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Submitted to: Engr. Junaid Sb.

Submitted By: Group # 02

Name Roll No.Muhammad Usama Nawab BT-14202

Zahid Iqbal BT-14204

Badar-Ul-Mustafa BT-14206

Ali Hussnain BT-14208

Muhammad Asad BT-14210

Muhammad Azam BT-14212

TOPIC

Application of Impulse Momentum Equation

There are situations in which force acting on an object is not constant, but varies with time.

Two new ideas: Impulse of the force and Linear momentum of an object

Impulse-Momentum Theorem

Impulse = MomentumConsider Newton’s 2nd Law

and the definition of acceleration

Units of Impulse: Units of Momentum:

NsKg x m/s

Momentum is defined as “Inertia in Motion”

Impulse – Momentum Relationships

Definition of ImpulseThe impulse J of a force is the product of the average force and the time interval during which the force acts:

tFJ =

Impulse is a vector quantity and has the same direction as the average force.

SI Unit of Impulse: newton.second (N.s)

Impulse UnitsJ = F t shows why the SI unit for impulse is the Newton · second. There is no special name for this unit, but it is equivalent to a kg · m /s.

proof: 1 N · s = 1 (kg · m /s2) (s) = 1 kg · m /s{

Fnet = m a shows this is equivalent to a newton.

Therefore, impulse and momentum have the same units, which leads to a useful theorem.

Definition of Linear Momentum:The linear momentum p of an object is the product of the object’s mass m and velocity v: p=mv Linear momentum is a vector quantity that points in the same direction as the velocity.SI Unit of Linear Momentum: kilogram. Meter/second(kg.m/s)

tvv

a t

0

amF

tmvmv

tvv

mF tt 00 )(

Impulse-Momentum Theorem

When a net force acts on an object, the impulse of this force is equal to the change in momentum of the object:

0)( mvmvtF f

Impulse Final momentum

Initial momentum

Impulse=Change in momentum

Impulse-Momentum Equation for ParticlesLinear, not Angular, Momentum: In this section, we deal with linear momentum (mv) of particles only. Another section of your book talks about linear(mvG) and angular(IGω) momentum of rigid bodies.

An Integrated Form of F=ma : The impulse-momentum (I-M) equation is a reformulation—an integrated form, like the work energy equation—of the equation of motion, F=ma.

Particle Impulse-Momentum EquationImportant! This is a Vector Equation!

mv1 + ∫Fdt = mv2

Initial Linear Momentum =mv1

Final Linear Momentum= mv2

Impulse = ∫Fdt

Derivation of the Impulse-Momentum EquationTypical Eqn of Motion: = m

Sub in = : = m

If mass is changing: (e.g. for a rocket...) (Newton wrote it this way...)

Net Force = time rate of change of momentum

= (m)

Separate variables: dt =md

dt =dSet up integrals:

Integrate: dt =m2 - m1

Usual form: m1 +dt = m2

“Impulse” vs. “Impulsive Force”

Particle Impulse-Momentum Equation

mv1 + ∫Fdt = mv2

Impulse = Area under Force-time curve = Any force acting over any time.... e.g. 100 lb. for two weeks....Impulsive Force: A relatively large force which acts over a very short period of time, like in an impact, e.g. bat-on-ball, soccer kick, hammer-on-nail, etc.

Initial Linear Momentum =mv1

Impulse = ∫Fdt

Final Linear Momentum= mv2

e.g. 1000 lb. acting in a 0.01 sec impact

Impulsive Force

Impulse= ∫Fdt

or 10 N actingfor 1 second... Non-Impulsive Force

F

t

Area under F-t curve= 10 lb-sec= Impulse

F

tArea under F-t curve= 10 N-sec= Impulse

Applications of the Impulse-Momentum Equation For any problems involving F, v, t: The impulse momentum equation

may be used for any problems involving the variables force F, velocity v, and time t. The IM equation is not directly helpful for determining acceleration, a, or displacement, s.

Helpful for impulsive forces : The IM equation is most helpful for

problems involving impulsive forces. Impulsive forces are relatively large forces that act over relatively short periods of time, for example during impact. If one knows the velocities, and hence momenta, of a particle before and after the action of an impulse, then one can easily determine the impulse. If the time of impulse is known, then one can calculate the average force Favgthat acts during the impulse.

For problems involving graph of F vs. t: Some problems give a graph of Force vs. time. The area under this curve is impulse. Important: You may need to find t start for motion!

Various Forms of the Impulse-Momentum Equation

Various Forms of the I-M Equation

Force During Impact:

t

F

0

Actual Force

FAVG

∆t

Often Modeled as

Impulse = Area under curve... =dt =FAVG ∆t

General Form: m1 +dt = m2

If force F is constant:

m1 + AVG t = m2

Know vectors v2 and v1:dt= m2 - m1 = m(2 - 1)

If force F is constant:AVG∆t= m2 - m1 = m(2 - 1)

Impulse produces change in

momentum

THAN

K YOU