The acceleration of a ramp and mass

[Luca 123]

[Mod note: Thread moved from New Member Introductions, so no template]

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 don't really understand them.
aM= 2mgsinxcosx/M+m(sinx)^2 . I don't understand why is there a msin^2 term here
am=[(M+m)gsinx]/M+(msinx)^2 . Again I don't 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?

 

[Svein]

aM= 2mgsinxcosx/M+m(sinx)^2 . I don't understand why is there a msin^2 term here
am=[(M+m)gsinx]/M+(msinx)^2 . Again I don't 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.

 

[Luca 123]

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 I am sorry by aM I mean acceleration of M and by am I mean acceleration of m.

 

[Svein]

Oops I am 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:

• a_M is acceleration.
• 2mgsinxcosx/M is acceleration.
• m(sinx)^2 is mass.

• a_m is acceleration.
• [(M+m)gsinx]/M is acceleration.
• (msinx)^2 is mass².

 

[Luca 123]

You are still in trouble. According to your statement now:

• a_M is acceleration.
• 2mgsinxcosx/M is acceleration.
• m(sinx)^2 is mass.

• a_m 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 don't understand why is (msinx)^2 a mass component of the acceleration

 

[Svein]

[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).

 

[Luca 123]

Exactly. That is what I don't understand about the ans. So is the ans given wrong?

 

[NascentOxygen]

I have a qns whereby a ramp of mass M rests on a frictionless floor

Homework questions belong in the homework forum. Very few people see posts in this Introduction forum.
https://www.physicsforums.com/threads/projectile-motion.795148/#post-4993780