In this chapter of Laws of Motion Class 11, our goal is to quantitatively explain a particle's motion in space. We saw that uniform motion requires only the concept of velocity, but non-uniform motion does not. The concept of acceleration is required in non-uniform motion addition. We haven't yet addressed the question of what determines how bodies move.In this chapter, we will turn to this basic question.
Let us first guess the answer based on our collective experience. Someone must kick a football in order for it to move when it is at rest.
To throw a stone upwards, one must first give it an upward push. A breeze causes the branches of a tree to swing; a strong wind can even move heavy objects. A boat moves in a flowing river without being rowed. Clearly, some external agency is required to provide force to move a body from rest. Similarly, an external force is required to retard or stop motion. Applying a force against the direction of motion of a ball rolling down an inclined plane will stop it.
In short, a force is required to move a stationary body or stop a moving body, and this force must be provided by an external agency.
The question posed in physics Law of motion of class 11 appears to be straightforward. However, it took a long time to respond. Indeed, Galileo's correct answer to this question in the seventeenth century laid the groundwork for Newtonian mechanics, heralding the birth of modern science. Aristotle (384 B.C.– 322 B.C.) was a Greek thinker who believed that if a body is moving, something external is required to keep it moving.
An arrow shot from a bow continues to fly, according to this viewpoint, because the air behind the arrow continues to push it. Aristotle's elaborate framework of ideas on the motion of bodies in the universe included this point of view. The majority of Aristotle's motion ideas are now known to be incorrect and do not need to be addressed. The Aristotelian law of motion can be stated as follows for our purposes: To keep a body moving, an external force is required.
Aristotle's law of motion is flawed, as we will see. However, based on their own experiences, it is a natural viewpoint that anyone would hold. Even a small child playing with a simple (non-electric) toy car on the floor intuitively understands that it must constantly drag the toy car's string with some force to keep it moving. If the string is released, it comes to a halt. This occurs frequently in most terrestrial motions. It appears that external forces are required to keep bodies moving. What is Aristotle's flaw in his argument? The answer is that a moving toy car comes to a stop due to the external force of friction exerted on the car by the floor.
opposes the motion To counteract this force, the child must apply an external force in the direction of motion to the car.
Galileo investigated the movement of objects on an inclined plane. (i)Objects moving down an inclined plane accelerate,(ii )while objects moving up slow down. (iii) Horizontal motion is an intermediate situation. Galileo came to the conclusion that an object moving in a frictionless horizontal plane must not experience acceleration or retardation. A double inclined plane is used in another experiment by Galileo that leads to the same conclusion. A ball that has been released from one of the planes rolls down and climbs the other. If the planes are smooth, the ball's final height is nearly the same as its initial height (a little less but never more). The final height of the ball is the same as its initial height in the ideal situation, when friction is absent.
Aristotelian mechanics was dethroned by Galileo's simple but revolutionary ideas. It was necessary to create new mechanics. Isaac Newton, one of the greatest scientists of all time, almost single-handedly completed this task. Newton expanded on Galileo's ideas and established mechanics in the form of three laws of motion that bear his name. Galileo's law of inertia, which he formulated as the first law of motion, was his starting point: Everybody remains in its state of rest or uniform motion in a straight line unless compelled to act otherwise by some external force.
The first law applies to the simple case in which a body's net external force is zero. The second law of motion applies to any situation in which there is a net external force acting on the body. It connects the net external force to the body's acceleration.
The behaviour of objects for which all existing forces are not balanced is described by Newton's second law of motion. According to the second law, an object's acceleration is determined by two variables: the net force acting on the object and the mass of the item. The acceleration of an item is proportional to the net force exerted on it and inversely proportional to its mass. The acceleration of an item increases in proportion to the force applied on it. The acceleration of an item decreases as the mass of the thing increases.
The formal formulation of Newton's second law of motion is as follows:
The acceleration of an item caused by a net force is proportional to its magnitude, in the same direction as the net force, and inversely proportional to its mass.
a = Fnet /m
The above equation is frequently rewritten into the form illustrated below. The net force is equal to the mass multiplied by the acceleration.
The acceleration is proportional to the net force; the net force equals mass times acceleration; the acceleration is in the same direction as the net force; a net force causes acceleration..
A unit of force is equal to a unit of mass times a unit of acceleration, as stated in the previous equation.
The following unit equivalence may be constructed by inserting standard metric units for force, mass, and acceleration in the preceding equation.
1 Newton = 1 kilogramme• m/s2
The preceding equation expresses the definition of the standard metric unit of force. The amount of force required to accelerate a 1kg mass at 1 m/s2 is specified as one Newton.
When objects A and B interact with each other, Newton says they exert forces on each other. Your body produces a downward pull on the chair, while the chair exerts an upward force on your body when you sit in it. This connection results in two forces: a force on the chair and a force on your body. Newton's third law of motion deals with these two forces, which are known as action and reaction forces. Newton's third law states that “there is an equal and opposite reaction to every action”.
The conservation of momentum is a fundamental rule of physics that asserts that if no external forces are acting on a system, its momentum will remain constant. Newton's First Law, sometimes known as the Law of Inertia, encapsulates this concept.
Experiment has abundantly proved the law of conservation of momentum, and it may even be analytically inferred on the plausible assumption that space is uniform. Conservation of linear momentum is based on Newton’s second law of motion which states that in an isolated system the total momentum remains the same.
A particle is considered to be in equilibrium if there is no net force acting on it, according to Newton’s first law. This does not imply that no forces operate on the particle; rather, it means that the sum of all forces acting on the particle is zero.
The direction in which a force acts is a crucial factor to consider when describing it.
As a result, force is a vector quantity, and the resultant of the forces can only be calculated using vector techniques. If we label the forces acting on the particle by A, B, C, ..............,
The condition for the equilibrium of a particle may be given in the form of an equation
R = A + B + C +............., = 0
where R is the resultant of the forces acting on the particle.
The following are the common forces in mechanics:
The force of contact
Force without contact
The spring force
The force of friction
When one item collides with another, a contact force is created. Mutual contact forces occur whenever two objects come into touch with each other, and they meet Newton's Third Law of Motion. 'Normal Reaction' refers to the component of the contact force that is normal to the contact surfaces. Friction is the term for the component that runs parallel to the surfaces. Even when solids come into touch with liquids, a contact force can form.
Circular motion is the movement of an object in a circular path. This is a circular motion in which items move in a circle. Examples include clock hands, fan blades, and the earth's rotation around the sun.
a). Uniform Circular Motion
If the magnitude of the velocity of the particle in circular motion remains constant, then it is called uniform circular motion.
b). Non-uniform Circular Motion
If the magnitude of the velocity of the body in circular motion is n constant, then it is called non-uniform circular motion.
a). A constant force acting on a body of mass 10 kg changes its speed from 6 ms-1 to 8.5 ms1 in 10s. The direction of the motion of the body remains constant. What is the magnitude and direction of the force?
Mass, m = 10 Kg
u = 6 m/s
v = 8.5 m/s
t = 10 s
F = ma
F = m [(v-u)/t] (since a = (v -u)/t)
F = 10 [ (8.5 – 6)/10] = 2.5/10 N =0.25N
The direction of motion is the same as the direction of force of the body.
b). The driver of a three-wheeler moving at a speed of 30 km/h sees a man standing in the middle of the road and brings his vehicle to rest in 2.0 s just in time to save the child. What is the average retarding force on the vehicle? The mass of the three-wheeler is 300 kg, and the mass of the driver is 60kg.
u= 30 km/h
v = 0 (since it supposed to be come in rest)
1= 300 Kg
m2 = 60 Kg
Time taken = 2.0 s
a = v- u/t = (0 – 30)/ 2 = – 30/2 m/s = -15m/s
Now, F = (m1 + m2)/ a = (300 + 60) x (-15)
= 360 *-15 N = – 5400 N
The negative sign shows that the force is retarding.
The First Law of Motion (Newton's First Law of Motion) (Law of Inertia)
The Second Law of Motion (Newton's Second Law of Motion) (Law of Mass and Acceleration)
The Third Law of Motion of Newton
A unit is an internationally recognised standard for measuring quantities. A numerical quantity as well as a specific unit of
measurement have been included. Fundamental units are defined in the case of base quantities (such as length, mass, and so on).
5.2 Aristotle’s fallacy
5.3 The law of inertia
5.4 Newton’s first law of motion
5.5 Newton’s second law of motion
5.6 Newton’s third law of motion
5.7 Conservation of momentum
5.8 Equilibrium of a particle
5.9 Common forces in mechanics
5.10 Circular motion
5.11 Solving problems in mechanics