Is Hooke's law related to the time-squared rate of acceleration?

In summary, there is no direct connection between the inverse square law of gravity and the time-squared rate that bodies fall. While the acceleration of falling bodies is affected by the gravitational field, it is not solely determined by the inverse square law. Additionally, the time-squared rate is a dimension of a quantity, while the inverse square law is a relationship between force and distance.
  • #1
jbmolineux
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Is there a connection between the inverse square law of gravity and the time-squared rate that bodies fall (i.e. (32ft/second)/second))?
 
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  • #2
jbmolineux said:
Is there a connection between the inverse square law of gravity and the time-squared rate that bodies fall (i.e. (32ft/second)/second))?

Not reallly. It doesn't matter how a force is related to distance between the objects, acceleration (by definition) is (distance/second)/second.
 
  • #3
For gravity, inverse square law meas that acceleration is a function of distance, so typically chain rule is used to convert time based acceleration into position based acceleration. Define the two masses as m1 and m2 :

a = dv/dt = v dv/dr = -G (m1 + m2) / r2

For an initial distance r0 and final distance r1, the above equation is integrated twice. The first integration isn't too bad, but the second one is complicated, and you end up with time as a function of initial and final distance, which can't be converted into distance as a function of time.
 
  • #4
jbmolineux said:
Is there a connection between the inverse square law of gravity and the time-squared rate that bodies fall (i.e. (32ft/second)/second))?
The rate at which falling bodies accelerate is the local strength of the gravitational field.
 
  • #5
A.T. said:
The rate at which falling bodies accelerate is the local strength of the gravitational field.
For a two body system, this would be the rate of acceleration towards a common center of mass for the two body system (use the common center of mass as the source for a reference frame). Each mass accelerates towards the common center of mass based on the gravitational field of the "other" mass.
 
  • #6
jbmolineux said:
Is there a connection between the inverse square law of gravity and the time-squared rate that bodies fall (i.e. (32ft/second)/second))?

I can falsify your notion of the universality of such a connection. Consider Hooke's law, where the force is proportional to the displacement from equilibrium, i.e. not an inverse square law. Yet, the acceleration of the oscillating mass is still L/T2.

One has nothing to do with the other. One is the relationship between force and distance from the source of that force. The other is the dimension of a quantity.

Zz.
 

Related to Is Hooke's law related to the time-squared rate of acceleration?

What is the difference between gravity and acceleration?

Gravity is a force that pulls objects towards each other, while acceleration is the rate of change in an object's velocity. Gravity causes objects to accelerate towards the Earth, but acceleration can also occur in other directions.

How does gravity affect acceleration?

Gravity affects acceleration by causing objects to accelerate towards the Earth at a constant rate of 9.8 meters per second squared. This means that for every second an object is falling, its velocity increases by 9.8 meters per second.

What is the relationship between mass and gravity?

The relationship between mass and gravity is that the more massive an object is, the stronger its gravitational pull will be. This means that larger objects, such as planets, have a stronger gravitational force than smaller objects.

How does acceleration due to gravity change on different planets?

The acceleration due to gravity on different planets depends on the planet's mass and radius. For example, the acceleration due to gravity on Earth is 9.8 meters per second squared, while on Mars it is 3.7 meters per second squared.

Can gravity and acceleration be manipulated?

Yes, gravity and acceleration can be manipulated through various means such as changing the mass or distance between objects. In addition, objects can experience different levels of acceleration depending on the forces acting upon them.

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