What is the magnitude of acceleration?

In summary, two objects X and Y are released from rest in outer space, with the only force acting on them being their mutual gravitational attraction. The mass of X is one-half that of Y. Using the equations Fg = GXY/r^2 and Fnet = ma, it can be determined that the acceleration of X is twice that of Y. However, the answer key shows that the correct answer is C, which means that the acceleration of X is equal to that of Y. This is because the magnitude of force X exerts on Y is equal to the magnitude of force Y exerts on X, and since the forces are equal, the acceleration of each object is inversely proportional to its mass. Therefore, the correct answer
  • #1
YMMMA
156
10

Homework Statement


Objects X and Y, shown below, are released fronm rest in outer space. The only force acting on the objects is their mutual gravitational attraction. The mass of X is one-half that of Y. With respect to the original rest frame, the magnitude of the acceleration of X is

(A) one-half that of Y
B) twice that of Y
C) equal to that of Y
D) directly proportional to the distance betweern X and Y
(E) directly proportional to the square of the distance between X and Y

Homework Equations


Gravitational force Fg = GXY/r^2, r is the distance between the two masses.
Fnet=ma

The Attempt at a Solution


Using both equations, Xa=GXY/r^2. Acceleration of X is Simplified to a=GY/r2. And Ya= GX/r^2 simplified to a=GX/r^2= acceleration of Y. Substituting X=½Y
So the ratio if acceleration of X to that of Y would be twice as much,B. Is there something wrong?
 
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  • #2
YMMMA said:
. Is there something wrong
What makes you think so?
 
  • #3
haruspex said:
What makes you think so?

Because in the answer key it is C, the same, so I had to check:rolleyes:
 
  • #4
YMMMA said:
Because in the answer key it is C, the same, so I had to check:rolleyes:
Ouch. Does this text have many such blunders?
 
  • #5
Probably yes. That’s a different book though.
 
  • #6
YMMMA said:
Because in the answer key it is C, the same, so I had to check:rolleyes:
What is the same is:
The magnitude of force X exerts on Y is the same as the magnitude of force Y exerts on X .

Since the (magnitudes of the) forces are equal, the acceleration of each is inversely proportional to its mass → B is correct.
 
  • #7
SammyS said:
What is the same is:
The magnitude of force X exerts on Y is the same as the magnitude of force Y exerts on X .

Since the (magnitudes of the) forces are equal, the acceleration of each is inversely proportional to its mass → B is correct.
Yes, thank you!
 

FAQ: What is the magnitude of acceleration?

What is the magnitude of acceleration?

The magnitude of acceleration refers to the rate of change of an object's velocity over time. It is a measure of how quickly the object's speed or direction is changing.

How is the magnitude of acceleration calculated?

The magnitude of acceleration can be calculated by dividing the change in velocity by the change in time. This can be represented mathematically as: a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

What is the unit of measurement for magnitude of acceleration?

The unit of measurement for magnitude of acceleration is meters per second squared (m/s^2). This means that for every second, the object's velocity changes by the specified amount.

How does the magnitude of acceleration relate to an object's motion?

The magnitude of acceleration is directly related to an object's motion. If the magnitude of acceleration is positive, the object is accelerating in the same direction as its velocity, which means it is speeding up. If the magnitude of acceleration is negative, the object is accelerating in the opposite direction of its velocity, which means it is slowing down.

Can the magnitude of acceleration change?

Yes, the magnitude of acceleration can change. It can change if the object's velocity changes, or if the time interval over which the velocity changes is altered. Additionally, external forces such as friction or air resistance can also affect the magnitude of acceleration.

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