# Math Is Fun Forum

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## #1 2023-06-13 07:46:24

paulb203
Member
Registered: 2023-02-24
Posts: 199

### Is an apple held in your outstretched hand accelerating?

One of the first examples of gravity given on this site explains that a force of 0.98 N is required to hold up an apple with a mass of 0.1kg.

F=ma is shown, which translates to F=mg, as a in this context is 9.8m/s/s due to gravity

So, 0.98N = 0.1kg x 9.8m/s/s

I think this is starting to make sense to me but at the same time I'm puzzled regards the use of acceleration in this example.

Is the apple accelerating? It seems to be at rest, in one's hand, no?

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## #2 2023-06-13 20:15:13

Bob
Registered: 2010-06-20
Posts: 10,472

### Re: Is an apple held in your outstretched hand accelerating?

An acceleration of zero is still an acceleration.  The situation is more complicated than this however as the person's hand is actually rotating about the polar axis as the Earth rotates. It's not easy to appreciate this if you're just holding an apple, but it's a major factor in causing the world's weather patterns.

The first law states that an object will continue with uniform motion unless acted upon by an external force.  An object travelling in a circle does not have uniform motion; it's 'trying' to avoid travelling on a tangential path by, instead, moving towards the centre of the circle.  That requires an inwards acting force.  Gravity is providing that force. If it were 'switched off' every thing and every one would float off into space.

Replace 'acceleration due to gravity' by 'weight of apple' and it's easy to see why you need a force balancing equation.

Bob

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

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## #3 2023-06-15 07:47:35

paulb203
Member
Registered: 2023-02-24
Posts: 199

### Re: Is an apple held in your outstretched hand accelerating?

Thanks, Bob.
“An acceleration of zero is still an acceleration.”
I Googled this, Bob, and got;
-‘Acceleration of an object can be zero when it is moving with a constant velocity. Since velocity is constant, there will be no change in velocity and so there will be no acceleration.’
But the apple, relative to the hand at least, is not in motion. I get that the two are moving with the Earth, and the solar system, etc, but the apple is at rest relative to the hand, no? So I’m thinking that if the apple has no motion in this respect how can it have velocity. And if it has no velocity, in this respect, how can it have acceleration.
“The situation is more complicated than this however as the person's hand is actually rotating about the polar axis as the Earth rotates. It's not easy to appreciate this if you're just holding an apple, but it's a major factor in causing the world's weather patterns.”
Thanks. It’s always helpful for me to be reminded of this, that nothing is at rest, except relative to something else.
“Replace 'acceleration due to gravity' by 'weight of apple' and it's easy to see why you need a force balancing equation.”
Thanks. I think I get the idea of weight being a force. My mass is 90kg. W=mg means there is a force of gravitational attraction between me and the Earth of 900N, approx, yes? But then I get confused again when I analyse w=mg, which is weight = mass x g, and g is acceleration due to gravity! Back to acceleration. I’m standing on my kitchen floor and, relative to the Earth, I’m at rest. Yet I’m accelerating? At 9.8m/s/s?

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## #4 2023-06-15 20:23:28

Bob
Registered: 2010-06-20
Posts: 10,472

### Re: Is an apple held in your outstretched hand accelerating?

A zero velocity is still a velocity so it can still have an acceleration (which can also be zero).

You on the kitchen floor is the same (in terms of Newton) as an apple in the hand.

When you stand on a bathroom scale (the type with a platform and a rotating scale) the Earth's gravity is still trying to pull you down. Your floor was solid enough that you didn't move, but the scale platform can move because under it is a spring which can be compressed. As this happens a set of rods and cams transfer this movement into a rotation of the scale so you get a reading. Strictly the scale is measuring a force but, as the value of g is fairly constant over the Earth's surface, the scale is calibrated in Kg and hence gives you your mass.  As you have moved on the platform closer to the centre of the Earth you have clearly experienced a change of velocity and hence an acceleration.

If you place the scale somewhere where you can push down (eg. under a door frame) you can exert extra force which will be shown as an apparent increase in Kg. If you can pull upwards your 'weight' will go down.

If you could take the scale to the Moon the lower gravitational pull would show a much lower 'weight'.

Bob

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

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