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Topics to be learn :
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Understanding Force in Everyday Life :
- Muscular effort required to move or stop objects.
- Push, hit, or pull actions required to alter motion.
- Force concept based on these actions.
Force : A push or pull acting on a body is known as force.
Force cannot be seen but it can be judged only by the effects which it produces in various bodies around us.
Effects of force :
- A force can move a stationary body.
- A force can stop a moving body.
- A force can change the direction and speed of a moving body.
- A force can change the shape and the size of a body.
Balanced and Unbalanced Forces :
Forces are of two types, (i) Balanced force (ii) Unbalanced force
(i) Balanced Forces : When the net effect produced by a number of forces acting on a body is zero, then the forces are said to be balanced forces.
- Balanced forces can only bring a change in the shape of the body.
Example : A block of wood is placed on a horizontal surface and two strings X and Y are connected to it as shown in figure. The block is in a state of rest.
If we pull X and Y strings with equal magnitude of forces, then the block does not change its state of rest. Such type of forces are known as balanced forces.
Balanced forces do not change
- The state of rest
- The state of motion
Example: In a game of tug of war, when both the teams apply similar forces from both sides, rope does not move either side, i.e. resultant force is zero. Hence, it is a balanced force.
(ii) Unbalanced Forces : When the net effect produced by a number of forces acting on a body is non-zero, then the forces are said to be unbalanced forces.
A boy wants to relocate the refrigerator in his house as shown in the figure.
Example : Some children try to push a box on a rough floor as shown in the figure.
- If they push the box with a small force, the box does not move because of friction acting in a direction opposite to the push [Fig. (a)]. This friction force arises between two surfaces in contact; in this case, between the bottom of the box and floor’s rough surface. It balances the pushing force and therefore the box does not move.
- In Fig. (b), the children push the box harder but the box still does not move. This is because the friction force still balances the pushing force.
- If the children push the box harder still, the pushing force becomes bigger than the friction force [Fig. (c)]. There is an unbalanced force. So the box starts moving.
In the above example, there is an unbalanced force which causes motion in the box. The unbalanced forces cause a change in the state of rest or in uniform motion of a body.
Example: In a tug of war, when one of the teams suddenly releases the rope, then an unbalanced force acts on the other team, due to which they fall backward.
- If an unbalanced force is applied on a moving object, there will be a change either in its speed or in the direction of its motion.
- Thus, to accelerate the motion of an object, an unbalanced force is required.
An object maintains its motion under the continuous application of an unbalanced force. E.g. We have to pedal again and again, to keep the bicycle in motion.
Resultant Force : The resultant force of a number of forces acting on a body
is a single force which produces the same effect as produced by all the individual forces taken together.
Case I : When two forces acting in same direction then the resultant force is the net force.
Case II : When two forces acting in opposite directions :
- If the two forces are equal in magnitude, then the resultant force will be zero because the opposite forces cancel each other out.
- If the two forces are not equal in magnitude, then the resultant force will be in the same direction as the force with the larger magnitude and will have the magnitude equal to the difference between the magnitudes of the two forces.
First Law of Motion :
Newton's Laws of Motion : Newton, inspired by Galileo's ideas on object motion, developed three fundamental laws known as Newton's laws of motion.
Newton's First Law of Motion : Newton's First Law of Motion states that an object remains in its state of rest or uniform motion along a straight line path unless an external force is applied, meaning all objects resist change in their state
The state of any object can be changed by applying external forces only.
Examples :
- A person standing in a bus falls backward when the bus starts moving suddenly. This happens because the person and bus both are in rest while the person is not moving. As the bus starts moving, the legs of the person start moving along with bus, but rest of the portion of his body has tendency to remain in rest. Because of this, person falls backward if he is not alert.
- A person standing in a moving bus falls forward, if driver applies brakes suddenly.
Inertia and Mass :
Inertia : The natural tendency of an object to resist a change in their state of rest or uniform motion along a straight line is called inertia of the object. It is the inherent property of all the objects. Newton's first law of motion is also known as law of inertia.
- Inertia of an object is measured by its mass.
- It is directly proportional to the mass. It means that inertia increases
- with increase in mass and decreases with decrease in mass.
- A heavy object will have more inertia than lighter one.
Types of Inertia : Inertia is divided into three types as given below
(i) Inertia of rest : The tendency of a body to resist (oppose) any change in its state of rest is known as inertia of rest.
Examples :
- When a bus suddenly starts moving forward, then the passengers in the bus fall backward.
- The carpet is beaten with a stick to remove the dust particles.
- When a tree is vigorously shaken, then some of the leaves fall from the tree.
(ii) Inertia of motion : The tendency of a body to resist (oppose) any change in its state of uniform motion is known as inertia of motion.
Examples :
- The passengers fall forward when a fast moving bus stops suddenly.
- A person falls forward while getting down from a moving bus or train.
- A luggage is usually tied with a rope on the roof of a bus.
(iii) Inertia of direction : The tendency of a body to oppose any change in its direction of motion is known as inertia of direction.
Examples :
- When a fast moving bus takes a turn on the curved road, then passengers fall away from the centre of the curved road.
- The sparks produced during sharpening of a knife against a grinding wheel leave tangentially to its rim.
- A stone tied to string is whirling in a horizontal circle. If the string breaks, then the stone flies away tangentially.
Momentum :
- Momentum measures the quantity of motion possessed by a body. It was introduced by Newton.
- It is defined as the product of mass and velocity of the body. Besides magnitude, momentum also has a direction.
- At any instant, its direction is the same as the direction of the velocity.
- If a body of mass m moves with a velocity v, then momentum p is given by p = mv
- The SI unit of momentum is kg-m/s.
- If a body is at rest, its velocity, v = 0 and so momentum p = 0.
Second Law of Motion :
Newton’s second law of motion states that, the rate of change of momentum is directly proportional to the applied force and the change of momentum occurs in the direction of the force.
Mathematical Formulation Of Second Law Of Motion :
Suppose an object of mass, m is moving along a straight line with an initial velocity, u. It is uniformly accelerated to velocity, v in time, t by the application of a constant force, F throughout the time, t.
Initial momentum of the body p1 = mu
Final momentum of the body p2 = mv
Change in the momentum of the body = mv − mu
Rate of change of momentum of the body = \(\frac{\text{Change in the momentum of body}}{time\,interval}\)
= \(\frac{mv-mu}{t}= \frac{m(v-u)}{t}\) = ma …..( ∵ a = \(\frac{v-u}{t}\) )
Now, according to Newton’s second law of motion,
Rate of change of momentum ∝ force
∴ ma ∝ F
∴ F = kma, where k is a constant of proportionality ….(1)
By defining unit force as that force which produces unit acceleration in a unit mass, we have,
F = 1 unit. If m = 1 unit and a = 1 unit
1 unit = k x 1 unit x 1 unit
k = 1
Substituting k = 1 in Eq. (1), we get.
F = ma
Force = mass x acceleration
This equation is known as the force equation or the equation of motion.
Force is a vector quantity. Its SI unit is the newton (N) and CGS unit is the dyne.
1 N = 1 kg-m/s2, 1 dyne = 1 g.cm/s2
Applications of Newton's Second Law of Motion
The following applications are based on Newton's second law of motion
(i) A cricket player (or fielder) moves his hands backward while catching a fast cricket ball.
- By pulling his hands backwards, the fielder increases the time over which the ball's momentum is brought to zero.
- If the time increases, the force experienced by the hands decreases, because
Force = \(\frac{\text{Change in the momentum of body}}{time\,interval}\)
- This reduces the impact on the hands and lowers the risk of injury or the ball bouncing out.
(ii) During athletics meet, athletes doing high jump and long jump land on foam or a heap of sand to decrease the force on the body for comfortable landing.
Newton's First Law from Mathematical Expression of Second Law
It can be stated from mathematical expression of second law of motion.
As we know,
F = ma = \(\frac{m(v-u)}{t}\)
∴ Ft = mv - mu
From this equation, if F = 0, then v = u for any value of time. This means that, in the absence of an external force, the object will continue moving with uniform velocity u throughout the time t and if u is zero, then v will also be zero, i.e. the object will remain at rest.
Impulse :
It is termed as the total impact of force acting for time t. This is equal to the change in momentum of the body. In other words, impulse is defined as the product of force and a small time in which force act.
According to Newton's second law, F = ma =
∴ Ft = mv - mu
Impulse, I = Ft = p2 - p1
or Impulse = Change in momentum
The SI unit of impulse is N-s or kg-m/s.
Third Law of Motion :
Every action force has an equal and opposite reaction force which acts simultaneously.
Explanation:
- When one object applies a force on another object, the latter object also simultaneously applies a force on the former object.
- The forces between two objects are always equal and opposite.
These action and reaction forces are equal in magnitude and opposite in direction. These forces may not produce accelerations of equal magnitudes. This is because each force acts on a different object, that may have a different mass.
Action and reaction forces are equal and opposite.
Q. When a bullet is fired from a gun, the gun recoils. Explain why.
- Before the bullet is fired, both the bullet and the gun are at rest. Hence, their total momentum is zero. When the bullet is fired, it acquires momentum due to motion.
- According to the law of conservation of momentum, the total final momentum of the gun and the bullet must be equal to their total initial momentum which is zero. Therefore, the gun acquires momentum equal in magnitude and opposite in direction compared to the bullet and recoils.
Applications of Newton's Third Law of Motion :
- Collision of Two Persons: Two individuals collide due to opposing forces in action and reaction.
- Walking of a Person: The ground pushes the person backward, enabling them to move forward.
- Recoil of Gun: A bullet from a gun also pushes the gun in the opposite direction.
- Propulsion of a Boat: The oar and water push the boat forward, resulting in equal force applied in both directions.
- Rocket Propulsion: The rapid burning of fuel produces hot gases, moving the rocket upwards due to equal and opposite reaction force.