The acceleration of a ramp and mass

In summary, the conversation discusses a problem involving a ramp of mass M and a mass m on a frictionless floor. The acceleration of both masses is given by aM= 2mgsinxcosx/M+m(sinx)^2 and am=[(M+m)gsinx]/M+(msinx)^2, but the asker does not understand the inclusion of (msinx)^2 in the equations and asks for clarification. The conversation concludes with the realization that the equations may be incorrect.
  • #1
Luca 123
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[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?
 
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  • #2
Luca 123 said:
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.
 
  • #3
Svein said:
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.
 
  • #4
Luca 123 said:
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:
  • 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
Svein said:
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 don't understand why is (msinx)^2 a mass component of the acceleration
 
  • #6
Luca 123 said:
[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
Exactly. That is what I don't understand about the ans. So is the ans given wrong?
 
  • #8
Luca 123 said:
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
 

FAQ: The acceleration of a ramp and mass

What is the formula for calculating acceleration on a ramp with mass?

The formula for calculating acceleration on a ramp with mass is a = g(sinθ - μcosθ), where a is the acceleration, g is the acceleration due to gravity (9.8 m/s²), θ is the angle of the ramp, and μ is the coefficient of friction between the ramp and the object.

How does the angle of the ramp affect the acceleration?

The angle of the ramp affects the acceleration by changing the magnitude and direction of the net force acting on the object. As the angle increases, the component of the force pulling the object down the ramp decreases, resulting in a smaller acceleration.

What is the relationship between mass and acceleration on a ramp?

The relationship between mass and acceleration on a ramp is inverse. This means that as the mass of the object increases, the acceleration decreases, and vice versa. This is because a larger mass requires a larger force to accelerate it, and the force of gravity remains constant.

How does the coefficient of friction affect the acceleration on a ramp?

The coefficient of friction affects the acceleration on a ramp by creating a resistance force that opposes the motion of the object. As the coefficient of friction increases, the resistance force increases, resulting in a smaller acceleration. This is because the force required to overcome friction also decreases the net force acting on the object.

Can the acceleration on a ramp ever be greater than the acceleration due to gravity?

No, the acceleration on a ramp can never be greater than the acceleration due to gravity. This is because the acceleration due to gravity is a constant value and is always acting on the object, while the acceleration on a ramp is affected by various factors such as the angle of the ramp and the coefficient of friction.

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