A contact force? The answer really depends on the level of the question. Primary school answer: A pushing or pulling force, or a friction force occur when objects touch. High school answer: Same as above, but 'pushing' and 'pulling' would be replaced with positive and negative. Friction would be defined as a force that opposes motion, and would include air resistance and drag. University answer: Technically, there is no such force, as all forces act at a distance without touching. In fact, objects don't actually 'touch' one another at all. The outer electrons in an object's atoms will repel said electrons from another object's atoms through the electromagnetic force. This only makes it feel like the objects have come into contact with one another, when in fact they haven't.
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Contact forces are forces that can only have an effect on objects that they touch, such as when you contact a box and apply force to move it. you might apply a contact force to bend, tear, stretch, compress, or twist and abject. Tension force, friction force, and elastic force are examples of contact forces.
At the macro level, there are only two forces that cause objects to be attracted toward each other:gravity applies to all objects; andmagnetism applies only to certain materials.
It is true that the force of gravity can be described as a force field. Any object having mass will create a gravitational attraction in all directions, with decreasing intensity as the distance from the object increases. Fields are like that. It is different from a force that results from being hit by a baseball, which is exerted only at a specific location.
A contact force, such as friction. If a car wheel wasn't on the ground there couldn't be friction. A non-contact force could be magnets, the two magnets don't need to touch to repel or attract :)
No, that is Newton's Third Law of Motion. The Law of Conservation of Momentum is that within a contained set of objects, the total momentum never changes. Objects can only transfer energy to each other, they can never really "get rid" of it.