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# Linear Momentum and Collisions Elastic Properties of Solids. Lecture 5

## 1.

1Lecture 5

Linear Momentum and Collisions

Elastic Properties of Solids

## 2.

YouTube Link to lecture 5https://youtu.be/Ug97oHED854

## 3.

3Linear Momentum and Collisions

## 4.

Linear Momentum4

Is

defined to be equal to the mass of an

object times its velocity.

p = mv

Momentum is a vector quantity.

The vector for linear momentum points in the

same p direction as the velocity v.

S.I unit of momentum : Kg . m/s

## 5.

5Linear Momentum

The relationship between m & v

Huge ship moving at a small velocity

P = Mv

High velocity bullet

P = mv

## 6.

Linear MomentumThe relationship between m & v

6

Example :

A 10,000 kg truck moving at 2 m/s has a linear momentum

of 20,000 kg.m/s ,while a 80 kg bicyclist moving at 2 m/s

has a linear momentum of 160 kg m/s.

The truck has a much larger linear momentum even though

both are moving at the same velocity.

It is easier to bring the bicyclist to a stop than it is to bring

the truck to a stop.

Similarly, it is easier to stop a bicyclist moving at 2 m/s

than a bicyclist moving at 5 m/s.

## 7.

7Collision & linear

momentum

The types of collision

• Elastic collision

• Inelastic collision

Momentum of the system is conserved

in all collisions, but kinetic energy of the

system is conserved only in elastic collisions.

## 8.

In elastic collision: both momentum and kinetic energy of the system are conserved.In inelastic collision: momentum is conserved BUT kinetic energy is not conserved.

Ref. https://www.physicstutorials.org/pt/44-Collisions

## 9.

9Collision & linear

momentum

Another way to compare linear momentum

is to consider a collision.

If a boy is running at you at full steam and hits you,

you'll probably be knocked down but will still be okay.

However, if a truck is coming at you at the same speed

and hits you, you will be hurt badly.

In this example, the boy has much less linear momentum

than the larger truck.

## 10.

10Conservation of momentum

Whenever two or more particles

in an isolated system (frictionless, no loss of

energy) interact,

the total momentum of the system remains

constant.

total linear momentum before = total linear momentum after

## 11.

Linear Momentum andIts Conservation

11

If an object's velocity is changing with time,

its linear momentum is changing. We have

dp/dt = d(mv)/dt

If the mass of the object is constant then

dp/dt = mdv/dt = ma

We write

dp/dt = F = ma

* If the force F = o , That means linear momentum is constant.

This is a more general statement of Newton's second law

which also holds for objects whose mass is not constant.

## 12.

12Example : The Archer

Let us consider the situation

proposed at the beginning of this

section. A 60-kg archer stands at

rest on frictionless ice and fires a

0.50-kg arrow horizontally at 50 m/s.

With what velocity does the archer

move across the ice after firing the

arrow?

## 13.

13Example : Conservation of

momentum

## 14.

Linear Momentum andIts Conservation

14

Quick Quiz 9.1 Two objects have equal kinetic

energies. How do the magnitudes of their momentum

compare?

(a) p1 > p2

(c) p1 < p2

(b) p1 = p2

(d) not enough information to tell.

## 15.

15Linear Momentum and

Its Conservation

## 16.

## 17.

Elastic Properties of SolidsAll objects are deformable

when external forces act on them.

That is,

it is possible to change the shape or the size

(or both) of an object by applying external forces.

## 18.

Elastic Properties of SolidsStress

is the external force acting on an object per unit

cross-sectional area.

Stress = F \ A

is a quantity that is proportional to the force

causing a deformation.

The unit of Stress in SI system is ……….

The result of a stress is strain, which is

a measure of the degree of deformation.

## 19.

Elastic Properties of SolidsThe result of a stress is strain, which is

a measure of the degree of deformation.

Strain is proportional to stress. ( Strain Stress )

The constant of proportionality ( ) is called

the elastic modulus.

## 20.

Elastic Properties of SolidsThe types of an elastic modulus :

1.

Young’s modulus, which measures the

resistance of a solid to a change in its length.

2.

Shear modulus, which measures

the resistance to motion of the planes

within a solid parallel to each other.

3., which measures the resistance of solids or fluids

to changes in their volume.

## 21.

Elastic Properties of SolidsThe elastic modulus:

Is defined as the ratio of the stress to

the resulting: strain.

Elastic modulus = stress / strain

The elastic modulus relates what is done to a solid object (a force is

applied) to how that object responds (it deforms to some extent).

## 22.

Elastic Modulush

Young’s modulus is defined as :

Tensile stress: the ratio of the magnitude of the

external force F to the cross-sectional area A.

Tensile strain: in this case the ratio of the change

in length ΔL to the original length Li.

## 23.

Elastic Modulush

Young’s modulus is defined as :

The unit of young ‘s modulus is the ratio of

that for force to that for area. ( N \ m2 )

## 24.

hThe elastic limit

The elastic limit of

a substance is defined

as the maximum stress

that can be applied to

the substance before it

becomes permanently

deformed and does not

return to its initial

length.

## 25.

Another type of deformation occurs when an object is subjectedto a force parallel to one

of its faces while the opposite face is held fixed by another

force.

## 26.

Shear stress: ratio of the tangential force to the area A of the face being sheared.Shear strain: ratio Δx/h, where Δx is the horizontal distance that the sheared face

moves and h is the height of the object.

The unit of shear modulus is

the ratio of that for force to that for area.

## 27.

Volume stress: ratio of magnitude of total force F exertedon a surface to the area A of the surface.

P = F/A is called pressure. If it changes by an amount ΔP

= ΔF/A, then the object will experience a volume change

ΔV.

Volume strain: is equal to the change in volume ΔV

divided by the initial volume Vi.

## 28.

The unit of bulk modulus isthe ratio of that for force to that for

area.

Note that both solids and liquids have

a bulk modulus. However, no shear

modulus and no Young’s modulus are

given for fluids. ( Why )

## 29.

Answer:Because a liquid does not sustain a shearing

stress or a tensile stress.

If a shearing force or a tensile force is applied to

a liquid, the liquid simply flows in response.

## 30.

Homework1. Can a bullet have the same momentum as a truck?

Explain.

2- Two materials, A and B, are used to make cables of

identical cross section and length, to lift identical loads.

If A has a greater Young’s Modulus than B, which cable

will stretch the most when loaded? Explain why.