1. Newton's third law states that every action has a n equal and opposite reaction. So this means that there is a reaction for every force we apply, right? So, consider this, a man is trying to pick up a carrot, so he's applying an upward force to lift the carrot, but according to newton's 3rd law there should be an equal and opposite reaction. So, there should be an opposite reaction equal to the force he exerted to pick up the carrot upward in the downward direction. So, as these forces are equal and opposite, shouldn't he not be able to pick up the carrot. There is also a force exerted by gravity, so shouldn't it be impossible for him to pick up the carrot.

2.

3. There is a downward force, on him. Pushing up on the carrot also results in him being pushed down ( and through him, the Earth being pushed down). The forces are equal, but because the combined mass of the man and the Earth is so much greater than that of the carrot, the carrot does most of the moving.

As far as gravity is concerned, it takes an upward force on the carrot just to hold it still. If you were just standing holding the carrot you have the following situation: Gravity exerts a downward force on the carrot. It exerts an opposite upward force on the Earth. You exert an equal upward force on the carrot, and through you an equal force is exerted downward on the Earth. All the forces balance and nothing moves. If you increase the upwards force on the carrot, you exceed the downward force of gravity and you increase the separation of Earth and carrot as explained above.

4. I think Janus explained this perfectly. If the carrot had sufficient mass, it would be not easy to lift it from the surface of the Earth but I think something else comes into play then. The person trying to lift the carrot has muscles and leverage which must come into play, I think.

5. Think about it like this. Attach a horse to a carriage. If the horse exerts a force on the carriage and there's an equal and opposite force acting on the force making the sum zero then how does the carriage move?

The answer is that the horse exerts a force on the carriage but the carriage exerts a force on the horse, not on the carriage itself. Therefore the sum is not zero.

6. Originally Posted by physicist
Think about it like this. Attach a horse to a carriage. If the horse exerts a force on the carriage and there's an equal and opposite force acting on the force making the sum zero then how does the carriage move?

The answer is that the horse exerts a force on the carriage but the carriage exerts a force on the horse, not on the carriage itself. Therefore the sum is not zero.
That was difficult to understand, but after thinking on it, I think it makes sense.

7. Originally Posted by physicist
Think about it like this. Attach a horse to a carriage. If the horse exerts a force on the carriage and there's an equal and opposite force acting on the force making the sum zero then how does the carriage move?

The answer is that the horse exerts a force on the carriage but the carriage exerts a force on the horse, not on the carriage itself. Therefore the sum is not zero.
Quite so.

In fact the Wiki formulation of Newton's 3rd Law is helpful to understand this: "When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body."

The point being that two bodies are interacting and the "action" force is experienced by one and the "reaction" by the other. So, if one considers only one of the two bodies, only one force will be involved and there is thus no cancellation taking place.

8. The horse and buggy are a system. If you are looking at their movement in relationship to the earth you need to look at their net force against the surface they are on instead of just viewing them in isolation.

It is as Janus said about pulling a carrot.

9. Originally Posted by exchemist
Originally Posted by physicist
Think about it like this. Attach a horse to a carriage. If the horse exerts a force on the carriage and there's an equal and opposite force acting on the force making the sum zero then how does the carriage move?

The answer is that the horse exerts a force on the carriage but the carriage exerts a force on the horse, not on the carriage itself. Therefore the sum is not zero.
Quite so.

In fact the Wiki formulation of Newton's 3rd Law is helpful to understand this: "When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body."

The point being that two bodies are interacting and the "action" force is experienced by one and the "reaction" by the other. So, if one considers only one of the two bodies, only one force will be involved and there is thus no cancellation taking place.
Exactly!

10. Originally Posted by Janus
If you increase the upwards force on the carrot, you exceed the downward force of gravity and you increase the separation of Earth and carrot as explained above.
Nice work Janus!

At this point it happens when the force is greater than the weight of the carrot as well as the friction between carrot and soil plus the tensile strength of the roots. When the tensile strength is overcome the roots break and you only have to over come the friction of the soil and the other sources of force involved lifting something out of dirt. After than you're only over coming weight.

Trivial stuff? Absolutely. But I'm extremely bored.

11. Let's carry a scale out to the garden and pick the carrot while standing upon it.
Keep in mind that the scale measures gravity acting on mass, and direct force.
Scale goes up, carrot pops loose, scale goes back down.

12. Originally Posted by physicist
Originally Posted by Janus
If you increase the upwards force on the carrot, you exceed the downward force of gravity and you increase the separation of Earth and carrot as explained above.
Nice work Janus!

At this point it happens when the force is greater than the weight of the carrot as well as the friction between carrot and soil plus the tensile strength of the roots. When the tensile strength is overcome the roots break and you only have to over come the friction of the soil and the other sources of force involved lifting something out of dirt. After than you're only over coming weight.

Trivial stuff? Absolutely. But I'm extremely bored.
I never get bored trying to explain the principles of science to people who want to know: that's one reason I come here.

13. Originally Posted by exchemist
I never get bored trying to explain the principles of science to people who want to know: that's one reason I come here.

It is shameful we cannot do it more frequently.

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