Mechanics is the science of motion. It deals with the speed, velocity, acceleration, force and energy of large objects such as cars, aeroplanes and tiny objects such as the electrons in your television set. Mechanics also helps to investigate the motion of athletes or the motion of a ball bowled in cricket or hit in golf.
If an objects moves, we are interested in how fast it moves, that is its speed. If the speed of the object changes with time, we are also interested in how much it changes with time, that is, the acceleration. Before we can fully understand why an object moves, we must be able to describe its motion precisely.
# Distance and Displacement:
1. Distance: Distance is the total length covered by a moving object irrespective of the direction of motion, that is, only the magnitude is of importance.
The SI unit of distance is the unit of length i.e. meter (m).
2. Displacement: Displacement is the distance measured in a straight line (linear distance) and in a specified direction so both magnitude and directions are important.
SI unit of displacement is also meter (m).
For example: Suppose a car travels 5 km due east and makes a U-turn back to travel a further distance of 3 km.
Find (a) the distance covered, (b) the displacement.
Soln: (a) distance covered = 5+3 = 8 km
3 km
E
O A
5 km
(b) Displacement = 5 – 3 = 2 km due east of the starting point o.
# Speed and Velocity:
1. Speed:
Speed is defined as the rate of change of distance. In other words, speed is the distance moved per unit time. It tells us how fast or slow an object is moving.
In symbols,
Where, v = speed
d = distance moved
and t = time taken
Most of the objects do not move at constant speed. For example, a train starts from rest at a station, moves faster and faster until it reaches a constant speed and then slows down to a stop at the next station. It is therefore more useful to define average speed
Thus, average
In symbols,
The common units for speed are meter per second (m/s) and kilometer per hour (km/hr).
The SI unit of speed is ms-1
1 km = 1000m and 1h = (60 ) s = 3600 s
Therefore, 1 km/hr =
Exercise: 1 An athlete ran a distance of 100 meters in 9.83 seconds. What was his average speed?
2. Velocity :
Velocity is defined as the rate of change of displacement. It is speed in a specified direction. When you are asked for the velocity of an object, you have to state the speed of the object and the direction it is traveling.
similarly, as in the case of average speed, we have
A body moving at a constant velocity moves at a constant speed in a straight line (that is both speed and direction are constant).
The units of velocity are the same as the units of speed.
Uniform velocity : A body is said to move with uniform velocity if its rate of change of distance moved with time in a specified direction is constant.
# Acceleration :
An object whose velocity (not speed) is changing is said to be accelerating. In other words, if the direction and/or the speed of a moving object change(s), the object is accelerating. Thus, if an object is moving at a constant speed but changes its direction as it moves (such as whirling a stone attached to a string) or if an object is moving in a straight line, but changes its speed as it moves (such as in a 100 m sprint), both objects are accelerating.
Acceleration is defined as the rate of change of velocity.
In symbols,
Where, a = acceleration
v = change in velocity
v = final velocity
u = initial velocity
and t = t = time interval or time taken.
Like velocity, acceleration has a direction. The direction of acceleration is the direction of change in velocity. Acceleration is regarded as positive if the velocity is increasing and negative if the velocity is decreasing. Negative acceleration is usually called a deceleration or retardation.
# Uniform acceleration:
A body is said to move with uniform acceleration if its rate of change of velocity with time is constant.
The SI unit for acceleration is meter per square of second, i.e. m/s2.
Acceleration due to gravity : The rate of change of velocity of a freely falling body under the influence of gravitational force is called the acceleration due to gravity.
An object thrown vertically upward is retarded or slowed down at the same rate.
Relation among the displacement velocity and acceleration:
v = u ± at
s = ut ± at2
v2 = u2 ± 2as
Fill in the blanks
1. Velocity has information on both speed and
2. The of and object is the same on earth and far away from it.
3. When a runner leaves the starting line and increases speed , the runner
4. When an object falls in vacuum its does not change
Exercise: 2: A bus starts from rest and achieves a velocity of 20 m/s in 10 s while moving
westwards from a starting point O. Calculate its average acceleration.
E v =20m/s u=0m/s
O
Exercise: 3: A car traveling eastwards at 30 m/s suddenly comes to a halt in 5s. Find its average acceleration (retardation). u = 30 m/s v = 0 m/s
t = 0 t = 5s
Exercise : 4 What is the speed, in km/hr, of a truck that travels 15 kilometers in 15 minutes at a constant speed?
Exercise : 5 Sound travels a speed of 330 meters per second. How long does it take of the sound of thunder to travel 1485 meters?
Exercise : 6 When traveling westward along a highway, a driver slows down from 24 meters per second to 15 meters per second in 12 seconds. What is the driver’s acceleration?
Exercise : 7 One car accelerates from rest to 50 km /hr in 4 s and a second car accelerates from rest to 80 km/hr in 8 s. does the faster car have larger acceleration?
Exercise : 8 A stone is thrown is thrown vertically upwards with an initial velocity of 14 m/s. neglecting air resistance , find (a) the maximum height reached; (b) the time taken before it reaches the ground. [ acceleration due to gravity g = 9.8 m/s2]
Exercise : 9 A car travels at a uniform velocity of 20 m/s for 5 s. The brakes are then applied and the car comes to rest with uniform retardation in a further 8 s. How far does the car travel after the brakes are applied?
Exercise : 10 A car starts from rest and is accelerated uniformly at the rate of 2 m /s2 for 6 s. It maintains a uniform velocity for 15 s. The brakes are then applied and the car comes to rest with uniform retardation in a further 8 s. (a) find the maximum speed reached in km/h and (b) the total distance covered in meters?
# Mass and Weight:
1. Mass: The mass of a substance is the quantity of matter contained in the substance. It depends on the number of atoms it contains and the size of those atoms. It is the basic property of the substance and cannot be changed by the location, shape and the speed of the body (speed less than the speed of light).
The unit of mass is kilogram.
2. Weight: If we take an object of, 1 kg into outer space, well away from the earth, it will become weightless. However, its mass – being the amount of substance in it – will still be 1 kg.
When it is brought back to earth, the earth exerts a gravitational attraction on the object. This gravitational pull on the object is known as the weight. We also say that the object is in the gravitational field of earth. The gravitational field is a region in which a mass experiences a force due to gravitational attraction.
The gravitational field strength, g, is defined as gravitational force acting per unit mass on an object. On earth’s surface the gravitational field is approximately 10N/kg, i.e. a 1 kg object on earth’s surface has force of 10 N pulling on it due to earth. On the other hand, the same 1 kg object on the Moon only experiences a gravitational pull of 1.6 N. hence we say that the gravitational field strength on the Moon is 1.6 N/kg.
Since, weight, W is the gravitational force acting on an object, we then have,
where, m is the mass of the object,
g is the gravitational field strength.
Weight is measured in Newton (N) which is the unit of force.
