Force And Laws Of Motion Class 9 CBSE Notes – Chapter 9
We do know that matter is composed of particles organized in a certain manner. While the particles in gases are well separated and may move freely, the particles in solids are closely packed, with little space for movement.
CBSE Class 9 Science notes will assist students in studying the topic thoroughly and clearly.
These CBSE Class 9 Science notes were written by subject experts who made the study material very basic, both in terms of language and format.
Any action that exerts a pull, a hit, or a push on a body is referred to as force.
Although force cannot be seen, it may be quantified by the impact it has on the many bodies around us.
Numerous effects of force are listed below:
- A force may cause a stationary object to move.
- A force may bring a moving body to stop.
- A force has the ability to alter the direction and speed of a moving body.
- A force has the ability to alter the form and size of a body.
This discussion leads to the definition of force.
Force is an external influence which changes or tends to change the state of rest or of uniform motion of an object.
The SI unit of force is Newton. It is a vector quantity.
BALANCED AND UNBALANCED FORCES
When the combined effect of many forces acting on a body is zero, the forces are said to be balanced forces.
Balanced forces can only result in a change in the body’s form.
As indicated in the image, a block of wood is put on a horizontal surface and two strings A and B are linked to it. The block is in a resting condition.
If we pull the A and B strings with equal magnitudes of force, the block maintains its resting condition. This is referred to as balanced forces.
Balanced forces have no effect on the following functions:
- The state of motion.
- The state of rest
When both teams apply equal force from both sides in a tug of war, the rope does not move on any side, i.e. the resulting force is zero. As a result, it is a well-balanced force.
- When the combined effect of many forces acting on a body is more than zero, the forces are said to be unbalanced forces.
Two persons wishes to reposition the box in his home in the manner shown in the picture.
- They pushes the box with a small force; however, the box remains fixed due to frictional force operating in the opposite direction of the push.
If they pushes the box harder, the pushing power exceeds the friction, and the box begins to move in the direction of the push, as seen in the picture.
- In the example, an unbalanced force causes the box to move. Unbalanced forces alter a body’s condition of rest or uniform motion.
When one of the teams suddenly releases the rope during a tug of war, an unbalanced force occurs on the other team, causing it to slide backwards.
When an unbalanced force is applied to a moving object, either its speed or direction of motion will change.
Thus, an unbalanced force is necessary to accelerate the motion of an object.
Newton’s Laws Of Motion
Newton investigated Galileo’s views on the motion of an object. He established three essential laws that govern how things move.
These three rules are referred to as Newton’s laws of motion, and they are as follows:
Newton’s First Law Of Motion
It implies that unless an external force occurs on an object, it will stay in its state of rest or uniform motion along a straight line route. This indicates that all things resist state change.
Any object’s state may be altered only by applying external forces.
- When a bus suddenly begins to move, a passenger falls backward. This occurs because both the individual and the bus are at rest, with the person staying motionless while the bus begins to move.
While the individual’s legs begin to move with the bus, the remainder of his body tends to stay still.
As a result, if a person is not attentive, he will fall backward.
- If the driver suddenly uses the brakes, a passenger standing in a moving bus falls forward.
The object’s unwillingness (or inability) to alter its state of rest or uniform motion along a straight line is referred to as its inertia.
It is a property that all objects possess by default. Galileo’s law of inertia is frequently referred to as Newton’s first law of motion.
The mass of an object is used to measure its inertia. The moment of inertia is proportional to the mass.
This suggests that inertia rises as mass increases and reduces as mass decreases. A heavier object will have a greater moment of inertia than a lighter object.
Types Of Inertia
Inertia is classified into three types as follows:
- Inertia Of Rest: The tendency of an organism to resist changes in its resting condition is referred to as inertia of rest.
- When a bus suddenly begins to move ahead, the passengers fall backward.
- To eliminate dust particles from the carpet, it is beaten with a stick.
- When a tree is violently shaken, some of its leaves fall.
- Inertia Of Direction: The tendency of a body to resist changes in its direction of motion is referred to as direction inertia.
- When a fast moving bus negotiates a curve in the road, passengers are pushed away from the curve’s centre.
- A stone suspended on a string spins in a horizontal circle. If the string snaps, the stone flies tangentially away.
- The sparks generated when a knife is sharpened against a grinding wheel travel tangentially to its rim.
- Inertia Of Motion: The tendency of a body to resist changes in its uniform state of motion is referred to as inertia of motion.
- When a fast-moving bus comes to a sudden stop, the passengers fall forward.
- While landing from a moving bus or train, a passenger falls forward.
- Typically, baggage is secured to the top of a bus by a rope.
- A bicycle continues its motion for sometimes even after the cyclist ceases pedalling.
- Athletes run some distance before taking a long jump. The inertia helps them to cover a longer distance.
Momentum is a quantity that describes the amount of motion possessed by a body.
It is defined as the product of the body’s mass and velocity.
Along with magnitude, momentum has a direction. At every point in time, its direction is equal to that of the velocity.
Suppose two identical trucks, one is loaded and another is empty, are moving with the same velocity.
As the momentum of the loaded truck is greater than the empty truck, thus to stop within equal distance the loaded truck requires more force than the empty one.
If a body of mass m travels at a velocity v, the momentum p is equal to, p=mv
The SI unit of momentum is kg-m/s.
Newton’s Second Law Of Motion
According to Newton’s second law of motion, an object’s rate of momentum change is exactly proportional to the applied external force and occurs in the direction of the applied external force.
Mathematical Formulation of Second Law of Motion
If a body of mass m accelerates uniformly with an acceleration a fig time t, changing its initial velocity to v, then
Initial momentum, p1=mu
Final momentum, p2=mv
Change in momentum = p2-p1=mv-mu=m(v-u)
According to the second law of motion,
force, F ∝ Change in momentumtime
F ∝P2 – P1t F ∝m(v-u)t
F ∝ ma [ ∴ (v-u )t = a ]
∴ F= kma
The quantity k is a constant of proportionality.
One unit of force is defined as the amount that produces an acceleration of 1 m/s2 on an object of 1 kg mass.
i.e. 1 unit of force = k1kg1m/s2 k=1
Thus, the force can be written as F=ma
The SI unit of force is newton, which is denoted by the symbol N and it is equivalent to kg-m/s2
Applications Of Newton’s Second Law Of Motion
Newton’s second law of motion is used in the following applications:
- While catching a fast cricket ball, a cricket player (or fielder) moves his hands backward.
- At athletic meets, athletes competing in the high jump and long jump land on foam or a heap of sand to reduce the stress on their bodies and ensure a pleasant landing.
Newton’s First Law From Mathematical Expression Of Second Law
The first law of motion may be expressed mathematically using the second law of motion’s mathematical expression.
As we know, F = ma
F = m (v-u)t [∴ a = (v-u )t ]
Ft = mv-mu
If F=0, then v=u for any time value. This indicates that if there is no external force acting on the item, it will continue to move with uniform velocity u during the period t. If u is zero, then v will also be zero, indicating that the object will stay at rest.
It is referred to as the total impact of force. This is equivalent to the body’s change in momentum.
In other terms, impulse is defined as the product of force and the shortest time period during which force acts.
According to Newton’s second law, F = ma
F = m (v-u)t [∴ a = v-u t ]
F = m (v-u)t
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.
If a large amount of force acts on a body for a very short interval of time then it is called an impulsive force.
For example, when a nail is hammered the applied large force acts for a very short time interval. Hence it is an impulsive force.
In cricket, an impulsive force is applied on the ball by the batsman.
NEWTON’S THIRD LAW OF MOTION
According to the third law of motion, anytime one object applies a force to another, the second object applies an equal and opposite force to the first object.
Thus, the magnitude and direction of action and response forces are equal. They continue to have no effect on each other since they operate on distinct things.
APPLICATIONS OF NEWTON’S THIRD LAW OF MOTION
Collision of two persons: When two people walking or running in opposing directions meet, both suffer injury as a result of the force applied to them.
Two different forces are involved in the action and response pair.
Walking of a person: Walking is possible due to Newton’s third law of motion. While walking, a person pushes the ground backward, and the ground reacts by pushing the person backward with an identical magnitude of force but in the opposite direction. This permits him to move against the push.
The recoil of gun: When a bullet is shot from a gun, it also pushes the gun in the opposite direction with equal power. Due to the fact that the gun has a bigger mass than the bullet, the gun’s acceleration is much smaller than the bullet’s acceleration.
Propulsion of a boat in forwarding direction: The sailor pulls water backward with his oar, causing the water to push the oar forward. As a result, the boat is pushed forward. The force applied by the oar and the force applied by the water is identical in magnitude but in opposing directions.
Rocket propulsion: Rocket propulsion is based on the action-reaction concept. Rapid burning of fuel produces hot gases that stream out of the rear end’s nozzle at breakneck speed. The equal and opposite reaction force accelerates the rocket upward.
Action And Reaction Cannot Cancel Out Each Other
An action and reaction pair of forces cannot exist without the presence of two bodies. They are equal and opposite.
They do not act on the same body at the same time. Hence they do not cancel each other and no question of equilibrium arises.
Law of Conservation of Momentum
Newton’s third law of motion results in the law of conservation of momentum. According to this rule, the overall momentum of a system of objects stays constant before and after their contact or collision, provided that no external unbalanced force acts on them.
Consider a system of objects with masses mA and mB travelling in the same direction with starting velocities uA and uB (where uA > uB). Following the impact, the bodies move with velocities vA and vB. The collision lasts t seconds.
Total initial momentum of the system is given by
= mA uA + mB uB
Total final momentum of the system is given by
= n2 AVA+ m BVB
To prove mA uA + mB uB = mA vA + m BVB
Proof From Newton’s third law of motion, force exerted
by mA on mB = – (force exerted by mB on mA )
from Newton’s second law,
Force, F = ma,
mB (vB – uBt)=- mA (vA – uAt)
[ ∴ acceleration, a = final velocity – initial velocitytime taken]
mB vB – mB uBt = – m AVA + m AuA t
mB vB – mB uB = – – m AVA + m AuA
or mA vA + mB vB = mAuA + mB uB
(mA uA + mBuB)
where, (mA uA + mBuB ) is the total momentum of two objects before collision and (mAvA + mBvB) is their total momentum after a collision. Thus, the total momentum of two objects is unchanged or conserved before and after the collision.
APPLICATIONS OF THE LAW OF CONSERVATION OF MOMENTUM
The following are some practical uses of the law of conservation of linear momentum:
- When a guy jumps from a boat to the shore, the boat moves slightly away from the shore in order to save momentum.
- Due to the recoil of the gun, the pistol should be gripped tightly to the shoulder when firing a round.
- Both the rocket and the jet aircraft operate on the idea of momentum conservation.
- In physics, all conservation laws, such as conservation of momentum, energy, angular momentum, and charge, are regarded as basic.
These conclusions are drawn from observations and experiments.
- It is essential to keep in mind that a conservation law cannot be proven. Experiments may be used to verify or reject it.
A conclusion that is consistent with the law validates or substantiates the law; it does not establish the law.
- On the other hand, a single experiment with a result that violates the law is sufficient to disprove it.
- From a great number of observations and tests, the law of conservation of momentum has been determined. This law dates all the way back to over three centuries.
- It’s worth noting that no situation has yet been realised that contradicts this law. Numerous common experiences may be described using the rule of conservation of momentum.
NCERT questions & answers from Force and Laws Of Motion
Which of the following has more inertia?
(a) a rubber ball and a stone of the same size?
(b) a bicycle and a train?
(c) a five-rupee coin and a one- rupee coin? (CBSE 2011, 2013)
(a) Because the mass of the stone is greater than the mass of the rubber ball, the stone has bigger inertia.
(b) A train’s inertia is greater than that of a bicycle.
(c) A coin worth five rupees has greater inertia than a coin worth one rupee.
In the following example, try to identify the number of times the velocity of the ball changes. “A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team.” Also, identify the agent supplying the force in each case.
- When the first player kicks the ball towards another teammate, the ball’s velocity changes.
- When another player kicks the football toward the goal, the football’s velocity changes as well.
- The football’s velocity also varies when the opposing team’s goalkeeper collects it.
- When the goalkeeper kicks the football toward a teammate, the ball’s velocity changes. As a result, the ball’s velocity changes four times in this scenario. In the first and second scenarios, the players’ feet provide the force. In the third situation, the goalkeeper’s hands supply the force. In the fourth example, the goalkeeper’s foot supplies the force when he strikes the football with his foot.
Why do you fall in the forward direction when a moving bus applies brakes to stop and fall backwards when it accelerates from rest? (CBSE 2011)
- When a moving bus applies brakes to stop, the lower portion of our body also comes to rest but the upper part of our body remains in motion due to inertia of motion. Hence, we fall in the forward direction.
- When a bus accelerates from rest, the lower portion of our body also comes in motion with the bus but the upper part of our body remains at rest due to inertia of rest. Hence we fall backwards.
If action is always equal to the reaction, explain how a horse can pull a cart.
Answer: The horse pushes the ground with its foot in the backward direction by pressing the ground. As a result of this force of action (i.e. backward push), the ground pushes the horse in the forward direction. Hence, the horse pulls the cart.
Explain, why is it difficult for a fireman to hold a hose, which ejects large amounts of water at a high velocity. (CBSE 2012, 2015)
Answer: A firefighter finds it difficult to maintain control of a hose-pipe that is ejecting a large amount of water at a high velocity. Because the force exerted by the stream of water coming out of the pipe in the forward direction is significant, the pipe must be reinforced. As a result of the reaction of the forward force, a force is applied to the pipe in the reverse direction of the force supplied to it. As a result, the firefighter has to work hard to maintain the hose pipe in place.
An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on the magnitude and direction of the velocity. If not, provide a reason. (CBSE 2010, 2011)
Newton’s first law of motion states that no net external force is needed to move an object with constant velocity. So an object travels with a constant velocity (non-zero) when it experiences a net zero external unbalanced force.
The magnitude of this velocity is constant and the direction is the same as in the beginning. An object may also not move at all if it experiences a net zero external unbalanced force. This is because the object may be at rest in the beginning.
When a carpet is beaten with a stick, dust comes out of it. Explain. (CBSE 2010, 2011, 2012, 2013, 2015)
When carpet is beaten with a stick, fibre of carpet comes in motion and the dust falls down due to inertia of rest.
Why is it advised to tie any luggage kept on the roof of a bus with a rope? (CBSE 2010, 2011, 2013)
When the bus suddenly stops, luggage may roll down and fall from the roof of the bus due to inertia of motion if not tied with a rope.
Using a horizontal force of 200 N, we intend to move a wooden cabinet across a floor at a constant velocity. What is the friction force that will be exerted on the cabinet?
Answer: The cabinet will move with constant velocity, if net external force acting on it is zero. Since a horizontal force of 200 N acts on the cabinet in the forward direction, therefore, net external force acting on it will be zero if frictional force of 200 N acts on it. Thus frictional force = 200 N will be exerted on the cabinet.
Two objects, each of mass 1.5 kg are moving in the same straight line but in opposite directions. The velocity of each object is 2.5 m s-1 before the collision during which they stick together. What will be the velocity of the combined object after collision
Let the two objects are A and B.
Mass of object A, m1 = 1.5 kg
Mass of object B, m2= 1.5 kg
Velocity of object A before collision, u1 = 2.5 m s-1
Velocity of object B before collision, u2 = -2.5 m s-1
Total momentum of objects A and B before collision = m1u1 + m2u2 = 1.5 x 2.5 – 1.5 x 2.5 = 0
Mass of combined object after collision = (m1 + m2) = 3.0 kg
Let, velocity of combined object after collision = V m s-1
∴ Total momentum of combined object after collision = (m1 + m2)V = (3V) kg m s-1
According to the law of conservation of momentum :
Momentum after collision = Momentum before collision 3V = 0 or V = 0