How is 1N enough to move a 0.1kg apple 1 meter high?

[M3D1]

Example: How much energy is needed to lift an 0.1 kg apple up 1 meter?​

To hold a 0.1 kg apple against gravity needs 1 Newton of force:
F = mg
F = 0.1 kg × 9.8 m/s2
F ≈ 1 N
But holding an apple is not work, the apple needs to move!

So, raising it using 1 N for 1 m (both in same direction!) gives:

Work = 1 N × 1 m × cos 0° = 1 J
‐--------‐-----‐------------
i am confused in that if 1N only holds the apple (since the force of gravity and my hand add up zero net force to apple) then how does apple moves up 1 meter by just 1N to a 1 meter distance to result in one J of energy. i don't know whether i misunderstood the concept of work or misunderstood sth about question .
thanks in advance for any help i could recieve

 

[Doc Al]

i am confused in that if 1N only holds the apple (since the force of gravity and my hand add up zero net force to apple) then how does apple moves up 1 meter by just 1N to a 1 meter distance to result in one J of energy.

I think what you're asking is how can exerting exactly 1 N of force actually lift the apple. If you start from rest, you have a good point. To start things moving you must at least exert a little more force than just enough to balance gravity! But the work you have to do against gravity is still just what you calculated. Any additional work you do goes to increasing the kinetic energy of the apple.

 

[kuruman]

If you apply a teeny tiny force greater than 1 N for a very short time to get the apple moving up and then reduce the force to exactly 1 N, the apple will keep on moving up at constant speed. When you get to 1 m higher, reverse the process to stop the apple and keep it there. The apple is still at rest, the change in kinetic energy is zero, the average force exerted by your hand is 1 N and the apple is 1 m higher than it was. The (positive) work done by your hand on the apple is equal to the change in potential energy of the apple plus Earth system.

On edit: I see that @Doc Al preempted me with essentially the same answer.

 

[PeroK]

Well, whatever the ups and downs of the apple, if it starts at rest and ends at rest $1m$ higher, then it has gained $1J$ of potential energy.

How it got there we can leave to those with a flair for engineering problems.

 

[Bandersnatch]

Sounds dangerous. I'd rather leave it to those with a flair for such problems ;)
https://brians.wsu.edu/2016/05/22/flair-flare/

 

[Baluncore]

If it takes 0.98 N to hold the apple in place against gravity, and you apply 1.00 N, so you will have an excess force of 0.02 N.
Since, F = m⋅a ; the apple will accelerate upwards, with; a = 0.02 N / 0.1 kg .
Given enough time, the apple could reach escape velocity.

 

[Doc Al]

If it takes 0.98 N to hold the apple in place against gravity, and you apply 1.00 N, so you will have an excess force of 0.02 N.
Since, F = m⋅a ; the apple will accelerate upwards, with; a = 0.02 N / 0.1 kg .
Given enough time, the apple could reach escape velocity.

LOL.

I'm sure the intention was to exert just enough upward force to balance the gravitational force on the apple. (But you are correct.)

 

[BvU]

i don't know whether i misunderstood the concept of work

You do not misunderstand the concept. As you prove by writing

But holding an apple is not work

The everyday experience that you get tired from holding up a bag of apples does not mean that it is work in the physics sense: a shelf or a hook on the wall can do exactly the same job and does not have to be provided with energy to do it.

But lifting a bag of apples from a lower shelf to a higher one does require work. Lifting the weight of an old fashioned clock requires work. The work (energy) that can run the clock for a while.

$\$

 

[Arjan82]

I think the concept of a conservative force field is important here. The gravitational force field is conservative. This essentially means that if you move something from location A to location B in that field, the energy used to get from A to B only depends on the field potential (height above ground in this case), and not on the path taken. This means that the amount of energy only depends on the height difference.