How Does Doubling Mass and Force Affect Acceleration?

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Doubling the mass of an object while also doubling the force applied results in the same acceleration as the original object. Initially, the object accelerates at 2 m/s² with two rubber bands. When the mass is doubled and four rubber bands are used, the acceleration remains 2 m/s² because the increased force compensates for the increased mass. The key takeaway is that acceleration is directly proportional to force and inversely proportional to mass. Understanding this relationship clarifies how changes in mass and force affect acceleration.
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Homework Statement


Two rubber bands stretched to the standard length cause an object to accelerate at 2 m/s^2. Suppose another object with twice the mass is pulled by four rubber bands stretched to the standard length. The acceleration of this second object is: ??

The correct answer is 2m/s^2.


Homework Equations


F = ma
a = F/m


The Attempt at a Solution


a = F/m
Therefore, a is inversely proportional to m.

a1/a2 = m2/m1

Second mass is twice the first mass.
a1/a2 = 2m/m

m's cancel out, leaving:
a1/a2 =2

Isolate a2:
a2 = a1/2

That would make my acceleration of the second object 1 m/s^2, not 2 m/s^2. Did I miss something?
 
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If you double the force and double the mass, how will acceleration be affected?

Perhaps do this in steps.

1. Double the force, by using 4 rubber bands, keeping the original mass. What is the acceleration now?

2. Using the same force as in (1.), 4 rubber bands, now double the mass. What is the acceleration now?
 
5.98e24 said:

Homework Statement


Two rubber bands stretched to the standard length cause an object to accelerate at 2 m/s^2. Suppose another object with twice the mass is pulled by four rubber bands stretched to the standard length. The acceleration of this second object is: ??

The correct answer is 2m/s^2.


Homework Equations


F = ma
a = F/m


The Attempt at a Solution


a = F/m
Therefore, a is inversely proportional to m.

a1/a2 = m2/m1

Second mass is twice the first mass.
a1/a2 = 2m/m

m's cancel out, leaving:
a1/a2 =2

Isolate a2:
a2 = a1/2

That would make my acceleration of the second object 1 m/s^2, not 2 m/s^2. Did I miss something?
You assumed the forces were the same when the mass doubled, which cuts the acceleration in half, as you noted, however, it is given that the forces were also doubled when the mass doubled, so doubling the force now doubles the halved acceleration back to the same acceleration of the first object. Do you follow, or does this double your trouble? :wink:
 
Ah, I see now.. forgot to consider the doubling of the forces.

Thank you both!
 
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