Mechanics and properties of Matters/Motion of objects
Exploring the properties of Matters
In this chapter: Discuss on Motion, Equation of motion and graphical representation of displacement and velocity.
Mechanics is the study of motion of objects.
MOTION:
When a body changes its position with respect to something else as time goes on, we say the body is in motion. Mechanical motion is of two types, translation (linear) and rotational (Spin) . The motion of a car on a road is translation where as the motion of a top, spinning on its axis is rotational.
SPEED: THE SPEED OF A MOVING BODY IS THE RATE AT WHICH IT COVERS DISTANCE, i.e. the distance it covers for unit of time.
Speed = distance travelled / time required
The SI unit of speed is metre/ second . Speed is a scalar quantity.
Velocity:
The distance covered by an object in a specified direction in unit time interval is called velocity. The SI unit of velocity is also metre/second.
Inordinary conversation the term velocity is confused with speed. The difference between them is that speed refers only to the distance covered by a moving object whereas velocity takes into account the direction also.
For example, a motorcyclist driving his vehicle at a uniform speed of 30 km per hour on a circular track is not moving with a uniform velocity since his direction is continuously changing. Velocity is a vector quantity.
Acceleration:
The velocity of a body changes due to change in its speed or direction or both. The rate of change of the velocity of a body is called its acceleration.
Acceleration= Change in velocity/ time.
As an example, latest consider a car who speed is increased from 30 km/h to 50 km/h in 2 minutes. The acceleration of the car is, then, = (50-30)/(1/30) here 2 min = 1/30 hr
So acceleration= 20 x 30 =600 km/hr².
Usually the term acceleration is used when the velocity of a body increases. When the velocity decreases the body is said to undergo retardation or deceleration.
Acceleration due to gravity:
The most familiar acceleration is due to gravity. When something is dropped it does not fall with uniform velocity. A cricket ball released from the top of a tall building strikes the ground with a mass higher velocity then a ball released from the first floor. If we jump of a table, we strike the floor with greater impact than if we jump off a small stool.
The value of the acceleration due to gravity (g) on the surface of the Earth is about 9.8 m/s². The value of g is constant at a place but varies slightly with the latitude and their food changes from place to place.
Equations of Motion:
Equations of motion are very useful in solving problems. If an object, travelling with an initially velocity u, accelerates for time t with uniform acceleration a, din the final velocity v is given by
v= u+at
Example 1
A train travelling at 36 km/h accelerates uniformly initia at 2 m/s². Calculate its velocity after 5 seconds. (We must use the same units in problems.)
Initial velocity
u = 36 km/h or 10 m/s
a = 2 m/s²
t = 5 s
.. Final velocity v=u+at = 10+2×5 = 20 m/s
v = 20 m/s or 72 km/h
Example 2
A train travelling at 72 km/h decelerates uniformly at 2 m/s². How much time does it take to stop?
Initial velocity u = 72 km/h or 20 m/s
Final velocity v = 0, Acceleration a = -2 m/s²
(Deceleration or retardation is negative acceleration.)
t = (v-u)/a =( 0-20)/-2 = 10 second.
Example 3
A ball is released from a height above the ground Calculate the velocity of the ball after 5 seconds.
Acceleration due to gravity is equal to 9.8 m/s² , u=0,a=9.8 m/s², t=5s
Final velocity =u+at
=0+9.8x5= 49 m/s
Example 4
A ball is thrown vertically upwards with an initial velocity of 49 m/s. In how much time will the ball reach the maximum height? (g = 9.8 m/s²)
Velocity at maximum height = 0
Initial velocity = 49 m/s
a =-9.8 m/s²
t= (0-49 )/-9.8 =5s
The distance S travelled by an object moving with uniform acceleration a for a time t from an initial velocity u is given by
S = ut + ½ at²
Example 5
A cyclist accelerates at 1 m/s² from an initial ve- locity of 3 m/s for 10 s. Find the distance covered by the cyclist in 10 seconds.
Initial velocity= 3 m/s
Acceleration = 1 m/s²
Time = 10 s
Distance covered S = ut + ½at²
= 3 x 10+½ x 1 x 100
=30+50=80 m
Another useful equation of motion is
v²-u²= 2as , where v,u,a and s are the final velocity initial velocity acceleration and distance respectively.
Displacement - Time graph 📈
In figure 1 shows displacement time graphs of two objects, A and B. Latest first considered the straight line graph of object A. It is seen that A covers 10 cm in the first second, 20 CM in 2 seconds, 30 cm in 3 seconds and so on. In other words A covers equal distance in equal times and is there for moving with uniform velocity. Does straight line displacement time graph represents uniform velocity. Since the graph of object B is also a straight line, it is also moving with uniform velocity. However, B commerce more distance than A does in the same time. It is seen that B covers 20 CM in the first second and 40 cm in 2 seconds. Therefore, B is travelling faster than A. Does straight line graph with higher slope represents higher uniform velocity.
Figure 2 shows the displacement time graph for the motion of a stone thrown vertically upwards in the air. As the stone goes higher, it's velocity decreases continuously till a time t1 , when it research the highest point it comes to rest momentarily. The stone then starts falling with increasing velocity and heats the ground at the time t2. This displacement time graph is an example of variable velocity.
Velocity - Time graph:
Another type of graphs, Hui sar very useful for studying motion, are the velocity time graphs. Figure 3 shows a velocity time graph of an object. It can be seen from the graph that starting from the rest the object attains a velocity of 20 m per second in 4 second. From this graph we can find Acceleration of the object and distance travelled by the object in a given time. We know that
acceleration = Change in velocity/ time
= 20/4 = 5 m/s²
The distance travelled by an object moving with uniform acceleration is given by the relation
Distance= average velocity x time
Since average velocity= (0+20)/2 = 10 m/s
Distance= 10 x 4= 40 m.
Not that the area of the triangle shown shaded in the figure is also 40 m. Hints the distance travelled by the object is given by the area between the velocity time graph and the time axis. This result is true for any motion even an irregular one.
This topics may help for all the student who interested in physics and also going to exam for job specially in United States United Kingdom Canada Australia India and other countries.