1. Two people-one twice as heavy as the other one, play tug-of-war with a 12m ideal rope while standing on a frictionless ice surface. Would any of them move and if he does, how far? Explain why?

A frictionless surface can exert no force on the combination of two people and rope. The people will move themselves closer together, however, by both pulling on the rope. Their center of mass would remain in the same place. The heavier person will have moved 4 m and the lighter person 8 m, when they come together.

In this scenario, we have two people playing tug-of-war. One person is twice as heavy as the other, and they are standing on a frictionless ice surface. We need to determine if either of them would move and, if so, how far.

To answer this, we need to consider the concept of net force. Net force is the overall force acting on an object, taking into account all the individual forces acting upon it.

In a tug-of-war scenario, the two people will be exerting forces on the rope in opposite directions. These forces can be considered as the tension forces acting on the rope. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that if one person exerts a force on the rope in one direction, the rope exerts an equal and opposite force on that person.

In our scenario, the person who is twice as heavy exerts a greater force on the rope compared to the lighter person. However, the rope exerts an equal and opposite force on each person. Since the force exerted by the heavier person is twice as much, the rope will exert an equal and opposite force on the lighter person, causing them to move.

Now, let's consider the distance the lighter person would move. This can be determined by looking at the force exerted by the heavier person and the force exerted by the lighter person.

Since the force exerted by the heavier person is twice as much, the lighter person would experience a net force in the direction of the heavier person. As a result, the lighter person would move in the direction of the heavier person.

As for the distance the lighter person would move, it depends on the specific force exerted by each person and their combined masses. Without specific values or additional information, we cannot calculate the exact distance.

In summary, in a tug-of-war scenario with a frictionless ice surface, the lighter person would move in the direction of the heavier person. The specific distance moved depends on the forces exerted by each person and their masses.