Newton's Second Law of Motion: F=ma

F = ma: Newton's second law of motion states that the net force acting on an object equals the product of the mass (m) times the acceleration (a) of the object. The direction of the force is the same as that of the acceleration.
    The units used for force are Newtons (N).
    The units used for mass are kilograms (kg).
    The acceleration units are meters per second squared (m/sec²).
When figuring out F=ma problems, it also necessary to use the equations of motion.
     1. v₂=v₁+at
        where v is velocity (m/sec), a is acceleration (m/sec²), and
        t is time in seconds.
     2. v₂²=v₁²+2as
         where s is the distance in meters.
     3. s=s_o+v₁t+1/2at²
Tension in a Rope: The force tension in a rope is also measured using Newton's Second Law. However, in this situation the formula for weight is needed.
    F=mg
The g for gravity is substituted for a (acceleration); the acceleration due to gravity is 9.8 meters per second (m/sec).
The formula for weight can also be used in problems involving objects on ramps. For this an object's weight is divided into two different vectors. The force parallel to the ramp accelerates the object down the ramp.

Up or Down: The last area of Newton's Second Law covers the changes in force as an object is accelerated up or down.
- As an object is moved upward, the force needed to accelerate the object must be added to the weight of the object.
- As an object is moved downward, the force needed to accelerate the object must be subtracted from the weight of the object.

Note: Newton's First Law is actually a special case of the Second Law; when the force is zero, so is the acceleration.