Concept of Impulse and Momentum
Impulse
Impulse is the change of momentum of an object when the object is acted upon by a force for an
interval of time. So, with impulse, you can calculate the change in momentum, or you can
use impulse to calculate the average impact force of a collision.
Explanation:
If you've ever kicked a ball, hit a punching bag, or played sports that involved any kind of ball,
you have been using the concept of impulse without even knowing it. So what exactly is impulse,
and what does it have to do with any of those situations?
Before we can define impulse, we need to talk about the concept of momentum. Momentum is a
measure of strength and a measure of how difficult it is to stop an object. An object that is not
moving has zero momentum. A slow-moving, large object has a large momentum. A fastmoving, small object also has a large momentum. For example, if a ping-pong ball and a bowling
ball have the same velocity, then the bowling ball has a greater momentum because it is more
massive than the ping-pong ball.
This is the formula for momentum:
In this formula, Momentum (p) equals Mass (m) times Velocity (v). Momentum is a vector
which is equal to the product of mass and velocity (which is also a vector).
But how is momentum related to impulse? When a force acts on an object for a short amount of
time, impulse is the measure of how much the force changes the momentum of an object.
The formula for impulse looks like this:
Because impulse is a measure of how much the momentum changes as a result of force acting on
it for a period of time, an alternative formula for impulse looks like this:
This formula relates impulse to the change in the momentum of the object. Impulse has two
different units, either kilogram time’s meters per second (kg m/s) or Newton times seconds (Ns).
Example:
In this example, we'll look at the impulse for an object that collides with a wall and stops after the
collision. If the 2.0 kg object travels with a velocity of 10 m/s before it hits the wall, then the impulse
can be calculated.
Δ p = pf- pi
Δ p = m vf- m vi
Δ p = (2.0 kg)(0 m/s) - (2.0 kg)(10 m/s) = -20 kg m/s
Momentum:
Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving,
then it has momentum - it has its mass in motion. The amount of momentum that an object has is
dependent upon two variables: how much stuff is moving and how fast the stuff is moving.
Momentum is a commonly used term in sports. A team that has the momentum is on the
move and is going to take some effort to stop. A team that has a lot of momentum is really on the
move and is going to be hard to stop. Momentum is a physics term; it refers to the quantity of
motion that an object has. A sports team that is on the move has the momentum. If an object is in
motion (on the move) then it has momentum. Momentum can be defined as "mass in motion."
All objects have mass; so if an object is moving, then it has momentum - it has its mass in
motion. The amount of momentum that an object has is dependent upon two variables: how
much stuff is moving and how fast the stuff is moving. Momentum depends upon the
variables mass and velocity. In terms of an equation, the momentum of an object is equal to the
mass of the object times the velocity of the object.
Momentum = mass • velocity
In physics, the symbol for the quantity momentum is the lower case p. Thus, the above equation
can be rewritten as
p=m•v
where m is the mass and v is the velocity. The equation illustrates that momentum is directly
proportional to an object's mass and directly proportional to the object's velocity.
The units for momentum would be mass units times velocity units. The standard metric unit of
momentum is the kg•m/s. While the kg•m/s is the standard metric unit of momentum, there are a
variety of other units that are acceptable (though not conventional) units of momentum.
Examples include kg•mi/hr, kg•km/hr, and g•cm/s. In each of these examples, a mass unit is
multiplied by a velocity unit to provide a momentum unit. This is consistent with the equation
for momentum.
Example:
1. A semi-truck full of logs has a large mass and must slow down long before a stop light
because even with a small velocity, it has a large momentum and is difficult to stop.
2. A four-wheeler moving at a relatively fast velocity has a smaller momentum than the semitruck because of its small mass and will stop much faster.
3. A bullet, although small in mass, has a large momentum because of an extremely large
velocity.
Law of Conservation of momentum:
The law of conservation of linear momentum states that if no external forces act on the system of
two colliding objects, then the vector sum of the linear momentum of each body remains
constant and is not affected by their mutual interaction.
Alternatively, it states that if net external force acting on a system is zero, the total momentum of
the system remains constant.
Proof:
Let us consider a particle of mass ‘m’ and acceleration ‘a’. Then, from 2nd law of motion,
If no external force acts on the body then, F=0,
Therefore, ‘P’ is constant or conserved.
(Note: If the derivative of any quantity is zero, it must be a constant quantity.)
Deduction of Law of Conservation of linear momentum for two colliding bodies
Let us consider two bodies of masses m1 and m2 moving in straight line in the same direction
with initial velocities u1 and u2. They collide for a short time ∆t. After collision, they move with
velocities v1 and v2.
From 2nd law of motion,
Force applied by A on B = Rate of change of momentum of B
FAB = (m2v2-m2u2)/∆t
Similarly,
Force applied by B on A = Rate of change of momentum of A
FBA = (m1v1-m1u1)/∆t
From Newton’s 3rd law of motion,
FAB = -FBA
Or, (m2v2-m2u2)/∆t = -(m1v1-m1u1)/∆t
Or, m2v2-m2u2 = -m1v1+m1u1
Or, m1u1 + m2u2 = m1v1 + m2v2
This means the total momentum before collision is equal to total momentum after collision. This
proves the principle of co conservation of linear momentum.