is SHM?

SHM stands for Simple Harmonic Motion. It is a type of periodic motion where the restoring force is directly proportional to the displacement from the equilibrium position. This means that the object will oscillate back and forth around the equilibrium position with a constant period.

How is the amplitude of brick separation calculated?

The amplitude of brick separation is calculated by measuring the maximum distance between the brick and the piston during the oscillation. This distance is then divided by 2 to get the amplitude.

What are the factors that affect the amplitude of brick separation in SHM?

The amplitude of brick separation in SHM can be affected by the mass of the brick, the spring constant of the system, and the initial displacement of the brick from the equilibrium position. These factors can be manipulated to change the amplitude of the oscillation.

How does the amplitude of brick separation relate to the energy of the system?

The amplitude of brick separation is directly proportional to the energy of the system. This means that as the amplitude increases, the energy of the system also increases. This is because the amplitude is a measure of the maximum displacement of the object, which is directly related to the maximum potential and kinetic energy of the system.

Can the amplitude of brick separation be used to determine the frequency of the system?

No, the amplitude of brick separation cannot be used to determine the frequency of the system. The frequency of SHM is determined by the mass of the object and the spring constant of the system, not the amplitude. However, the amplitude can be used to calculate the period of the oscillation, which is the inverse of the frequency.

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