Lesson 5 Week2

8/13/2019 Lesson 5 Week2

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Lesson 5 & 6: Momentum and Newtons Laws

Contents:

Newtons Second and Third Law

Momentum

Centre of Mass

Introduction

When an object travels at faster speed it can causes more damage to a colliding object.Similarly an object of a larger mass can also causes more damage even the velocity is the

same. This difference comes because of difference in momentum.

Momentum

Momentum is the product of mass and velocity. The SI unit of momentum is kgm/s.

Momemtum = mass velocity

Example:! trolley of mass "# kg has a velocity of $# m/s% calculate the momentum.

Momentum = mv = "#kg $#m/s = "## kgm/s

Newtons Second Law of Motion

The rate of change of momentum of an object is directly proprtional to the force acting%

and takes place in the direction in &hich the force acts.

Force Rate of Change of momentum

Force Change of momentum

Time

F m! " mu

t&here ' is resultant force% m is mass of the object% v final velocity% u is initial velocity

and t is time taken for the change in velocity.


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' = m (v)u*

t

Force mass x acceletation (second form of ne&ton+s second la& of motion*Therefore kgm/s is the derived unit of force. The base unit is ,.

$, = $kgm/s

Impulse

#mpulse Ft m!$mu(change of momentum*

Example

T&o forces act on an object. ! force of -#, left and #, right. If the mass of the objet is

$#kg% calculate the acceleration.

esultant 'orce = #)-# = 0#,

a = '/m = 0#, / $#kg = 0 m/s0

1ample

! space rocket has a mass

Law of Conservation of momentum

When t&o or more objects act on each other% their total momentum remains constant%provided no eternal forces are acting.

Elastic and Inelastic Collison

!n elastic collisionis a collision &here the both the momentum and the kinetic energy

are conserved.

In an inelastic collisionthe momentum is conserved but the kinetic energy is not.

Collsision

1ample

! trolley of mass 0kg has a velocity of 0m/s. It collides a stationary of 0 kg mass. !fter

the collision both the trolleys stick togetherand move in a common velocity. 'ind this

velocity.


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Total momentum before = Total momentum after

(m$u$* 2 (m0u0* = (m$2 m0*v(0 kg 0 m/s* 2 (kg # m/s* = (0 kg 2 kg*v

- kg m/s = 3 kg v

v = 3/-

= #." m/s

Example

! 0 kg trolley travels right at avelocity of 0m/s and clides a trolley of mass kg &ith a

velocity of -m/s left. Then they both travel together at a common velocity. 'ind this

velocity and their direction.


(m$u$* 2 (m0u0* = (m$2 m0*v(0 kg 0 m/s* 2 (kg )- m/s* = (0 kg 2 kg*v

- kg m/s )0- kgm/s = 3 kg v

)0# kg m/s = 3 kg v


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v = )0#/3

v =)0." m/s

The velocity of the trolley is 0." m/s left

Explosion

Example

! Troley of mass 0 kg and trolley of mass kg are attached together. 0 kg trolleycontains a spring loaded piston% held in place by a pin. When the pin is realeased.

0 kg trolley moves left &ith a velocity of 0 m/s. 'ind the velocity of kg trolley thatmoves right.


(m$2 m0*v = (m$u$* 2 (m0u0*

(0 k 2 kg* # = ( 0 kg )0 m/s* 2 ( kg u0*

# = ()- kg m/s* 2u0u0 = -

u0 = -/

u0 = #.4 m/s

5elocity of the trolley is #.4 m/s right.

Newtons !ird Law

#f o%&ect ' exerts a force on o%&ect ( then o%&ect ( will exert an e)ual %ut opposite force

on o%&ect '* +To e!er, action there is an e)usl %ut opposite reaction-


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Centre of Mass

The mass of an o%&ect acts as if it is concentrated at a single point called the centre of

mass +centre of gra!it,-*

'or regular object centre of mass is same as the geometrical centre

'or object to be in e6uilibrium and to be stable the &eight acting vertically through thecentre of mass must pass through the base.

! is stable% 7 is unstable% 8 is neutral

"ctivit#:

9sing a lamina% a pin and a plumb line find centre of mass of a rectangle &ith length $#

cm and &idth 3 cm.


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:ractice ;uestions

$uestion %

$uestion

$uestion '

$uestion (


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$uestion 5

$uestion 6

! trolley of mass 0 kg rests net to trolley of mass kg on a flat table. When a springloaded piston on one trolley is realeased% the trolleys are pushed apart. The lighter trolley

travels at m/s.

a* What is the momentum of each trolley

Lesson 5 Week2

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