moment of the force

UNIVERSITY OF HARGEISA 2014

CABDIRISAAQ

AFGAAB

2/23/2014

PHYSICS

UNIVERSITY OF HARGEISAUNIVERSITY OF HARGEISAUNIVERSITY OF HARGEISAUNIVERSITY OF HARGEISA

Faculty of engineering

Assignment Title: momentum and collision

By: AFGAAB 2

Name: ___________________________________________

Class: ___________________________________________

ID: _____________________________________________

Deadline: ___________________________________________




By: AFGAAB 3

CONTENTS

1. Definition and over view of the momentum

and collision.

2. Formulae

3. Drawing and figures

4. In collision of a cars how injuries of

passenger can be reduced




By: AFGAAB 4

Introduction of momentum

Figure (1)

� Momentum

� Momentum is product of objects, mass and velocity of particle.

It is a vector quantity directed through the particle in the directed of motion.

The linear momentum of a body or of a system of particles is the vector sum of

the linear moment of the individual particles.

If a body of mass M is translated with a velocity V, its momentum is MV, which

is the momentum of particle of mass M at the centre of gravity of body.

The momentum which depends on the mass and the velocity.

Momentum= mass × velocity

(kg) (m/s)

P P P P = m × × × × v




By: AFGAAB 5

Example

Figure (2)

Calculate the momentum of a bus of mass 2000kg travelling 5ms-1?

Solution

Given

M=2000kg

V=5ms-1

P P P P =?

P P P P = m × × × × v

2000kg×5ms-1

=10000kgms-1 or 10000Ns



Title: momentum and collision

6

Momentum and Newton’s Second Law

The importance of momentum, unlike the importance of energy, was recognized early in the development of classical physics. Momentum was deemed so important that it was called the “Newton actually stated his The net external force equals the change in momentum of a system divided by the time over which it changes. Using symbols, this law is

Where Fnet is the net external force,

change in time.

Law of conservation of momentumThe law of conservation states that when two or more bodies act upon one another, their total momentum remains constant, provided no external force are acting.

Applying the law of conservation of momentum to a collision of mass

travelling at u1 and u2 before collision, and

Momentum before collision=Momentum after collision

If the two bodies travel on coupled to gather with a common velocity




By: AFGAAB


The importance of momentum, unlike the importance of energy, was recognized early in the development of classical physics.

deemed so important that it was called the “quantity of motionNewton actually stated his second law of motion in terms of momentum:

external force equals the change in momentum of a system divided by the time over which it changes. Using symbols, this law is

Fnet = ∆p

∆t, is the net external force, ∆p is the change in momentum, and

Law of conservation of momentumThe law of conservation states that when two or more bodies act upon one another, their total momentum remains constant, provided no external force are acting.

Applying the law of conservation of momentum to a collision of mass

before collision, and v1 and v2 after collision:


If the two bodies travel on coupled to gather with a common velocity




AFGAAB


The importance of momentum, unlike the importance of energy, was recognized early

quantity of motion.” terms of momentum:-

external force equals the change in momentum of a system divided by the time

is the change in momentum, and ∆t is the

Law of conservation of momentum The law of conservation states that when two or more bodies act upon one another, their total momentum remains constant, provided no external force are acting.

Applying the law of conservation of momentum to a collision of mass m1 and m2, after collision:


If the two bodies travel on coupled to gather with a common velocity v.




By: AFGAAB 7

Conservation of Momentum

Momentum is an important quantity because it is conserved. Yet it was not conserved in the examples in Impulse and Linear Momentum and Force, where large changes in momentum were produced by forces acting on the system of interest. Under what circumstances is momentum conserved? The answer to this question entails considering a sufficiently large system. It is always possible to find a larger system in which total momentum is constant, even if momentum changes for components of the system. If a football player runs into the goalpost in the end zone, there will be a force on him that causes him to bounce backward. However, the Earth also recoils —conserving momentum—because of the force applied to it through the goalpost. Because Earth is many orders of magnitude more massive than the player, its recoil is immeasurably small and can be neglected in any practical sense, but it is real nevertheless. Consider what happens if the masses of two colliding objects are more similar than the masses of a football player and Earth—for example, one car bumping into another, as shown in Figure (3) on next page . Both cars are coasting in the same direction when the lead car (labeled m2) is bumped by the trailing car (labeled m1). The only unbalanced force on each car is the force of the collision. (Assume that the effects due to friction are negligible.) Car 1 slows down as a result of the collision, losing some momentum, while car 2 speeds up and gains some momentum. We shall now show that the total momentum of the two-car system remains constant.




By: AFGAAB 8

Figure (3)

Impulse Impulse is product of force and time interval over which it act.

Impulse of constant force F, of the force and the time t for which it act. If the force

varies with time, the impulse is the integral of the force with respect to the time during

which the force acts. In either case, impulse of force equals the change of

momentum produced by it. An impulsive force is one that is very large but acts

only for a very short time; it can be represented by a DIRAC FUNCTOIN.




9

1. Two stationary rocks of mass 100kg and 200kg respectively are held together.

An explosion between the rocks pushes then apart with no less of mass.

velocity of the 100kg

rock after the explosion.

Given

Before

m1=100kg m

m2=200kg

u1=0

u2=0

0=100(4) + 200(v2)

200v2=-400

V2=-2m/s




By: AFGAAB

Example

Two stationary rocks of mass 100kg and 200kg respectively are held together.

An explosion between the rocks pushes then apart with no less of mass.

velocity of the 100kg rock after the explosion is 4m/s. Find the velocity

rock after the explosion.

Solution

After

100kg m1=100kg

=200kg m2=200kg

=0 v1=4m/s

v2=?




AFGAAB

Two stationary rocks of mass 100kg and 200kg respectively are held together.

An explosion between the rocks pushes then apart with no less of mass. The

rock after the explosion is 4m/s. Find the velocity of 200kg




10

Introduction of




By: AFGAAB

Introduction of collision

� Collision

Figure (4)




AFGAAB

)

Figure (5)




11

� A collision is thought of as being one of three kinds

1. Elastic collision

unchanged after the collision, none bein

nuclear

particle is scattered without exiting or breaking up the struck nuclear.

This formula:

2. Inelastic collision (or Inelastic collision of the first kind):

the total kinetic energy

some other form of energy increased.

Figure




By: AFGAAB

Figure

A collision is thought of as being one of three kinds

Elastic collision: - One in which the total kinetic energy of transl

unchanged after the collision, none being translated into other forms. In

nuclear physics, an elastic collision is the one in which the incoming


This formula:

Inelastic collision (or Inelastic collision of the first kind):

the total kinetic energy of translation is decreased by

some other form of energy increased.

Figure (7)




AFGAAB

Figure (6)

One in which the total kinetic energy of translation is

g translated into other forms. In

physics, an elastic collision is the one in which the incoming


Inelastic collision (or Inelastic collision of the first kind):- One in which

of translation is decreased by the collision while




By: AFGAAB 12

3. Superelastic collision (or inelastic collision of the second kind):- One in

which the total kinetic energy of translation is increased by the collision

while some other form of energy decreased.

In all kind of collision total energy, mass, momentum, and angular momentum are conserved.

Figure (8)

Figure (9) Figure (10)




By: AFGAAB 13

Figure (11)

Figure (12)

Figure (13)




14

1. A 3kg mass with velocity 4m/s collides with stationary any 2kg mass. After

impact, the 3kg mass continue indirection at 2m/s. The 1kg mass moves at 6m/s

in the same direction as the 3kg mass. Is this an

collision?

given

KE before

m1=3kg

m2=1kg

u1=4m/s

u2=0

1/2(3) (4)2 + 1/2(1) (0)2 =

24j + 0j = 6j + 18j

24j = 24j

It was the elas




By: AFGAAB

Example

A 3kg mass with velocity 4m/s collides with stationary any 2kg mass. After


in the same direction as the 3kg mass. Is this an example of elastic or inelastic

Solution

KE after

m1=3kg

m2=1kg

v1=2m/s

v2=6m/s

= 1/2 (3) (2)2 + 1/2 (1) (6)2

24j + 0j = 6j + 18j




AFGAAB

A 3kg mass with velocity 4m/s collides with stationary any 2kg mass. After


example of elastic or inelastic




By: AFGAAB 15

moment of the force

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