# Two Skaters on Ice - Forces and Acceleration

Two skaters, a man and a woman, are standing on ice. Neglect any friction between the skate blades and the ice. The woman pushes on the man with a certain force that is parallel to the ground. Must the man accelerate under the action of this force? If so, what three factors determine the magnitude and direction of his acceleration? Is there a corresponding force exerted on the woman? If so, where does it originate? Is this force related to the magnitude and direction of the force the woman exerts on the man? If so, how? The mass of the man is 82 kg and that of the woman is 48 kg. The woman pushes on the man with a force of 45 N due east. Determine the acceleration (magnitude and direction) of the man and the woman.

## Answer:

**Yes**, the man will accelerate under the action of the force applied by the woman. The magnitude and direction of his acceleration are determined by three factors: the mass of the man, the magnitude of the force applied by the woman, and the direction of the force.
The acceleration can be calculated using Newton's second law, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass. In this case, the force exerted on the man by the woman originates from the woman herself, and it is related to the magnitude and direction of the force she applies.
The acceleration of the man will be in the same direction as the force applied by the woman, and its magnitude can be calculated using the equation a = F/m.