Force And Laws Of Motion

1. Force And Laws Of Motion CONTENTS • Force • Balanced Force • Unbalanced Force • Introduction – Sir Isaac Newton • The three Laws of Motion • First Law of Motion • An activity – First Law Of Motion • Momentum • Second Law of Motion • Mathematical formulation of Second Law of Motion • An example for the Second Law • Third Law of Motion • Third Law-Some more examples • Third Law – An activity • Conservation of Momentum • An example for Conservation of Momentum • Conservation Laws • Conclusion

2. In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described as a push or pull that can cause an object with mass to change its velocity(which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction making it a vector quantity. The SI measuring unit of force is Newton(N).Force is the product of mass and acceleration. So, F=ma. Force A boy pushing a trolley A man pulling a wooden box

3. Balanced FORCE Equal forces acting in the opposite directions, which don’t change the state of rest or state of motion are called balanced force. E.g. :- When two men push a wooden box from opposite sides with equal force, the box won’t move due to a balanced force. Two men pulling a block. Two men pushing a car.

4. Unbalanced force Unequal force acting acting in opposite direction, which change the state of rest or state of motion of an object are called unbalanced force. E.g. :- While two men push a wooden box in opposite direction with different force, the body will move to the direction to which the greatest force is acting. Tug of war in which one team pull the opposite team with a greater force. Block moves left or right, when a higher force is applied than the other one.

5. Introduction – Sir Isaac Newton Sir Isaac Newton FRS(4 January 1643 – 31 March 1727)was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian who is considered by many scholars and members of the general public to be one of the most influential people inhuman history. His 1687 publication of the Philosophiae Naturalis Principia Mathematica(usually called the Principia) is considered to be among the most influential books in the history of science, laying the groundwork for most of classical mechanics. In this work, Newton described universal gravitation and the three laws of motion which dominated the scientific view of the physical universe for the next three centuries. Sir Isaac Newton

6. Newton showed that the motions of objects on Earthand of celestialbodies are governed by the same set of natural laws by demonstrating the consistency between Kepler’s law of planetary motion and his theory of gravitation, thus removing the last doubts about heliocentrism and advancing the scientific revolution.Newton built the first practical reflecting telescope and developed a theory of colour based on the observation that a prism decomposes whitelight into the many colours that form the visible spectrum. He also formulated an empirical law of cooling and studied the speed of sound. In mathematics, Newton shares the credit with Gottfried Leibniz for the development of the differential and integral calculus. He also demonstrated the generalized binomial theorem, developed Newton’s method for approximating the roots of a function, and contributed to the study of power series. Newton was also highly religious, though an unorthodox Christian, writing more on Biblical hermeneutics and occult studies than the natural science for which he is remembered today.

7. The Three Laws of Motion Newton's laws of motion are three physical laws that form the basis for classical mechanics. They describe the relationship between the forces acting on a body and its motion due to those forces. They have been expressed in several different ways over nearly three centuries. The laws of motion were first compiled by Sir Isaac Newton in his work Philosophiae Naturalis Principia Mathematica, first published on July 5, 1687.Newton used them to explain and investigate the motion of many physical objects and systems. Newton's laws are applied to bodies (objects) which are considered or idealized as a particlein the sense that the extent of the body is neglected in the evaluation of its motion, i.e., the object is small compared to the distances involved in the analysis, or the deformation and rotation of the body is of no importance in the analysis. In their original form, Newton's laws of motion are not adequate to characterize the motion of rigid bodies and deformable bodies.

8. First Law of Motion A body will continue in its state of rest or state of motion in a straight line, unless and until an external force compels to change its state of rest or state of motion. This is the Newton’s First Law of Motion. It can be also called as Law of Inertia. The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. This is why the first law of motion is also said to be law of inertia. E.g. :- We tend to remain at rest with respect to the seat until the driver applies a braking force to stop a vehicle like car or bus. With the application of brakes, the vehicle slows down but our body tends to continue in the same state of motion because of its inertia.

9. AN ACTIVITY – FIRst Law of Motion • Take an empty glass tumbler standing on a table and cover it with a stiff card. • Set a five-rupee coin upon that. • Give the card a sharp horizontal flick with a finger. When we do it fast, then • the card shoots away, allowing the coin to fall vertically into the glass tumbler due to inertia. • The inertia of the coin tries to maintain its state of rest even when the card flows off. Flicking off the coin

10. Momentum The force possessed by a body due to the combined effect of mass and velocity is called momentum. Mathematically, it is the product of mass and velocity, i.e. p=mv. The SI unit of momentum is Newton-Second (Ns).

11. Second Law of motion The rate of change of momentum of a body is directly proportional to the applied unbalanced force and takes in the same direction in which the force acts. Whether big or small, impact produced by the object depends on their mass and velocity. The momentum, ‘p’ of an object is defined as the product of its mass, ‘m’ and velocity, ‘v’. That is, p = mv

12. Mathematical Formulation of Second Law of Motion Suppose an object of mass, ‘m’ is moving along a straight line with an initial velocity, ‘u’ with uniform acceleration, to velocity, ‘v’ in time, ‘t’ by the application of a constant force, F throughout the time, ‘t’. The initial and final momentum of the object will be, p1 = mu and p2 = mv respectively. The change in momentum = p2 - p1 = mv – mu = m(v-u) The rate of change of momentum = m(v-u) t Or, the applied force, F = m(v-u) t = km(v-u) t = kma Here, a[a=v-u/t] is the acceleration, which is the rate of change of velocity. The quantity, ‘k’ is a constant of proportionality. 1 unit of force = k(1 kg) (1 m s-1) Thus, the value of k becomes 1(F=kma) F = ma

13. An example for the Second Law While catching a fast moving cricket ball, a fielder in the ground gradually pulls his hands backwards with the moving ball. This is because in doing so, the fielder increases the time during which the high velocity of the moving ball decreases to zero. Thus, the acceleration of the ball is decreased and therefore, the impact of catching the fast moving ball is also reduced. If the ball is stopped suddenly then its high velocity decreases to zero in a very short interval of time. Thus, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for holding the catch that may hurt the palm of the fielder.

14. Third Law of Motion To every action, there is an equal and opposite reaction. This is the Third Law. It states that when one object exerts a force on another object, the second object immediately exerts a force back on the first. These two forces are always equal in magnitude, but opposite in direction. These forces act on different objects and never on same object.

16. Let us consider two spring balances connected together. The fixed end of balance B is attached with a rigid support, like a wall. When a force is applied through the free end of spring balance A, it is observed that both the spring balances show the same readings on their scales. It means that the force exerted by the spring balance A on balance B is equal but in opposite direction to the force exerted by the balance B on balance A. The force which balance A exerts on balance B is called the action and the force of balance B on balance A is called the reaction. Third Law – An Activity

17. Conservationof Momentum Suppose two objects(two balls A and B, say) of masses mA and mB are travelling in the same direction along a straight line at different velocities uA and uB respectively, and there are no other external unbalanced forces acting on them. Let uA>uB and the two balls collide with each other. During collision which lasts for a time t, the ball A exerts a force FAB on ball B and the ball b exerts a force FBA on ball A. suppose vA and vB are the velocities of the two balls A and B after collision, respectively. The momenta of ball a before and after the collision are mAuA and mAvA respectively. The rate of change of its momentum(or FAB, action) During the collision will be, mA (vA-uA) t Similarly, the rate of change of momentum of ball B(=FBA or reaction)during the collision will be, mB(vB-uB) t According to the third law of motion, the force FAB exerted by ball A on ball B(action) and the force FBA exerted by the ball B on ball A(reaction)must be equal and opposite to each other. FAB = -FBA Or mA(vA-uA) = -mB(vB-uB) t t

18. This gives, mAuA + mBuB = mAvA + mBvB Since(mAuA + mBuB) is the total momentum of the two balls A and B before the collision and(mAvA + mBvB) is their total momentum after collision, we observe that the total momentum of the two balls remains unchanged or conserved provided no other external forces act. As a result of this ideal collision we say that the sum of momenta of the two objects before collision is equal to the sum of momenta of the two objects after the collision provided there is no external unbalanced force acting on them. This is known as the law of conservation of momentum. This statement can alternatively be given as the total momentum of the two objects is unchanged or conserved by the collision.

19. An Example for Conservation of Momentum When a bullet is horizontally fired with a certain velocity from a pistol, the total momenta before firing and after firing will remain same. Total momenta after the fire = Total momenta before the fire

20. Conservation Laws All conservation laws such as conservation of momentum, energy, angular momentum, charge etc. are considered to be fundamental laws in physics. These are based on observation and experiments. The law of conservation of momentum has been deduced from large number of observations and experiments. This law was formulated three centuries ago, but not a single situation has been realized so far.

21. Conclusion All the Three Laws are common in our daily life. It is very important in Physics, or modern science. Newton has done a great contribution to this field. The history behind the invention is a marvel. The activities which are related to this laws teach and conclude the functioning of these laws.

22. Done By :- Adarsh.K. IX.A.