Newton's Second Law: This law states that the net force acting on an object is directly proportional to the rate of change of its momentum. Mathematically, it's written as:
F = Δp / Δt
where:
F is the net force acting on the object (measured in Newtons, N)
Δp is the change in momentum (vector quantity)
Δt is the time interval over which the change in momentum occurs (measured in seconds)
Relating Momentum and Mass: We know momentum is defined as the product of mass (m) and velocity (v) of the object:
p = mv
Expressing Change in Momentum: If the mass of the object remains constant during the motion (common scenario), then a change in momentum (Δp) can be written as the product of mass and the change in velocity (Δv):
Δp = mΔv
Substituting into Newton's Second Law: Combining equations (1) and (3), we get:
F = (mΔv) / Δt
Deriving the Force Formula: To arrive at a more familiar form, we can rewrite the equation using the concept of acceleration (a). Acceleration is defined as the rate of change of velocity with respect to time:
a = Δv / Δt
Substituting this into the previous equation:
F = m (a) = ma
Therefore, we obtain the formula for force based on momentum and Newton's second law:
F = ma
This equation tells us that the force acting on an object is equal to the product of its mass and its acceleration. In simpler terms, the greater the force applied, the greater the acceleration experienced by the object (assuming constant mass).