Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 377

Accleration due to gravity

What is the acceleration due to gravity OF THE EARTH in the following scenario?

A 5kg bowling ball is dropped from a height of 2m above the surface of the Earth.

Use 10m/s^2 for g for the ball
And 6x10^24kg for the mass of the Earth

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,702

Re: Accleration due to gravity

Bring the ball to rest by embedding it in the frame of reference and it's now the Earth that moves and at the same (but sign reversed) magnitude.  Should we worry about this?  Well people have been dropping things for many years without any problem.  The crust is flexible* so maybe it just bends a bit.

*We're used to the Earth's tides ie water moving about, but actually I read somewhere that the crust moves too.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 377

Re: Accleration due to gravity

“Bring the ball to rest by embedding it in the frame of reference...”

Thanks, Bob. What does that mean, to embed it in the frame of reference? I did Google it but I’m not sure that I’ve got it.

“...and it's now the Earth that moves and at the same (but sign reversed) magnitude.”

Do you mean; in my scenario the ball moved 2m downwards towards Earth; but in your scenario Earth moved 2m upwards towards the ball?

“Should we worry about this?”

I’m not sure. When I’m about to carry out the actual experiment I will give you notice, maybe you can strap everything down, warn the neighbours, reassure nervous dogs, etc.

I did a crude calculation, ignoring the distance of 2m (I think I just put a distance to illustrate that it was ‘near the surface of Earth’).

Earth on ball;

F=ma
F=5kg(10m/s/s)
F=50N downwards

From there I inferred that if Earth is exerting 50N on the ball, pulling it with a force of 50N, the ball must be exerting a force of 50N on Earth, pulling it with a force of 50N.

Then;

Ball on Earth;

F=ma
50N=6x10^24kg(a)
a=50N/(6x10^24kg)
a=8.3recurring x 10^-23m/s/s

So if I drop a bowling ball I cause Earth (with you, Commander Bob, and the jittery poodle at no.42, on it) to accelerate at approx 1 ten billionth of trillionth m/s/s ?

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,702

Re: Accleration due to gravity

Sorry I used 'embed'. I just mean consider the situation from the ball's viewpoint.  So what if you're an ant on the ball. Then yes that means the Earth is now moving.

We do this all the time. If you're in a car or train, the world seems to be moving past.  Just standing on the Earth we see the Sun, Moon and stars rotating above our head.

Thanks for the calculation.  I think we can safely ignore the Earth's movement here.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ktesla39

Member

From: Nepal

Registered: 2024-10-08

Posts: 125

Website

Re: Accleration due to gravity

Wait....
So u mean gravity is relative?
I had also heard about inertial frame of reference. But don't know wthat it is.

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"Talent hits the target no one else can hit. Genius hits the target no one else can see." - Arthur Schopenhauer

Bob

Administrator

Registered: 2010-06-20

Posts: 10,702

Re: Accleration due to gravity

A frame of reference is just a way to formulate the model of a problem by placing one object at rest.  eg.  If I'm on a train (speed T) looking at a cyclist (speed C) alongside the track, I can make my frame of reference the train,  in which case the cyclist appears to be going at
speed T-C.

As no acceleration is involved the frame is said to be inertial.

If you wish to analyse the rotational properties of the Earth, the oceans and the winds, then acceleration is involved because a rotating object needs a central acceleration in order to follow a circular path.  The frame of reference in non inertial.

So u mean gravity is relative?

Not sure how to answer this.  If you mean that the gravity I measure could be different from someone else's measurement of the same gravity, the best I can come up with is maybe.

When scientists measure the gravitational pull of the Earth they get the same answer if they measure at the same place (it does vary around the surface of the Earth) but if you tried to measure gravity in a moving lift you would get a different result from a static lift.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob