Force and Motion
Category : 9th Class
Force and Motion
Motion
The body that is in motion changes its position with time. Therefore, a body is said to be in motion when its position changes continuously with respect to a stationary object taken as a reference point.
Car in motion
Distance
The distance travelled by a body is the actual length of the path covered by a moving body irrespective of the direction in which body travels.
Displacement
When a body moves from one position to another position, the shortest distance between initial and final position of the body along with the direction is known as its displacement.
The actual length of the path travelled to reach R, starting from P is PQ + QR = 8 + 6 = 14 km. So, 14 km is the distance travelled by a person.
The shortest distance from P to R is 10 Km, which is the displacement from P to R in north direction.
Scalar Quantity
A physical quantity having only magnitude or size is known as scalar quantity. It does not have direction. For example, distance.
Vector Quantity
A physical quantity having magnitude or size and direction is known as vector quantity. For example, displacement.
Types of Motion
The following are the different types of motion:
Uniform Motion
If a body travels equal distance in equal intervals of time, no matter how small these time intervals are then it is called uniform motion.
Distance - time graph for a body having uniform motion
Non Uniform Motion
If a body travels unequal distance in equal intervals of time then it is called non uniform motion.
Distance - time graph for a body having non uniform motion
Speed, Velocity and Acceleration
Speed
The distance travelled by a body per unit time is called speed.
Speed = Distance / Time taken
The S.I. unit of speed is metre per second (m/s).
Example:
Bus travels a distance of 200 km in 8 hours, then calculate the speed of the bus.
Solution:
Speed = 200 km/B hours
Speed = 25 km/h
Average Speed
The average speed of a body is the total distance travelled divided by the total time taken to cover this distance.
\[\text{Average}\,\text{speed}\,\text{=}\,\,\frac{\text{Total}\,\text{distance}\,\text{travelled}}{\text{Total}\,\text{time}\,\text{taken}}\]
Note:
(i) When the distance travelled in two cases is same, then
\[{{\text{V}}_{\text{av}}}\,\text{=}\,\,\frac{\text{2}{{\text{V}}_{\text{1}}}{{\text{V}}_{\text{2}}}}{{{\text{V}}_{\text{1}}}\text{+}{{\text{V}}_{\text{2}}}}\]
(ii)When time taken in two cases is same, then
\[{{\text{V}}_{\text{av}}}\,\text{=}\,\,\frac{{{\text{V}}_{\text{1}}}\text{+}{{\text{V}}_{\text{2}}}}{\text{2}}\]
Example:
A bus travels 40 km at a uniform speed of 40 km/h and the next 40 km at a uniform speed of 20 km/h. Find the average speed.
Solution:
The time taken to travel the first 40 km is:
Time taken = 40/40 = 1 h
The time taken to travel the next 40 km is:
Time taken = 40/20 = 2 h
Total distance travelled is
Total time taken is 1 h + 2 h = 3 h
average speed = 80/3 = 26.66 km/h
Velocity
Velocity is the speed of an object with the specification of its direction of motion.
\[\text{Velocity = }\frac{\text{Distance}\,\text{travelled}\,\text{in}\,\text{a}\,\text{given}\,\text{direction}}{\text{Time}\,\text{taken}}\]
\[\text{Average velocity = }\frac{\text{Initial}\,\text{velocity}\,\text{+}\,\text{Final}\,\text{velocity}}{\text{2}}\]
\[\text{Vav = }\frac{\text{u+v}}{\text{2}}\]
Where u = initial velocity of a moving body.
v = final velocity of a moving body.
Acceleration
The rate of change of velocity with time is called acceleration. The S.I. unit of acceleration is m/\[{{s}^{2}}\]
\[\text{Acceleration}\,\text{=}\,\frac{\text{Change}\,\,\text{in}\,\,\text{velocity}}{\text{Time}\,\text{taken}\,\text{to}\,\text{change}}\]
Or
\[\text{Acceleration}\,\text{=}\,\,\frac{\text{Final}\,\text{velocity}-\text{Initial}\,\text{velocity}}{\text{Time}\,\text{taken}\,\text{to}\,\text{change}}\]
So, \[a=\frac{v-u}{t}\]
Example: A driver increases the speed of a bus from 10 m/s to 20 m/s in 5 seconds. Find the acceleration of the car.
Solution: \[a=\frac{v-u}{t}\]
\[a=\frac{20-10}{5}=\frac{10}{5}=2m/{{s}^{2}}\]
The bus accelerates by \[2m/{{s}^{2}}\]
Retardation
When the velocity of a body decreases with time its acceleration is negative. Negative acceleration is also called retardation.
Equations of Motion
The first equation of motion is given by \[v=u+at,\]
Where, v = final velocity, u = initial velocity, a = acceleration, t = time taken. This equation gives the velocity acquired by a body in time t.
The second equation of motion is given by \[s=ut+\frac{1}{2}a{{t}^{2}}\]Where, s = distance travelled, u = initial velocity, t = time and a = acceleration. It gives the distance travelled by the body in time t.
The third equation of motion is given by \[{{v}^{2}}-{{u}^{2}}=2as\]
Where, v = final velocity, u = initial velocity, a = acceleration and t = time taken. It gives the velocity acquired by the body in travelling a distance.
Graphical representation of motion
Distance-time graph for non-uniform speed
Distance-Time Graphs
Distance-time graph for uniform speed
Force
A push or pull on a body is called force. The direction in which a body is pushed or pulled is called the direction of force. For example, opening and closing a door. Force can be used for various purposes such as pushing, pulling, twisting, lifting, throwing, etc.
There are two types of forces. They are the following:
Balanced forces: If the resultant of all the forces acting on a body is zero, the forces are called balanced forces. When balanced forces are applied on a body, it does not change its position of rest motion and it appears as if no force is acting on it.
Unbalanced forces: If the resultant of all the forces acting on a body not zero, the forces are called balanced forces. The unbalanced force can produce a change in the position of a body.
Effects of Force
The following are the effects of force:
(i) Force can move a stationary object or stop a moving object.
(ii) Force can change the speed and direction of a moving object.
(iii) Force can change the shape and size of an object.
Newton’s Law of Motion
Newton, the great physicist, has given three laws of motion. These laws are known as Newton’s laws of motion.
First Law of Motion
An object remains in the state of rest or in uniform motion along a straight line until and unless it is compelled by an external force to change its state of rest or of uniform motion.
Second Law of Motion:
The rate of change of momentum of an object is proportional to the net force applied on the object. The direction of the change of momentum is the same as the direction of the net force.
\[Force=\alpha \]Change in momentum/Time taken
\[Force=Mass\times Acceleration\]
\[F=m\times a\]
Third Law of Motion
Whenever one body exerts a force on another body, the second body exerts an equal and opposite force on the first body. In other words, we can say that to every action there is an equal and opposite reaction.
Inertia
Inertia is that property of a body due to which it resists a change in its state of rest or of uniform motion. In other words, mass is the measure of the inertia of a body. If a body has more mass then it has more inertia.
Momentum
The momentum of a body is defined as the product of its mass and velocity.
\[Momentum=Mass\times velocity\]
\[P=m\times v\]
Example: What is the momentum of a vehicle of mass 200 kg moving with uniform velocity 4 m/s?
Solution: \[momentum=200\times 4=800kg\]m/s
Application of Newton’s Laws of Motion
First Law of Motion
When a car or bus starts suddenly the passengers fall backward. The reason is that the passengers tend to remain in the state of rest, even when the car or bus starts moving. When a running car or bus stops, suddenly the passengers are jerked forward because they tend to remain in their state of motion. Also when a bus turns at a corner sharply, the passengers tend to fall sideways because of their tendency to continue moving in a straight line.
Second Law of Motion
Catching a cricket ball: A fielder moves his hands backward after catching a cricket ball just to prevent any injury to the hands. A fast moving ball has large momentum. To stop this ball, its momentum has to be reduced to zero. When a fielder moves back his hands on catching the fast ball, the time taken to reduce the momentum of ball to zero is increased. Due to more time taken to stop the ball the rate of change of momentum of ball is decreased and hence a small force is exerted on the hands of the fielder.
Fast moving ball coming towards a fielder and fielder moves is hand back on catching the ball to reduce movement
Third Law of Motion
Walking: When we walk on the ground, our feet push the ground backward and in return the ground pushes our feet forward. The forward reaction exerted by the ground on our feet makes us walk forward.
Law of conservation of linear momentum:
If the net external force on a system of particles is zero, the linear momentum of the system remains constant.
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