Effect of doubling a mass Newton's law of universal gravitation

[Tiven white]

Homework Statement

Particle A having mass mA is placed at a fixed distance r from particle B which has twice the mass of particle A. Which of the following statements will be true?
Select one:
a. The magnitude of the force on A will be twice the magnitude of the force on B.
b. The magnitude of B's acceleration will be twice the magnitude of A's acceleration.
c. The magnitude of the force on B will be twice the magnitude of the force on A.
d. The acceleration of B will be equal and opposite to the acceleration of A
e. The magnitude of A's acceleration will be twice the magnitude of B's acceleration.

Homework Equations

F = (G*MA*MB)/(r^2)
Newtons law of gravitation.

The Attempt at a Solution

i used trial values for G, MA, MB and r
eg 1,1,1,2 respectively then satisfied the initial condition by varying the mass of B to be twice that of A and found F will be twice its value when the mass of be is doubled. so i know the force is doubled. but the wording of the solutions is a bit confusing any help would be appreciated.

 

[PhanthomJay]

Homework Statement

Particle A having mass mA is placed at a fixed distance r from particle B which has twice the mass of particle A. Which of the following statements will be true?
Select one:
a. The magnitude of the force on A will be twice the magnitude of the force on B.
b. The magnitude of B's acceleration will be twice the magnitude of A's acceleration.
c. The magnitude of the force on B will be twice the magnitude of the force on A.
d. The acceleration of B will be equal and opposite to the acceleration of A
e. The magnitude of A's acceleration will be twice the magnitude of B's acceleration.

Homework Equations

F = (G*MA*MB)/(r^2)
Newtons law of gravitation.

The Attempt at a Solution

i used trial values for G, MA, MB and r
eg 1,1,1,2 respectively then satisfied the initial condition by varying the mass of B to be twice that of A and found F will be twice its value when the mass of be is doubled. so i know the force is doubled. but the wording of the solutions is a bit confusing any help would be appreciated.

if the mass of one object is twice the other, then the force between the two is double the force that would exist if the masses were equal . But, the problem is asking about the force of A on B compared to the force of B on A. Is one double the other?

 

[lightgrav]

there is only one situation here, it is not a before/after comparison.
Calculate the Force applied to A (by B), and then calculate the Force applied to B (by A).
If they're the same strength (but opposite direction,of course), then a) and c) are out.
But what about A's acceleration? What about B's acceleration? Are they the same? (no)

 

[Tiven white]

So I worked out the force on both bodies and it turns out both receive an equal and opposite force of 2F now equating the force the body say A receive to F=ma this implies 2N = m*a
For two bodies apart I just want to know this the force A receives will be equal to the mass of A * the acceleration of the body B right since the acceleration it receives will be due to the gravitational pull of B doing the same calculations now for b with the acceleration of A yeilds the results that ' the acceleration of B will be twice that of A. Is this correct? Any comment will be appreciated

 

[Tiven white]

I would really appreciate a response to this question please

 

[Doc Al]

So I worked out the force on both bodies and it turns out both receive an equal and opposite force of 2F now equating the force the body say A receive to F=ma this implies 2N = m*a
For two bodies apart I just want to know this the force A receives will be equal to the mass of A * the acceleration of the body B right since the acceleration it receives will be due to the gravitational pull of B doing the same calculations now for b with the acceleration of A yeilds the results that ' the acceleration of B will be twice that of A. Is this correct? Any comment will be appreciated

No, not correct.

Think this way. Newton's law of universal gravity describes the force that the masses exert on each other. Given that force, Newton's 2nd law tells you the resulting acceleration.

 

[Tiven white]

So the opposite is true then that is the acceleration of a is twice that of b

 

[Tiven white]

Does this then mean the acceleration of a is twice that of b

 

[Doc Al]

So the opposite is true then that is the acceleration of a is twice that of b

Right.

 

[Tiven white]

Thanks

 

[lightgrav]

acceleration of A's mass results from the total Force that is applied to A. Subject - predicate - object:
The subjects (here, only gravity caused by B's mass) apply Force; the object A is Forced to accelerate.
Every symbol in Newton's 2nd Law is about the object, the sub-system (contained inside) whose behavior is changed by all the influences (from external subjects) that penetrate the system-boundary.
Those influences are the object's environment.