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Force and laws of motion Page 1
CHAPTER 9
FORCE AND LAWS OF MOTION Q 1. What is a force? Ans: Force is a push or pull which tries to bring the change in the state of rest or of uniform motion in a straight line. Unit of force: force is a vector quantity and its SI unit is newton (N). Q 2. What are the effects of force? Ans: 1. Force can make a stationary body in motion. Eg: A football can be set to move by kicking it, i.e. by applying a force.
2. Force can be used to change the magnitude of velocity of an object (that is, to make the object move faster or slower)
Eg: By accelerating, the speed of a running vehicle can be increased or by applying brakes the speed of a running vehicle can be decreased.
3. Force can stop a moving body. Eg: by applying brakes, a running cycle or a running vehicle can be stopped. 3. Force can change its direction of motion.
Eg: when a moving cricket ball is hit by a bat, the cricket ball moves in a different direction. The force applied by the bat changes the direction of the moving cricket ball.
4. Force can change the shape and size of objects. Eg: By hammering, a block of metal can be turned into a thin sheet. By hammering a stone can be broken into pieces.
Forces can be classified into two classes:- 1. Contact forces 2. Action at a distance forces. 1. The contact forces: It represent the result of physical contact between two objects, one by which force is exerted and the other on which force is exerted. Eg: pulling of a coiled spring, pulling of a cart. 2. The action at a distance forces: They are the forces, which do not involve physical contact between the two objects but act through the space between the two. Eg: the gravitational force, electrical force etc.
Note: Types of force:-Forces are of main two types
1. Balanced forces 2. Unbalanced Forces
Force and laws of motion Page 2
Q 3. Differentiate between balanced and unbalanced forces? Ans. 1. Balanced force: A force is said to be balanced if the resultant of all the forces acting on
a body is equal to zero. A body under the influence of a balanced force does not change its position of rest or uniform motion and appears as if no force is acting on it. The resultant of balanced forces is always equal to zero (because the forces are equal and opposite). Example : - In the tug of war if both the teams apply similar magnitude of forces in opposite directions, rope does not move in either side. This happens because of balanced forces in which resultant of applied forces become zero.
2. Unbalanced force: A force is said to be unbalanced if the resultant of all the forces acting on a body is not equal to zero. A body under the influence of unbalanced force changes its position of rest and uniform motion. The resultant of unbalanced forces is always greater than zero. Unbalanced forces can do the following:
Move a stationary object. Increase the speed of a moving object. Decrease the speed of a moving object. Stop a moving object Change the shape and size of an object
Galileo’s Observation and Origin of Newtonian Mechanics
Galileo observed that, when a ball was made to roll up the inclined plane, its speed increased. Fig (a) shows it i.e, an object moving down an inclined plane with increasing speed similarly, when it was made to roll up the inclined plane, its speed decreased.fig (b) shows it. He then tried rolling it on a horizontal plane. Galileo repeated this experiment by making the surface very smooth. He observed that the ball continued to move for a longer time. Galileo suggested that the speed of the ball moving on a horizontal plane would remain constant in the absence of an external force or force of friction.fig (c) shows it.
Force and laws of motion Page 3
Newton’s Laws of Motion: (1692 – 1772) Newton devised three basic laws based on his name, to describe motion. All these laws are known as Newton’s laws of motion and are explained as under:- Newton’s First Law of Motion or Galileo’s Law of Inertia:- It states that, “An object continues to be in a state of rest or of uniform motion along a straight line unless an external force acts up on it”. In other words, the first law of motion recognizes that everybody has some inertia i-e the property of a body to remain in a state of rest or uniform motion. This law is accordingly also known as, “Law of inertia”. For example: (i) A book lying on a table will remain there unless and until somebody will come and change its place. (ii) A cricket ball will remain in motion after hit by the player unless and until the force of friction and the resistance of air stop it and changes its motion into rest. Inertia:-The word inertia means unchanging. It has been derived from the Latin word inert. It is defined as the property of a body to remain in the state of rest or uniform motion. In other words, inertia may be defined as the property of a body to remain in the state of rest or uniform motion. In other words, inertia may be defined as the inability of a body to change its any state. Note: A heavier body has more inertia than a lighter body. Therefore, we can say that “The larger the mass, the larger is the inertia, and smaller the mass, smaller is the inertia.” In other words we can say that “The mass of a body is a measure of its inertia.” Inertia is of three types:
i) Inertia of motion: i.e, the body opposes any change in its state of motion ii) Inertia of rest: i.e, the body opposes any change in its state of rest iii) Inertia of direction: i.e, the body opposes any change in its direction of motion.
Examples of inertia:- 1. Why are passengers thrown in the forward direction when a running bus stops suddenly?
Passengers sitting or standing in a running bus share the motion of the bus. This means, the passengers in a running bus are also moving with the same speed in the same direction. When the running bus stops suddenly, the lower part of the passenger’s body comes to rest, while the upper body portion continues to remain in motion. As a result, the passengers are thrown in the forward direction when a running bus stops suddenly. 2. Why do Passengers tend to fall sideways the bus takes a sharp turn?
When a bus runs along a straight-line path, all the passengers traveling in the bus also move with the same speed in the same direction. When the bus takes a sharp turn, the upper body portion of the passengers still continues to move in the original (straight line) path, while the lower portion tends to turn with the bus. As a result, passengers tend to fall/ lean sideways.
Force and laws of motion Page 4
3. Why should a passenger hold on to a support to prevent himself from swaying in a turning bus?
A person traveling in a bus shears the motion of the bus. When the bus takes a turn, it changes its direction of motion. The passenger due to his inertia of motion, however, continues to move in the original direction. So, if the passenger does not hold on to a support, he will be swayed away. 4. Why do passengers in a bus tend to fall backward when it starts suddenly?
When a passenger in sitting or standing in a stationery bus, both the bus and the passenger are at rest. When the bus starts moving suddenly, the lower part of the passenger’s body starts moving forward with the bus. The upper part of the body tends to remain in the position of rest due to its inertia of rest. As a result, the passenger falls or leans backwards.
Similarly a rider on horseback falls backwards when the horse suddenly starts running. 5. Why does a passenger jumping out of a rapidly moving bus fall forward with his face downwards, if he does not run forward?
A passenger traveling in a bus shares the motion of the bus. Thus, the passenger’s body is moving in the direction of the bus with the same speed. When a passenger jumps out of a fast moving bus, his feet on touching the ground come to rest, whereas the upper part of his body continues to move forward due to inertia of motion. As a result, if he does not run forward he falls with his face downwards. 6. why can dust be removed from a carpet by shaking it, or by beating it with a stick?
Initially, both the carpet and the dust therein are at rest. When the carpet is shaken or beaten with a stick, the carpet is set into motion. Due to inertia of rest, the dust particles tend to remain at rest. As a result, the dust particles fall off. Momentum:- Momentum of an object is considered as the product of its mass and its velocity. In other words it is considered to be the measure of the quantity of motion of a moving body. Momentum is a vector quantity and its direction will be same as that of velocity. It is represented by p. momentum = mass velocity
i.e, p = mv where, m = mass of body v = velocity. SI unit of momentum is kilogram metre per second (kgm/s)
Force and laws of motion Page 5
Newton’s Second Law of Motion:- Newton’s second law of motion states that the rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of force. Explanation:- Consider a body of mass m, having an initial velocity u. Let the body be acted upon by some external force F for time t, such that its final velocity is v. Then, initial momentum p1= mu Final momentum, p2= mv Therefore, change in momentum = final momentum – initial momentum = p2 p1
= mv – mu i.e, Change in momentum = m( v - u)
rate of change of momentum =
………………………………………………(1)
but, (acceleration) a =
Therefore, from eqn (1) rate of change of momentum = ma According to Newton’s second law Rate of change of momentum ∝ F Or, applied force, F ∝ ma
Or, F = k ma
Where k is a constant of proportionality.
Experimentally,
If k =1 F = ma
This is the mathematical form of Newton’s second law of motion. It state that Force acting on a
body is the product of mass of the body and acceleration of the body.
Relation between force and acceleration:-
From the Newton’s 2nd law of motion, we have:
F = m × a
Or, a =
From the above equation, it is clear that acceleration produced in a body is directly proportional
to the force acting on it and inversely proportional to its mass. Note:- The unit of force is kilogram metre per second square ( kg m/s2) or newton, which has the symbol N. Q4. Define one newton of force? Ans: One newton is the force produces an acceleration of 1 m/s2 on an object of mass 1 kg.
Force and laws of motion Page 6
Q5. Deduce Newton’s first law of motion from Newton’s second law? Newton’s first law of motion can be deduced from Newton’s second law of motion. According to Newton’s second law of motion, F = ma
=
Or F × t = mv – mu
When no external force is applied, F = 0
Therefore, mv – mu = 0
or mv = mu
or v = u
It means the body will continue to move with the same uniform velocity, u throughout the time t, when no external force is applied on the body. Further, if u = 0, then v will also be zero. It means if the object is initially at rest, it will continue to be at rest, when no external force is applied on the body. This is Newton’s first law of motion. Impulse:- It is defined as the product of as the product of force and time. In other words, it is large force acting for a short duration. From Newton’s second law of motion, F = ma
=
Or F × t = mv – mu …………………………… (2)
Where, mu= Initial momentum of the body.
mv= Final momentum of the body.
F = force t = time taken
Thus, force time = final momentum – initial momentum
Or Impulse = Change in momentum = force time Note: - SI unit of impulse is newton second (Ns) or kgm/s Q6. In a cricket match, why does a player lowers his hands slightly while catching the ball? Ans: The player lowers his hands so that the momentum of ball changes to zero in a longer duration of time. This reduces the force acting on the hands of the player due to the ball and the fielder does not get hurt.
OR
Force and laws of motion Page 7
Q.8. While catching a fast moving cricket ball, a fielder in the ground gradually pulls his hands backwards with the moving ball? Ans: In doing so, the fielder increases the time during which the high velocity of the moving ball decreases to zero. Thus, the rate of change of momentum 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. Newton’s Third Law of motion:- It states that, “for every action, there is an equal and opposite reaction and they act on two different bodies”. For example:
1. When we walk on the ground, then our foot pushes the ground backward (action force) and the ground in turn exerts a force on the foot (reaction force) pushing the foot forward.
2. The birds, while flying, push the air downwards with the help of their wings (action force) and the air in turn exerts a force in the bird upward direction (reaction force).
3. A swimmer pushes the water in the backward direction (action force) and the water exerts a force on the swimmer (reaction force) which pushes him forward.
Note: 1. Action and reaction forces acts on different bodies 2. Action force = - Reaction force. 3. The action and reaction forces are always equal in magnitude, 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. Application of Newton’s III rd law of motion. 1.Recoil of gun:- When a gun is fired, it exerts a forward force on the bullet. The bullet exerts an equal and opposite reaction force on the gun. This results in the recoil of the gun (fig 2). Since the gun has a much greater mass than the bullet, the acceleration of the gun is much less than the acceleration of the bullet.
Fig 2
Force and laws of motion Page 8
2.Rocket propulsion:- The rocket expels out high speed hot gases produced in it by burning of fuel. These gases exert an equal and opposite force on rocket and propel it upwards. Law of conservation of momentum:- Consider two balls A and B, 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 as shown in figure. 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 the collision, respectively.
The momenta of ball A before the collision = mAuA The momenta of ball A after the collision = mAvA
Similarly, The momenta of ball B before the collision = mBuB The momenta of ball B after the collision = mBvB The rate of change of momentum of ball A during the collision (or FAB, action) = mA(vA – uA) t The rate of change of momentum of ball B during the collision (or FBA, reaction) = mB(vB – uB) t According to third law of motion FAB FBA
Or, mA(vA – uA) mB (vB – uB) t t Or, mA(vA – uA) mB (vB – uB) Or, mAvA – mA uA mBvB +mBuB
i.e, 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 the collision. The total momentum of the two balls remains unchanged or conserved provided no other external force acts.
Force and laws of motion Page 9
The sum of momenta of the two objects before collision is equal to the sum of momenta after the collision provided there is no external unbalanced force acting on them. This is known as the law of conservation of momentum.