2.2 Newton’s Second Law of Motion

Newton’s second law describes how an object’s motion is affected by the application of a force. The change of motion is proportional to the magnitude of the applied force and inversely proportional to the object’s mass. Take the example of two steel marbles, both of the same size and same mass, resting on a smooth table. A greater force is applied to marble 1, and a lesser force applied to marble 2. We know that the motion of marble 1 will change (marble 1 will accelerate) more than that of marble 2. The second law also states that the effect of a force is always in the direction of its application. If a man pushes a car west, it will move west (unless other forces counteract that exerted by the man). The second law is often written as follows:

where F represents the net applied force, m is mass, and a is acceleration. The SI unit for force is the Newton (abbreviated N), which is equal to the force that produces an acceleration of one meter per second per second on a mass of one kilogram (N = kg[m/s²]).

Let us use this definition of a force to examine the motion of a bullet shot horizontally from 4.9 meters above the earth’s surface. According to Newton’s first law, the bullet will continue to travel in a straight line forever if no forces act upon it. However, (discounting air friction), we know that the bullet will fall and hit the ground after 1.0 second (using 9.8 m/s² as the acceleration of gravity). This change in motion (falling) must be the result of a force: the force of gravity (the weight of the object). Gravity pulls the bullet toward the earth, at a right angle to its initial direction of travel. We know that the acceleration caused by gravity is equal for all objects, regardless of mass , which allows us to arrive at another important conclusion: applying Newton’s Second Law, the force that gravity exerts on an object is directly proportional to the object’s mass. If it were the same for all objects, less massive objects would accelerate at a greater rate than more massive objects.