Finding Acceleration: Mass Ratio & Force Applied to Particles

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A force applied to particle m1 results in an acceleration of 20 m/s², while the same force applied to particle m2 yields an acceleration of 30 m/s². The relationship between mass and acceleration indicates that acceleration is directly proportional to force and inversely proportional to mass. To find the acceleration of the combined particles when glued together, the equation F = ma can be used for each particle to establish a relationship among their masses and accelerations. The initial attempt to use the ratio m2/m1 = a2/a1 is deemed incorrect without specific mass values. The correct approach involves applying the same force to both particles and calculating the resulting acceleration based on their combined mass.
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Homework Statement


A certain Force applied to a particle of m1 gives it an acceleration of 20m/s2. The same Force applied to a particle of m2 gives it an acceleration of 30m/s2. If the two particles are glued together and the same force is applied to the combination, find the acceleration.

Homework Equations


F=ma

The Attempt at a Solution


m2/m1=a2/a1 would be helpful if a mass was given. No idea how to set up this problem.
 
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SalsaOnMyTaco said:

Homework Statement


A certain Force applied to a particle of m1 gives it an acceleration of 20m/s2. The same Force applied to a particle of m2 gives it an acceleration of 30m/s2. If the two particles are glued together and the same force is applied to the combination, find the acceleration.

Homework Equations


F=ma

The Attempt at a Solution


m2/m1=a2/a1 would be helpful if a mass was given. No idea how to set up this problem.
Have you learned that acceleration is directly proportional to force, and inversely proportional to mass ?
 
Yes, when mass increases, acceleration decreases/Mass decreases, acceleration increases.
 
SalsaOnMyTaco said:
Yes, when mass increases, acceleration decreases/Mass decreases, acceleration increases.

So, m2/m1=a2/a1 is incorrect.

Why not use F = ma for each particle:

The force is the same for each particle. That should give you a correct relation among m2, m1, a2, and a1 .
 
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