Two Skaters on Ice: Calculating Accelerations with Forces

Understanding the Physics Behind the Skaters' Accelerations

The scenario presented involves the application of Newton's laws of motion, specifically Newton's second law which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.

When the 60-kg woman pushes the 82-kg man with a force of 45 N due east, both skaters experience accelerations in response to this force. The man's acceleration can be calculated using the formula a = F/m, where a is acceleration, F is force, and m is mass. Substituting the values, we get a = 45 N / 82 kg = 0.55 m/s², which represents the magnitude of the man's acceleration in the eastern direction.

Newton's third law of motion states that for every action, there is an equal and opposite reaction. Therefore, when the woman exerts a force of 45 N due east on the man, she experiences an equal and opposite force of 45 N due west. This results in the woman having an acceleration of a = 45 N / 60 kg = 0.75 m/s² in the western direction.

It is important to note that these calculations demonstrate how forces between objects can lead to accelerations in accordance with Newton's laws. By understanding these principles, we can analyze and predict the motion of objects in various scenarios.