# 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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Svein
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.

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.

Svein
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.

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

Svein