Application Of Impulse Momentum Equation

From Rana Muhammad Usama Nawab
For Public

1. Presentation of H ydraulic Machinery

2. Submitted to: Engr. Junaid Sb. Submitted By: Group # 02

3. 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

4. TOPIC

5. Application of Impulse Momentum Equation

6. 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

7. Impulse-Momentum Theorem

8. Impulse = Momentum Consider Newton’s 2 nd Law and the definition of acceleration Units of Impulse: Units of Momentum: Ns Kg x m/s Momentum is defined as “Inertia in Motion”

9. Impulse – Momentum Relationships

10. Definition of Impulse The impulse J of a force is the product of the average force and the time interval during which the force acts: J = Impulse is a vector quantity and has the same direction as the average force. SI Unit of Impulse: newton . second (N . s)

11. Impulse Units J = F t shows why the SI unit for impulse is the Newton · s econd. There is no special name for this unit, but it is equivalent to a kg · m /s. proof: 1 N · s = 1 ( kg · m /s 2 ) (s) = 1 kg · m /s { F net = m a shows this is equivalent to a newton. Therefore, impulse and momentum have the same units, which leads to a useful theorem.

12. 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 )

13. 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: Impulse Final momentum Initial momentum Impulse=Change in momentum

14. Impulse-Momentum Equation for Particles Linear, 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 Equation Important! This is a Vector Equation! mv 1 + ∫ Fdt = mv 2 Initial Linear Momentum =mv 1 Final Linear Momentum= mv 2 Impulse = ∫ Fdt

15. Derivation of the Impulse-Momentum Equation Typical 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 = d   Set up integrals: Integrate: dt =m 2 - m 1   Usual form: m 1 + dt = m 2  

16. “Impulse ” vs . “Impulsive Force” Particle Impulse-Momentum Equation mv 1 + ∫ Fdt = mv 2 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 =mv 1 Impulse = ∫ Fdt Final Linear Momentum= mv 2 e.g. 1000 lb. acting in a 0.01 sec impact Impulsive Force Impulse= ∫ Fdt or 10 N acting for 1 second... Non-Impulsive Force F t Area under F-t curve = 10 lb -sec = Impulse F t Area under F-t curve = 10 N -sec = Impulse

17. 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.

18. 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!

19. Various Forms of the Impulse-Momentum Equation Various Forms of the I-M Equation Force During Impact: t F Actual Force F AVG ∆t Often Modeled as Impulse = Area under curve... = dt   =F AVG ∆t General Form: m 1 + dt = m 2   If force F is constant: m 1 + AVG t = m 2   Know vectors v 2 and v 1 : dt= m 2 - m 1 = m( 2 - 1 )   If force F is constant: AVG ∆t = m 2 - m 1 = m( 2 - 1 )   Impulse produces change in momentum

20. THANK YOU