CLASS 9 Chapter : 9 Force and Laws of Motion
Chapter: 9 Force & Laws of Motion
Introduction:
For many centuries, the problem of motion and its causes has puzzled scientists and philosopher’s .
A ball on the ground , when given small hit , does not move forever.
Such observations suggest that rest is the natural state of an object.
This remained the belief until Galileo Galilei and Isaac Newton developed an entirely different approach to understand motion.
Force :
It is defined as push or pull which tries to change or changes the state of rest or motion of body.
Effects of Force:
The force acting on a body , can do three things:
1) A force or a set of forces can change the speed of body
2) It can change direction of motion
3) It can change shape of body
Types of forces:
- Balanced forces:
If the resultant of all the forces acting on a body is zero, the forces are called balanced forces.
Example: In a tug of war , when the forces exerted by the two teams on the rope are balanced , then the rope does not move in either direction.
- Unbalanced Forces:
If the resultant of all the forces action on a body is not zero , the forces are called unbalanced forces.
Example: If there were no unbalanced force of friction and air resistance , then the moving bicycle would go on moving ever (without stopping)
Newton’s First Law of motion or Law of inertia
A body at rest will remain at rest and a body in motion will continue in motion in a straight line with a uniform speed , unless it is compelled by an external force to change its state of rest or of uniform motion.
A tendency of a body to remain at rest or if moving to continue moving in a straight line is called Inertia. Inertia is that property of a body due to which it resists a change in state of rest or of uniform motion.
Mass is a measure of the inertia of a body.
Heavier objects have more inertia than lighter objects.
A stone has more inertia than a football because stone has more mass .
To overcome inertia and make a body move from rest, we must apply an external force.
If there were no air resistance and no friction to opposes the motion of a bicycle , then according to the first law of motion , a moving bicycle would go on moving forever. It would not stop by itself .
Momentum
The force required to stop a moving body is directly proportional to its mass.
The force required to stop a moving body is also directly proportional to its velocity.
The momentum of body is defined as the product of its mass and velocity.
Momentum (p) = mass (m) × velocity(v)
If a body is rest , its velocity is zero hence its momentum is zero.
- I. unit of momentum is kilogram meters per second (kg.m/s)
A karate player can break a pile of tiles or a slab of ice with a single blow of his hand. This because a karate player strikes the pile of tiles or the slab of ice with his hand very , very fast . In doing so , the large momentum of the fast moving hand is reduced to zero in a very , very short time . This exerts a very large force on the pile of tiles or the ice slab which is sufficient to break them apart.
Though a cricket ball is not very heavy but when it is thrown with a high speed acquires a very large momentum and sometimes hurts the batsman.
- What is the momentum of a man of mass 75 kg when he walks with a uniform velocity of 2 m/s?
Solution: Given : mass (m) = 75 kg
velocity (v) = 2 m/s
Momentum (p) = mass (m) × velocity(v)
Momentum (p) = 75 kg × 2 m/s
Momentum (P) = 150 kg m/s
Newton’s Second Law of motion:
According to Newton’s second law of motion:
“The rate of change of momentum of a body is directly proportional to the applied force, and takes place in the direction in which the force acts. ”
Force α (Change in momentum)/(Time taken) ; F α (mv -mu)/t
F α (m (v -u))/t ; F α m ( (v -u))/t ;
F α ma ; F = k ma ;
where k is constant, the value of constant k in S.I units is 1.
F = ma i.e. a = F/m
Acceleration produced in a body is directly proportional to the force acting on it and inversely proportional to the mass of the body.
The S.I. unit of force is newton which is denoted by N.
Applications of Newton’s second Law of Motion:
- Catching a cricket ball: A cricket player moves his hands backwards on catching a fast cricket ball.
- The case of high Jumper
- The use of seat Belts in Cars
- A truck starts form rest and rolls down a hill with constant acceleration . It travels a distance of 400 m in 20 second. Find Its acceleration . Find the force acting on it if its mass is 7 metric tonnes.
Solution: Given : u = 0 m/s , d = 400 m, t = 20 s m = 7000 kg
First finds acceleration using equation motion,
s = ut + 1/2 at2 a = 2 m/s2
400 = 0 × 20 + 1/2 × a × 202 F = m × a
400 = 0 + 1/2 × a × 400 F = 7000 kg × 2 m/s2
400 = 200 a F = 1400 N
The force acting on the truck is 1400 newtons.
Newton’s Third Law of Motion
According to Newton’s 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.
“To every action there is equal and opposite reaction”
Action (force) and reaction (force) act on two different bodies, but they act simultaneously.
Example: 1 Gun recoils
When bullet is fired from a gun , the force sending the gun backword. But due to high mass of the gun , it moves only a little distance backward and gives a backward jerk or kick to the shoulder of the gunman. The gun is said to have recoiled.
Example 2: The flying of Jet Aeroplanes and Rockets :
Jet aeroplanes utilize the principle of action and reaction.
In the modern jet aircraft , the hot gases obtained by the rapid burning of fuel rush out of a jet (a nozzle) at the rear end (back end) of the aircraft at a great speed. The equal and opposite reaction of the backward going gases pushes the aircraft forward at a great speed.
Conservation of momentum:
According to the law of conservation of momentum: when two or more bodies act upon one another their total momentum remains constant (or conserved) provided no external forces are acting.
Momentum is never created or destroyed.
Suppose two objects (two balls A and B ) of masses m1
and m2 are travelling in the same direction along a
straight line at different velocities u1 and u2 respectively.
If u1 > u2 and no external force then two balls collide
with each other. During collision which lasts for a time t,
the ball A exerts a Force F12 on ball B and
the ball B exerts a force F21 on ball A.
Suppose v1 and v2 be the velocities after
collision respectively.
Force F12 on object B is …
F12 = m1 × (v_1- u_1)/t
Force F21 on object A is …
F21 = m2 × (v_2- u_2)/t
According to third law of motion , the action and reaction are opposite
F12 = – F21
m1 × (〖(v〗_1- u_1))/t = m2 × ((v_2- u_2))/t
m1v1 – m1 u1 = m2v2 – m2 u2
m1u1 + m2u2 = m1v1 + m2 v2
Total momentum before collision = Total momentum after collision
- The car A of mass 1500 kg , travelling at 25 m/s collides with another car B of mass 1000 kg travelling at 15 m/s in the same direction. After collision the velocity of a car A becomes 20 m/s. Calculate the velocity of car B after the collision.
Solution:
mass of car A = m1 = 1500 kg
mass of car B = m2 = 1000 kg
velocity of car A before collision = u1 = 25 m/s
velocity of car B before collision = u2 = 15 m/s
velocity of car A before collision = v1 = 20 m/s
velocity of car B after collision = v2 = ?? m/s
Total momentum before collision = m1u1 + m2u2
= 1500 ×25 + 1000 ×15 = 52500
Total momentum after collision = m1v1 + m2 v2
= 1500 ×20 + 1000 × v2 = 30000 + 1000 × v2
Total momentum before collision = Total momentum after collision
m1u1 + m2u2 = m1v1 + m2 v2
52500 = 30000 + 1000 × v2
52500 – 30000 = 1000× v2
22500 = 1000 × v2
V 2 = 22.5 m/s
Thus , the velocity of car B after the collision will be V 2 = 22.5 m/s.
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