## Machines: Mechanical Advantage, Velocity Ratio and efficiency formula

Machines

A machine is a device that makes work to be done easier and faster. It uses a basic concept of applying effort to overcome load.

## Liquid expansion: Real and apparent expansion, cubic expansivity.

Expansion of liquid; Real and apparent expansivity

Like solid, liquid expands on heating and contracts on cooling, because liquid is always held in a container, the expansion of liquid is always complicated because of the expansion of the container itself.

## Physics: Anomalous Expansion of Water

This means something that is unusual. The temperature range of water from 0°C to 4°C is unlike most substance because is volume decreases as the temperature increases.

## Principles of Expansion: Advantages,Bimetallic strip, Uses in Electric iron, Fire alarm and thermostat

Expansion of objects

The expansion of an object is the process of increasing in size, amount or number. It is relative, when we tall about expansivity

## What is electricity?

The is a form of energy that occurs when electrons flows through a conductor.

### Areas Covered

• Definition of static electricity
• Nature of atoms of static electricity
• Electricity charges
• Law of charges
• Conductor and insulator

### Definition of static electricity

Static electricity is  produced by the friction between two materials. For example, when rod is rubbed with silk.

## Physics: Introduction to radioactivity,types and properties.

It is a spontaneous emission of radiation from a substance usually an unstable   .This process is also known as nuclear or radioactive decay). In the year 1896, Henri Becquerel a French scientist working with phosphorescent materials discovered that a uranium compound placed on a photographic plate which was covered with light black paper causing the plate to be exposed by blackening the pate itself. This implied that some sort of radiation was coming from the uranium which could pass through. The material was radioactive given-off radiation. Other scientists that researched on radioactivity were;v This radioactivity was spontaneous with the radiation being omitted without anything causing it apparently.

### Types of radioactivity

From several experiments that have been carried out, it has shown that there are three different types of radioactive emission called;
Alpha particles ; whose emission is easily stopped by paper or thick card
Beta particles ; whose emission is easily stopped by aluminium sheet of different thickness and are negatively charged.
Gamma particles ; whose emission is easily stopped by thick sheet of lead.

#### Properties of alpha particles

1)  Alpha rays are deflected by magnetic field.
2)      The direction of deflection of alpha rays shows that they are positively charged
3)      They are relatively massive and so have more momentum and tend to continue in their direction of travel.
4)      Alpha particles are absorbed by paper and air and are easily stopped aluminium thin sheet.
5)      They have little penetrating power, travelling no more than 5cm. Being large, it is soon stopped by air molecules.
6)      They are capable of stripping electrons from their atoms because alpha particles have comparatively large mass and momentum.

#### Properties of beta particles

1)      There are also deflected by magnetic field but in the opposite direction to alpha particles.
2)      The direction of deflection of beta rays shows that they are negatively charged with –e .
3)      They are relatively light and as a result easily deflected.
4)      They are deflected by different amount showing that they have varying speed..
5)      They have good penetrating power of about 1 metre.
6)      They can penetrate a few millimetre of aluminium.
7)      They produce less ionisation in air than alpha particles.

#### Properties of gamma rays

1)      They are electromagnetic waves similar to light wave but of very short wavelength.
2)      They are electrically uncharged since they are not deflected by a magnetic field.
3)      They are highly penetrative compared to the other two types and can only be stopped by thick lead blocks.
4)      They have high penetrating power compared to the other two types.
5)      They have much less ionisation than alpha rays.

## Expansivity

This is defined as amount a material expands or contracts per unit length, per-degree change in temperature.
The addition of heat will usually cause expansion of the body. during expansion, the dimension of the body increases.

## Physics: Equations of Motion, derivation, Questions and solutions

In my last article, The definition and types of Motion were discussed. Now this is an article to better understand Equations of motion with several questions solved.

Related Terms

• Displacement: It is the distance moved in a specified direction. It is a vector quantity.
• Distance: It is the magnitude of separation between two points. It is a scalar quantity.
• Speed: It is the rate of change of distance with time. It is a scalar quantity.
• Velocity: It is the rate of change of displacement with time. It is a vector quantity.
• Acceleration: It is the increasing rate of change of velocity with time. It is a vector quantity.
• Retardation: It is the decreasing rate of change of velocity with time.

Equations of motion

1) 2) 3) 4) Derivation

Average speed = s/t

(V+u)/2 =s/t

where, V =final velocity
U = Initial velocity
S = Distance
T = time
Make "s" subject of the formula. ..........(1)

Average acceleration= change in Velocity/time

a = (v-u)/t

at = (v-u)

V = U + at ...........(2)

Substitute (2) in (1)

S =[ (u + at +u)/2]t.

S =[(2u+at)/2]t ........(3)
From (2)

V = u + at
t =(v-u)/a

Substitute the value of t in (1)

S = (v+u)/2 x (v-u)/a  .....(4)

Question 1:
A car travels with a uniform velocity of 30m/s for 5s and then comes to a rest in the next 10s with a uniform deceleration.
Find,
a) deceleration
b) total distance travelled.

Solution,
a) using, V = u + at
Deceleration= -a
0 = 30m/s - a(10)
10a = 30
a = 3m/s/s

b) Let, "Stage A" be the period before          deceleration.
"Stage B" be the period after deceleration.

At Stage A,

U= 30m/s
t1= 5s
S1= Distance travelled at stage A  ?
Using,
From the V-T graph,
Initial Velocity (U) = S1/T1

S1 = ( 30 x 5) m

S1 = 150 m

At Stage B,

U= 30 m/s
V = 0
T2 = 10s
S2 = Distance travelled at stage B ?

Using, 0 = (30)(30) + 2(-3)(s2)

900 = 6(s2)

S2 =150m

Total distance travelled (S) = S1 + S2

S = (150 + 150) m/s

S = 300m.

Question 2:
A bus moves from rest with an initial acceleration of 2m/s^2 for the first 10 s. It then accelerates at a uniform rate of 1m/s^2 for another 15s. It continues at a constant speed for 70s and finally comes to a rest in 20s by a uniform deceleration. From the graph calculate.
I)Total distance travelled
II) Average speed for the journey
III) Average retardation as it is brought to rest.
IV) Maximum speed attained by the motion.

Solution,

From the V-T graph

I).  for the first 10s,
U= 0

a = 2m/s/s

t1 = 10s

Velocity (V)= u + at

V = 0 + (2)(10)
V = 20m/s
Distance (S1) = [(v +u)/2] t

S1 = [ (20 +0)/2] x 10

S1 = [10 x 10] = 100m

For the second 15s
U= 20m/s

t2 = 15s
Velocity (v)  = ( 20 + 15) m/s
V = 35 m/s

Distance (S2) = [(v +u)/2] t

S2 = [ (35 +20)/2] x 10

S2 = [41.25 x 10] = 412.5m

For the third 70s,
V = constant at 35m/s
t3 = 70s

V =  S3/t3

S3 = (35 x 70) m

S3 = 2450m

For the last 20s (Retardation or deceleration).

V = 0

U = 35m/s

t4 = 20s

S4 = [(v +u)/2] t4

S2 = [ (0 +35)/2] x 20

S2 = [35 x 10] = 350m

Total distance travelled(S)= S1 + S2 + S3 + S4

S = [ 100 + 412.5 + 2450 + 350]

S = 3312.5m

II) Average velocity =  S / T

T = [ 10 + 15 + 70 + 20] s

T = 115s

V = 3312.5/115 = 28.8 m/s

Average velocity spent for the journey = 28.8m/s

III) Average Retardation = (v-u)/t4

V = 0
U = 35m/s
AR = (0 - 35)/20
AR = 1.75 m/ s (square)

Average Retardation as it's brought to rest = 1.75m/s^2

Motion under gravity
Motion under the influence of gravity is based on acceleration due to gravity(g)  of a free falling object and  +/- g sign conventions.

Formula   Question 1
A cricket ball is thrown vertically upwards with an initial velocity of 40m/s . Find,
I) it's velocity after 3s
II) Maximum height attained and the time it
III) The total time taken for the ball to return to the ground again.

Solution,

I) V = u - gt
V = 40 - 10 (3)
V = 40 -30 = 10m/s

II) using, V = 0
U = 40m/s
g = 10m/s/s
From formula,

(40)(40) = 2 (10) h

1600 = 20 h

h =80 m Therefore,
80 = 40t -  5t^2 ( it is now a quadratic equation)

16 =  8t - t^2

t^2 - 8t + 16 = 0

(t - 4)(t - 4) = 0

t = 4s

Conclusion

## Physics: All about Acceleration due to gravity (g)

### Acceleration due to gravity

Acceleration due to gravity (g) is known when a free falling object from a certain is attains a final velocity. Then take g=9.81m/s/s because this will give you a more accurate answer.The second decimal place in this numerical value are dependent primarily upon on altitude, that is why g = 9.8m/s/s sometimes. Take it as 9.8 or 10m/s/s if you are given in the question.

## Motion

This is the change in the position of a body in respect to time. It also involves how things move and what makes them to move.

## Physics: Fundamental, derived quantity, Units, and Dimensions.

Fundamental Vs Derived quantity

Fundamental quantities

These are independent quantities with units. The dimension of a physical quantity indicates how it is made up in terms of S.I base quantity.

In other words, the physical quantities is said to have been expressed in terms of fundamental units [Length (L), Mass (M), Time (T), kelvin (k), mole etc].

Quantity Dimension

length         L
Mass          M
Time           T
Kelvin        K
Mole          m

Derived quantities:

These are obtained by some simple combinations of the fundamental quantities and units.

They are thus, dependent on the fundamental quantities and units. Example of the derived quantities, their derivation and their units are summarised in the table below:

 Derived quantity Derived unit Dimension Area  (length x breadth) m^2 L^2 Volume(length x breadth x height) m^3 L^3 Density (Mass/volume) kg/m^3 M/L/L Velocity (Displacement/time) m/s L/T Acceleration (Velocity/time) m/s/s L/T/T force (Mass x acceleration Newton (N) ML/T/T Energy & work (force x distance). joules ML^2/T/T power (work/time) joules/s ML^2/T/T/T Momentum (Mass x velocity) kg m/s ML/T Pressure  (force/area) N/m^2 ? Frequency (no of oscillation/time) 1/s 1/T

Watch video

Example

What is the dimension of EMF?

EMF(Electromotive Force) is a derived quantity. It is work done by the chemical force to move unit positive charge from negative terminal to positive terminal of the battery.
EMF = Workdone / charge
Work=Force * displacement
=MLT^-2 * L =ML^2T^-2
Charge=Current * time
=IT
Now,
Dimensional formula of
EMF=Work/charge
=ML^2T^-2 / IT
=ML^2T^-3I^-1

Exercise:

What is the dimension of pressure?

Solution
Watch how to derive the dimension of Pressure.

Conclusion

A  derived quantity is derived from fundamental quantity, simple and short. I hcomments article was helpful. If you have any questions or comments, please don't hesitate to write it in the comments section. All comments are appreciated.