Auto-Closing Gate (Relative Acceleration problem homework)

In summary: To "M" f=ma→\end{equation}mass M will move downwards on the inclined plane with an acceleration of f.
  • #36
The quantities of acceleration of two masses are same right?
 
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  • #37
Zer0 said:
The quantities of acceleration of two masses are same right?
The distance from the central point to the pulley plus the distance from the pulley to the sliding mass is constant. Thus the second derivatives of those distances are equal and opposite. The first of those two is indeed the scalar acceleration of the gate, but the second is not the scalar acceleration of the sliding mass. Rather, it is the acceleration of the mass relative to the gate.
 
  • #38
So if i take " x +(x+y) " woild that be a constant?
 
  • #39
Zer0 said:
So if i take " x +(x+y) " woild that be a constant?
No, you were right to say that |x|+|y| is constant, but ##\ddot {|y|}## is not the magnitude of the acceleration of the sliding mass in the ground frame. It is the magnitude of its acceleration relative to the gate.
 
  • #40
Yeah i just relaized that is there a way to get displacement from middlepoint to the mass and get x (x as mention before) both a constant?
 
  • #41
So'll have the mass's acceleration in relative to ground
 
  • #42
Zer0 said:
So'll have the mass's acceleration in relative to ground
Just add the accelerations vectorially.
amass relative to ground=agate relative to ground+amass relative to gate
 
  • #43
Thank you so much. I just managed to understand relative acceleration much more than i knew earlier. Thank you so much. I've found the same problem which has given the answer and i got it. Thank you.
 
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