F=ma proportional reasoning

In summary, the acceleration of the second object with twice the mass is 2 m/s^2, as the forces acting on it are also doubled. This is in accordance with the equation F = ma, where acceleration is directly proportional to the force and inversely proportional to the mass.
  • #1
5.98e24
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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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  • #2
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?
 
  • #3
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:
 
  • #4
Ah, I see now.. forgot to consider the doubling of the forces.

Thank you both!
 
  • #5


Your reasoning is correct. However, in this scenario, the second object is being pulled by four rubber bands instead of two, which means the force acting on it is twice as much as the force acting on the first object. This is because the force is directly proportional to the number of rubber bands (assuming they are all stretched to the same standard length). So, using the equation F=ma, the acceleration of the second object would be:

a2 = F/m2 = (2F)/(2m) = F/m = a1/2 = 2m/s^2

In other words, the force acting on the second object is twice as much as the force acting on the first object, but since the mass is also twice as much, the acceleration remains the same. This is an example of how proportional reasoning can be applied to understand and solve problems in physics.
 

1. What is F=ma proportional reasoning?

F=ma proportional reasoning is a fundamental concept in physics that describes the relationship between force, mass, and acceleration. It states that the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.

2. How is F=ma proportional reasoning used in science?

F=ma proportional reasoning is used in many scientific fields, such as mechanics, engineering, and astronomy. It is used to calculate the force and acceleration of objects, predict the motion of objects, and understand the behavior of systems.

3. Can you provide an example of F=ma proportional reasoning?

One example is when a car is accelerating on a flat road. The force of the engine (F) is directly proportional to the mass of the car (m) and the acceleration (a). This means that if the force increases, the car's acceleration will also increase, but if the mass increases, the acceleration will decrease.

4. What are the units for F=ma proportional reasoning?

The units for force, mass, and acceleration in F=ma proportional reasoning are typically Newtons (N), kilograms (kg), and meters per second squared (m/s^2), respectively. However, other units can also be used as long as they are consistent.

5. Why is F=ma proportional reasoning important in understanding the world around us?

F=ma proportional reasoning is important because it helps us understand the fundamental principles of motion and how objects interact with each other. It allows us to make predictions and calculations about real-world situations, such as the trajectory of a projectile or the behavior of a moving vehicle.

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