Impulse is a concept of physics that involves the study of dynamics, especially momentum. It expresses the effect of forces on the objects of motion over some time. Well, here is a simple guide that can help the students understand the formula of impulse and its applications.
Impulse is conventionally defined as the change in momentum an object undergoes, due to a force applied for some duration. It is a quantity, essentially, measuring the effect of a force on the state of an object's motion.
The formula for impulse (J)
J=F⋅Δt
where:
J is the impulse,
F is the average force applied,
Δt is the time interval over which the force is applied.
Impulse can also be said as the rate of change of momentum.
J=m×v
Where,
The mass of the body is taken as m
The velocity with which the body moves is given as v.
Velocity is given as
v=vf-vi
Where,
Initial Velocity is defined as vi
Final Velocity is defined as vf.
Hence, the Impulsive force is expressed as
Impulse is expressed in Kgms-1 and Impulsive force is expressed in Newton(N).
The formula of Impulse-momentum is obtained from the impulse-momentum theorem, which states that the alteration in momentum of an object is equal to an impulse applied to the object. The formula is expressed as:
Impulse-momentum formula:
J=Δp
When the mass is constant:
FΔt=mΔv
When the mass is varying:
Fdt=mdv+vdm
Since the SI unit of impulse and momentum are the same, thus it is expressed as Ns=kg.m.s-1
Following are some questions on impulse:
Problem 1: A batsman sends the ball straight back in the direction from where it was sent from without changing the initial speed of 12 m/sec. If the ball has a mass of 0.15kg. Find the impulsive delivered to the ball?
Solutions:
Given:
vi (Initial Velocity) = 12 m/s,
vf(Final Velocity) = -12m/s,
m (mass) = 0.15kg,
J (Impulse) =?
Impulse is expressed as
Problem 2: A golfer hits a ball of mass 45g at a speed of 40m/s. The golf club is in contact for 3 s with the ball. Find out the average force applied by the club on the ball.
Answer:
m (Mass)= 0.045 kg,
vi (Initial Velocity) = 0,
vf (Final Velocity) = 40m/s,
Impulse force F = ma =
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