The acceleration of a ramp and mass

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I have a qns whereby a ramp of mass M rests on a frictionless floor and a mass m rests on the ramp, with no friction in between the mass and ramp. I need to find the acceleration of ramp M and mass m.
I have the answers but I dont really understand them.
aM= 2mgsinxcosx/M+m(sinx)^2 . I dont understand why is there a msin^2 term here
am=[(M+m)gsinx]/M+(msinx)^2 . Again I dont understand why is there a msin^2 and how does M factor into the acceleration.
Can someone pls teach mr how to get the ans?
 
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  • #2
Svein
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aM= 2mgsinxcosx/M+m(sinx)^2 . I dont understand why is there a msin^2 term here
am=[(M+m)gsinx]/M+(msinx)^2 . Again I dont understand why is there a msin^2 and how does M factor into the acceleration.
Something is very wrong here.
Dimensional analysis:
  • aM is force.
  • 2mgsinxcosx/M is acceleration.
  • m(sinx)^2 is mass.
  • am is force.
  • [(M+m)gsinx]/M is acceleration.
  • (msinx)^2 is mass.
 
  • #3
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Something is very wrong here.
Dimensional analysis:
  • aM is force.
  • 2mgsinxcosx/M is acceleration.
  • m(sinx)^2 is mass.
  • am is force.
  • [(M+m)gsinx]/M is acceleration.
  • (msinx)^2 is mass.
Oops Im sorry by aM I mean acceleration of M and by am I mean acceleration of m.
 
  • #4
Svein
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Oops Im sorry by aM I mean acceleration of M and by am I mean acceleration of m.
You are still in trouble. According to your statement now:
  • aM is acceleration.
  • 2mgsinxcosx/M is acceleration.
  • m(sinx)^2 is mass.
  • am is acceleration.
  • [(M+m)gsinx]/M is acceleration.
  • (msinx)^2 is mass2.
 
  • #5
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You are still in trouble. According to your statement now:
  • aM is acceleration.
  • 2mgsinxcosx/M is acceleration.
  • m(sinx)^2 is mass.
  • am is acceleration.
  • [(M+m)gsinx]/M is acceleration.
  • (msinx)^2 is mass2.
I am very sorry. I should have made this clearer.
Acceleration of M=(mgsinxcosx)/[M+(msinx)^2]
Acceleration of m=[(M+m)gsinx]/[M+(msinx)^2]
It should be correct now
I dont understand why is (msinx)^2 a mass component of the acceleration
 
  • #6
Svein
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[M+(msinx)^2]
You are still wrong. If M and m are masses, (msinx)^2 is mass squared, and you cannot add mass and mass2 (whatever that might be).
 
  • #7
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Exactly. That is what I dont understand about the ans. So is the ans given wrong?
 

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