What is Impulse?
An impulse is the sum of a force, F, over the period of time it acts, t. Since force is a vector quantity, impulse also belongs to this category. When an object receives an impulse, it experiences an equivalent vector change in its linear momentum and also in the direction that results.
SI unit: newton-second (N⋅s) (kg⋅m/s in SI base units)
Other units: pound⋅s
What is Momentum?
The sum of a particle's mass and velocity is known as momentum. Momentum has a magnitude and a direction because it is a vector quantity. The second law of motion of Isaac Newton states that the force acting on a particle is equal to the time rate of change of momentum.
For example,
If a football game ends in a tie, each team is given a certain number of penalty shots. As a result, when the player kicks the ball, which is at rest and has no momentum, to shoot for the goal, the momentum increases due to the development of velocity. This sudden change in momentum causes an impulsive force to be generated. The impulsive force assists the ball in traveling long distances in a short amount of time.
The impulse is a large force that acts for a very short period of time. It is represented by J
The Impulse Formula is expressed as
J=F×t
Where,
- The applied force is denoted as F.
- The time interval during which force is applied is denoted by the symbol t.
Impulse can also be defined as the rate of change of momentum.
J=m×v
Where,
- The body's mass is denoted as m.
- The velocity with which the body moves is denoted by v.
Velocity is expressed as
v=vf – vi
Where,
- The initial velocity is denoted by vi.
- The final velocity is denoted as vf.
As a result, the Impulsive force is expressed as
f=mvf−vit
The impulsive force is articulated in Newton(N) and the impulsive force is articulated in Kgms-1.
Equation of Impulse Momentum
The following equation can be used to calculate Impulse:
J = m * Δv
To put it simply,
Impulse = mass (m) * (Velocity2-Velocity1)
- There are two points in time where velocity1 and velocity2 represent different speeds of movement. This is referred to as velocity change.
We can calculate the unit of impulse using the above equation:
Mass = in kg
Velocity = in m/s
J = kg . m/s or N.s
Solved Examples
Q1.After a free fall from a height, a 5-gram ball lands on the ground. Gravitational acceleration, g = 10 ms-2. The ball has a velocity of 6 ms-1 before colliding, and it is reflected upright at 4 m/s after the collision. Determine the impulse.
Ans:
Mass of the ball (m) = 5 gm = 0.005 kg
Before collision, velocity of ball (vo) = -6 m/s
After collision, velocity of ball (vt) = 4 m/s
The plus and minus signs indicate that the direction before the collision is opposite the direction after the contact.
Since we need to find out Impulse (J), so the solution will be
Impulse (J) = Total change in momentum (Δp)
J = Δp = m * vt – m * vo
= m * (vt – vo)
J = (0.005)(4 – (-6)) = (0.005)(4 + 6) = (0.005)(10) = 0.05 N.s (Ans.)
Q2. A batter hits a straight ball at the bowler while maintaining its initial 12 m/s speed. If the ball's mass is 0.15kg, calculate the impulse transferred to it.
Ans: Given vi (Initial Velocity) = 12 m/s
vf (Final Velocity) = -12m/s
m (mass) = 0.15kg
Impulse is articulated as J = m * vf – m * vi
= m (vf – vi)
= 0.15 Kg (-12 -12) m/s = -3.6N.s
So, impulse = -3.6N.s (Ans.)