Lesson 3 notes – Newton’s Second Law
Objectives
Be able to define net force on a body as equal to rate of change of its
momentum;
Be able to select and apply the equation F Δt =Δp To solve problems;
Be able to explain that F = ma is a special case of Newton’s second law when
mass m remains constant.
Outcomes
Be able to define net force on a body as equal to rate of change of its
momentum.
Understand what the symbol Δ means.
Be able to apply the equation F Δt =Δp to solve problems correctly in a
number of situations.
Be able to explain that F = ma is a special case of Newton’s second law when
mass m remains constant.
Newton’s Second Law
From lesson 15 of the Mechanics Module (G481.2) we know that:
His 2nd law said that the force applied to an object is directly proportional to its
acceleration and that as an object grew in mass it would be harder to make
accelerate. So mass becomes the property of a body that resists change in
motion. This is summed up by the equation:
Force (N) = mass (kg) x acceleration (ms-2)
Since force and acceleration are both vectors they must act in the same
direction.
This law gives us a definition for the Newton (the unit of force):
1 N = 1 kg m s-2.
Change in momentum
If the velocity of the object changes then the momentum of that object will also
change.
It can be written as:
Momentum change = mv – mu
Δp = Δ(m v) (Δ means “the change in…”)
This can be shown to also be written as:
Force x time = momentum change = mv – mu
Ft = Δp = Δ(mv)
F=ma
Since FΔt = Δp = Δ(mv);
And acceleration is the change in velocity (Δv) in a change in time (Δt)
or a = Δv/Δt;
If an object of constant mass has a changing velocity we can write that:
FΔt = m Δv
If we rearrange this to make F the focus of the equation we can get:
F = m Δv/Δt
We have said that Δv/Δt = a and so substituting this in we now get
F = ma which is a special case of Newton’s Law when mass remains constant
and velocity changes.
Examples
Extension
For those of you studying mathematics and happy with differentiation you will be
understand he following:
Newton actually expressed the equation as: the rate of change in momentum of an
object is directly proportional to the applied force in the direction of that force. Or
using mathematical notation:
You should be able to derive this special case without looking at your notes
from a definition of momentum and acceleration.