How can an object have an acceleration of 9.81m/s^2 when there is

[student34]

no change in velocity? How can a rock that isn't moving have acceleration?

 

[JimJam]

Acceleration is the rate of change of velocity, isn't it? So it is speeding up in whatever direction 9.81m/s every second, therefore there must be a change in V?

 

[mfb]

How can a rock that isn't moving have acceleration?

It cannot have a (net) acceleration in a frame where it stays at rest.
It can have forces acting on it (like gravity, and a force from the floor), but they have to cancel.

 

[student34]

It cannot have a (net) acceleration in a frame where it stays at rest.
It can have forces acting on it (like gravity, and a force from the floor), but they have to cancel.

Hmmm, then there must be another definition of acceleration other than a change in velocity. Unless a change in velocy only applies to net acceleration.

 

[student34]

Acceleration is the rate of change of velocity, isn't it? So it is speeding up in whatever direction 9.81m/s every second, therefore there must be a change in V?

Sorry, I meant that it does not make sense to me that still object has acceleration g. There is no change in velocity, yet Einstein says that it has the same acceleration as something that has a changing velocity.

 

[JimJam]

As in the object may be running parallel to an object with the same acceleration, in the same direction, so they have no relative movement between the two?

 

[Drakkith]

Sorry, I meant that it does not make sense to me that still object has acceleration g. There is no change in velocity, yet Einstein says that it has the same acceleration as something that has a changing velocity.

First, are we talking about simple classical acceleration, or about General Relativity?
In classical physics the answer is that an object that isn't changing velocity has no acceleration. Gravity provides a force on an object, but for those on the ground there is no acceleration. The force on an object is equal to the force that would accelerate that object at 9.8 m/s².

 

[student34]

First, are we talking about simple classical acceleration, or about General Relativity?
In classical physics the answer is that an object that isn't changing velocity has no acceleration. Gravity provides a force on an object, but for those on the ground there is no acceleration. The force on an object is equal to the force that would accelerate that object at 9.8 m/s².

Oh, I am in the first year of university physics, and we have not got to relateivity yet. They should probably have told us that a change in velocity is true except for with g. That really screwed me up.

 

[WannabeNewton]

No it is always true that $\sum F_{i} = m\sum a_{i} = m\sum \frac{\mathrm{d} v_{i}}{\mathrm{d} t}$ for a single particle constant mass system (the indexes label the motion coupled to the respective force). The point is that when you place a pebble on the ground, there is an upwards reaction force from the ground on the pebble (loosely put it arises out of the electrostatic repulsions between the pebble and the ground) and this reaction force just happens to cancel out the weight of the pebble so that the net acceleration given above vanishes.

 

[student34]

No it is always true that $\sum F_{i} = m\sum a_{i} = m\sum \frac{\mathrm{d} v_{i}}{\mathrm{d} t}$ for a single particle constant mass system (the indexes label the motion coupled to the respective force). The point is that when you place a pebble on the ground, there is an upwards reaction force from the ground on the pebble (loosely put it arises out of the electrostatic repulsions between the pebble and the ground) and this reaction force just happens to cancel out the weight of the pebble so that the net acceleration given above vanishes.

Then why do they tell us that acceleration is a change in velocity all thoughout our textbook?

 

[WannabeNewton]

Then why do they tell us that acceleration is a change in velocity all thoughout our textbook?

Because it is; What has been said thus far that has contradicted that?

 

[elfmotat]

Then why do they tell us that acceleration is a change in velocity all thoughout our textbook?

The rock has an "acceleration due to gravity" which is -9.8 m/s². It has an "acceleration due to the ground" which is +9.8 m/s². Add them together and you get zero.

 

[Dale]

There is no change in velocity, yet Einstein says that it has the same acceleration as something that has a changing velocity.

There are two kinds of acceleration.

First, there is coordinate acceleration. This is the second time derivative of position, or the first time derivative of velocity. You don't get coordinate acceleration without change in velocity.

Second, there is proper acceleration. This is the acceleration measured by an accelerometer. Most likely you currently have a proper acceleration of 9.8 m/s² upwards although I suspect that you probably consider yourself to be at rest thus having a constant velocity of 0. So proper acceleration can be non-zero even with zero change in velocity.

 

[DrGreg]

Acceleration and velocity are always relative to something. You need to know what the "something" is, or is assumed to be, before you can say whether an object is accelerating or not.

In Newtonian physics we measure acceleration relative to the Earth's surface.

In General Relativity we measure (proper) acceleration relative to falling objects.

 

[student34]

Acceleration and velocity are always relative to something. You need to know what the "something" is, or is assumed to be, before you can say whether an object is accelerating or not.

In Newtonian physics we measure acceleration relative to the Earth's surface.

In General Relativity we measure (proper) acceleration relative to falling objects.

Oh, so are you saying that to a rock falling, a different still-object will seem to be accelerating - hence relativity?

 

[student34]

Because it is; What has been said thus far that has contradicted that?

So a rock with zero velocity and zero speed has velocity!?

You may as well type Chineese instead of those formulas because it would mean the exact same to me.

 

[cepheid]

So a rock with zero velocity and zero speed has velocity!?

You may as well type Chineese instead of those formulas because it would mean the exact same to me.

A rock sitting on the ground has zero acceleration because zero net force acts on it. Period. That's it. It doesn't have an acceleration of g.

 

[Whovian]

So a rock with zero velocity and zero speed has velocity!?

You may as well type Chineese instead of those formulas because it would mean the exact same to me.

Well, it has zero velocity. I don't quite understand. (The formulas were saying that "the sum of the forces on an object is mass * acceleration, or the sum of the accelerations depending on if you define acceleration to be the total change in velocity or the result of the force, in which case the total acceleration, or the change in velocity, is just the sum of the accelerations." A little wonky.)

 

[DrGreg]

Oh, so are you saying that to a rock falling, a different still-object will seem to be accelerating - hence relativity?

Yes. If a rock falls, there's 2 ways to look at it.

1. The rock is accelerating downwards relative to the ground.
2. The ground is accelerating upwards relative to the rock.

The revolutionary aspect of General Relativity was to base it on (2) instead of (1).

 

[student34]

Yes. If a rock falls, there's 2 ways to look at it.

1. The rock is accelerating downwards relative to the ground.
2. The ground is accelerating upwards relative to the rock.

The revolutionary aspect of General Relativity was to base it on (2) instead of (1).

Wow, thanks!

 

[NewtonsHead]

It's all about the reference frames.

 

[ehild]

no change in velocity? How can a rock that isn't moving have acceleration?

At the instant when you release a stone it has zero velocity, but a very short time Δt later the velocity is gΔt. Acceleration is defined as change of velocity over change of time: a =Δv/Δt. From zero to Δt the velocity changed by gΔt, divided by Δt it is g.

Newton's second law says that the acceleration is equal to the resultant force divided by the mass of the object.
The Earth pulls all objects with the force of gravity G=mg where g is about 9.8 m/s^2. If the object is released it accelerates downward: ma=G, a=G/m=g, with acceleration g. If the object is supported, sits on a table for example, the table exerts a force N (normal force) on it that prevents the object from falling: the object does not move, no change of velocity, the acceleration is zero, as the sum of the downward force of gravity and the upward normal force cancel: N-G=ma=0.

ehild

 

[A.T.]

Yes. If a rock falls, there's 2 ways to look at it.

1. The rock is accelerating downwards relative to the ground.
2. The ground is accelerating upwards relative to the rock.

The revolutionary aspect of General Relativity was to base it on (2) instead of (1).

Here the 2 ways visualized:

https://www.youtube.com/watch?v=DdC0QN6f3G4

 

[mikemeg]

I could be wrong, but I think we're going wayyyyy beyond what the original poster was talking about. A lot of questions are not particularly deftly phrased in textbooks.

"g", commonly referred to as "the acceleration due to gravity" can be used for calculations without the object actually accelerating. You can think of it as "a falling object would accelerate at 9.81 m/s²," and that gives you a sense of the gravitational field. Dimensionally, m/s² is the same as N/kg. So you could equally think of "g=9.81m/s² near the Earth's surface" as "there's a gravitational force of 9.81N for every kg of mass near the Earth's surface".

In other words: "there's a 5kg rock. The acceleration due to gravity is 9.81" tells you that the weight of the object, mg, is 5kg*9.81m/s² = 49.05 N.

 

[A.T.]

I could be wrong, but I think we're going wayyyyy beyond what the original poster was talking about.

I don't think so. In post #5 he clarified that he actually asks about Einstein's General Relativity where objects at rest on the Earth’s surface have a proper acceleration upwards of 1g.

 

[soothsayer]

He also clarified that he is in first year physics, so I don't think GR is going to help him understand much.

I'm not sure where the confusion comes from, but I don't think previous posts are really helping a lot.

Student34, can you tell us who or what told you that an object has an acceleration of 9.8 m/s² even if there is no change in velocity? It's just not true. Acceleration is change in velocity.

If the rock is falling, it will be accelerating at 9.8 m/s², but if the rock is resting out the ground, the force from gravity, which normally accelerates things at g, is being balanced out by the force from the ground. You know the gravitational force near Earth's surface for an object is mg, where m is the mass of the object, and g is 9.8 m/s², but the rock is at rest, so acceleration is zero, which means the normal force from the surface of the Earth has to equal exactly mg as well, so there are two forces on the rock that we can calculate using g, but they are in exact opposite directions so there is no net force, no acceleration, no change in velocity, the rock just sits there. Just because we're still evoking g = 9.8 m/s² in a free body diagram of a rock sitting at the Earth's surface, doesn't mean it is ACTUALLY accelerating, we just use the value for g to determine the magnitude of the normal and gravitational forces.

 

[A.T.]

He also clarified that he is in first year physics, so I don't think GR is going to help him understand much.

He was specificaly asking about Einstein's view on acceleration in post #5

Acceleration is change in velocity.

That is coordinate acceleration. But the OP is confused about statements regarding proper acceleration.

 

[arydberg]

see my webpage

http://www.maverickexperiments.com/fma/Force.html

 

[soothsayer]

He was specificaly asking about Einstein's view on acceleration in post #5

I think you're right now. I was thinking back to the thread after I posted this and I think I see now where the confusion arose.

That is coordinate acceleration. But the OP is confused about statements regarding proper acceleration.

Right, I was only approaching it from a Newtonian perspective.

It seems like the OP had a moment of clarity regarding Einsteinian gravity, so I'll assume the question has been dealt with.

 

[Paramadman]

no change in velocity? How can a rock that isn't moving have acceleration?

It can't. As phrased the query is meaningless.

Paramadman