F=ma proportional reasoning

5.98e24

1. 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.

2. Homework Equations
F = ma
a = F/m

3. 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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SammyS

Staff Emeritus
Homework Helper
Gold Member
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?

PhanthomJay

Homework Helper
Gold Member
1. 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.

2. Homework Equations
F = ma
a = F/m

3. 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? 5.98e24

Ah, I see now.. forgot to consider the doubling of the forces.

Thank you both!

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