ASHAQ HUSSAIN BHAT
TEACHER SCHOOL
EDUCATION DEPARTMENT
JAMMU AND KASHMIR
Force and Laws of Motion
Introduction
We have described the motion of an object along a straight line in terms of its position, velocity and acceleration. We have seen that such a motion can be uniform or non-uniform. We have not yet discovered what causes the motion. Why does the speed of an object change with time? Do all motions require a cause? Here we will learn about the cause of motion. This study about the cause of motion is called Dynamics.
Force
It is that physical quantity which we can neither see nor touch, but its effect can be felt on the objects on which it is applied. Some effort is required to move a stationary toy-cart or a ball or box or applying effort opposite to its motion. anything lying at rest on ground. On the other hand, we can stop a roller rushing down the road by The effort required to bring such changes in the state of an object is called force. A force can bring following changes:
It can move a stationary body. eg, A soccer player kicks the ball forward.
It can stop a moving body.eg, A fielder stops the ball hit by batsman reverses its
direction of motion.eg, While cycling against the blowing wind, wind exerts
It can change the speed of a moving body.eg, force which slows down speed.
It can change the direction of a moving body.eg, Cricket ball hit by the batsman.
It can change the shape and size eg, a body A spring pulled at either end at both its ends gets elongated.
Thus we observe that a force is a push or a pull that produces or tends to produce above mentioned effects. It has both direction and magnitude. So it is a vector quantity
Resultant Force
If a single force acting on a body produces the same acceleration as produced by a number of forces on the body acting simultaneously, that single force is called the resultant force of all these forces acting simultaneously. The resultant force is also called the net force.
Balanced and Unbalanced Forces
When two or more forces acting simultaneously on an object produce no acceleration in it, i.e. do not bring about any change in its state of rest or of uniform motion in a straight line, the forces are said to be balanced forces or we can say that the net force acting on the object is zero.
Example: In the game of tug of war, the two teams apply force of pull on the rope in opposite directions. If both teams pull with equal force, rope remains at rest and the forces are balanced.
When two or more forces acting simultaneously on a body produce a non-zero acceleration in it it. produce a change in its state of rest or of uniform motion in a straight line, the forces are said to be unbalanced. The resultant force is not zero.
Examples :
- In tug of war, the team applying greater pull will pull the rope and draw the opposite team towards itself.
- While pushing a heavy box lying on a rough floor, a person starts it moving when force of push is greater than the force of friction.
Types of Forces
There are mainly two kinds of forces:
(a) Contact force
(b) Field force or non-contact forces
- Contact Force : The force exerted by an object on another object only when downward they are in contact with each other is called contact force.
For example: We push a door to close it, we create contact force on the door, load carried by porter on his head creates a downward contact force on him due to its weight. Mentioned below are some important types of contact forces.
(i) Normal force: If contact forces between the bodies are perpendicular to the surfaces in contact, the forces are known as normal forces.
For example a wooden block kept on a table is in equilibrium. Block applies a downward force on table due to its weight and table pushes the block upwards. Thus both table and block apply a normal force on each other.
(ii) Frictional force : When we try to slide a heavy box on a rough floor by pushing it, a force acts parallel to the surface in contact force of Box with the floor and opposes the pushing force. This parallel force friction Floor is called the frictional force.
- Field Force : This may also be referred as non-contact force. If an object attracts or repels another object from a distance i.e. without being in contact we say it applies a field force on the other.
For example:
(1) Gravitational pull: It is the downward force acting on an object due to gravitational pull of earth. Now even if the object is not in contact with the earth, the earth pulls it. If we release an apple or a stone or anything from a height, it falls to the ground.
(ii) Magnetic force and Electrostatic force : We know that a magnet can pull an iron piece from
distance. Also when we rub a comb with hair and bring it near bits of paper, it attracts them from a distance. These are examples of field force.
Newton's First Law
An object remains in a state of rest or of uniform motion in a straight line unless compelled to change that state by an applied unbalanced force. In other words, if a body is in a state of rest, it will remain so and if it is in the state of motion, it will keep moving in same direction with same speed unless an external unbalanced force is applied on it. An equal and opposite force is required continuously to cancel or balance the force of friction acting on the ball to keep it moving with constant velocity, on a rough surface Thus an unbalanced force is required to change speed or direction of an object. And if this unbalanced force is removed completely, the object would continue to move with a velocity it has acquired till then. The tendency of undisturbed objects to stay at rest or to keep moving with same velocity is called inertia. Therefore, Newton's first law is also known as law of inertia. In general a heavier body has greater inertia than a lighter body. Thus we can say that mass of a body is the measure of its inertia. It is more difficult to push a heavy box than to push a light book. Similarly it is easier to stop moving ball with our hand than to stop a moving bicycle. Thus a heavier object has greater inertia.
Inertia of rest
The tendency of the body to maintain its state of rest is called inertia of rest. Example :
(1) Jerks while travelling : When we stand in a bus and the bus starts moving suddenly, we tend to fall backward. This is because our feet are in contact with the floor of the bus and the friction at the contact is high. This force does not allow the feet to slip on the floor. The feet, therefore, move forward with the floor. The upper part of the body does not feel the forward force immediately and remains at rest for a while. So the upper part of our body gets jerked backward.
(ii) Make a pile of similar carrom coins on a table. Attempt a sharp horizontal hit at the bottom of the pile using another carrom coin or the striker. If the hit is strong enough, the bottom coin moves out quickly. Once the lowest coin is removed, the inertia of rest of the other coins makes them fall vertically on the table
Inertia of direction
The tendency of the body to maintain its direction of motion is called inertia of direction.
Example :
If a car takes a sudden turn along a curved track, it appears as the passengers are pushed sideways. This is the result of tendency of the passengers to continue moving along a straight path.
(ii) Tie a stone to on end of a string and then holding other end of the string in hand, rotate the stone in a horizontal circle. If during rotation, the string breaks at certain stage, the stone is found to fly off tangentially at that point of the circle.
(iii) The water drops sticking to the cycle tyre are found to fly off tangentially while tyre rotating.
(iv) The sparks produced during the sharpening of a knife or a razor against a grinding wheel leave the rim of the wheel tangentially.
Linear Momentum
The product of mass of a body and its velocity is called the linear momentum or simply momentum of the body. It is a very important physical quantity which measures the quantity of motion in a body.
For example, let us take a plastic ball and an iron ball both of same size. If we push them one by one to strike a sand hill with same velocity and from same distance, it can be observed that plastic ball (lesser mass) causes no damage or little damage to the sand hill. But the iron ball (greater mass) causes greater damage to the sand hill. So though both the balls have same velocity, heavier ball has greater impact or it strikes the sand hill with a greater force. Similarly if two identical plastic balls are made to strike a sand hill, one with a greater velocity than the other causes greater damage to the sand hill than the slower one. So the impact produced is directly proportional to both the mass and the velocity.
Thus, mass and velocity, simultaneously give the idea about magnitude of impact produced by the object. Momentum (m×v) was introduced by Newton. It is a vector quantity and acts in the direction of velocity. It is denoted by symbol 'p.'
Thus p = mv.
Its S.I. unit is kg m s-¹.
Newton's Second Law
Force applied on an object is not only proportional to change in momentum, but it also depends on home fast momentum changes. Newton's second nationals that, the rate of change of momentum of an object is proportional to the net force applied on the object the direction of the change of momentum is the same as the direction of the net force.
Mathematical formulation :
Suppose an object of mass 'm' is moving along a straight line with an initial velocity 'u' It is uniformly accelerated to velocity 'v' in time 't' by the application of a constant force 'F' Suppose an object of mass, 'm' is moving along a straight line with an initial velocity 'u'. 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
or, F=km×(v-u) /t
F=kma {v-u/t=a}
Here 'a' is the acceleration, which is the rate of change of velocity. 'k' is the constant of proportionality. The unit of force is so chosen that the value of 'k' becomes one.
S.I. unit of force is kg m s-² or newton which has the symbol N. One newton is defined as force, which when applied on a man of 1 kg, can create an acceleration of 1 m/s.
Impulse
When a cricketer smashes a ball, a large force acts on the ball for a very short time. Even in this short time the force varies, as shown in the figure,
Such a large variable force acting for a short interval of time is called impulsive force. As the impulsive force varies, its measurement is difficult. But we can measure the impact of the impulsive force with the help of change in momentum it produces
in the body on which it acts. The impact produced by impulsive force is called impulse and is measured by change in momentum produced in the body.
Impulse (l) =Change in momentum = Final momentum - Initial momentum
=mv-mu...... eq 1st
where 'u' and 'v' are initial and final velocities of the body and 'm' is the mass of the body.
- Impulse in terms of average force and time of impact:
We know that F=ma = m{v-u/t}=mv - mu/t
=>mv-mu=F×t ............ eq 2nd
From (i) and (ii), we have,
Impulse I = mv – mu = F×t
I= F×t
Thus impulse is equal to the product of the average force and the time for which it acts.
Unit of impulse : S.I. unit is kg m s-¹or newton second, i.e. NS
C.G.S. unit is g cms-¹ or dyne second
- Reducing the impact of impulsive force :
Impulse (1) = F × t = mv - mu
Average impulsive force = F =m(v - u)/t
=Change in momentum/Time for which force acts
To reduce the impact of impulsive force, the time for which it acts should be increased. Other wise we can say, lesser the time of impact more is the damage caused.
Newton's Third Law
Newton's third law deals with the relationship between the forces that two objects exert on each other but if we punch a wall hard, it hurts very much. Newton hypothesized that at If we push on a wall it pushes us back. This doesn't hurt if we push it gently, of ground Reaction any time two objects interact in such a way that when a force is exerted on one of them, there is always a force that is equal in magnitude, exerted in opposite direction on the other object. This is called Newton's third law. Newton's third law of motion states that, if a body A exerts a force +F on a body B, then body B exerts a force -F on A, which is a force of the same size acting along the line of interaction in the opposite direction. This law says that forces always occur in pairs as a result of interaction between two objects. The two opposing forces are also known as action and reaction forces and they always act on interacting objects separately. Thus Newton's third law can not be applied to a single body. For example when a bullet is fired, the gun recoils with equal force. When we walk, our feet push the ground backward and the reaction acts in the opposite direction. This reaction makes us to move forward. It is important to note that though action and reaction forces are always equal, they do not produce acceleration of same magnitude. For example, when a bullet is fired from a gun, the gases produced due to the burning of explosive powder, exert same force on the bullet as well as on the gun. However, the bullet leaves the gun with large acceleration due to its smaller mass whereas the gun jerks back with small acceleration due to its larger mass.
Law of Conservation of Momentum
The principle of conservation of linear momentum follows from Newton's laws of motion. We will show this through an example.
Suppose two objects A and B of masses m, and m2 respectively are kept on a horizontal table, which is so smooth that friction can be neglected.
Suppose A is made to move with a velocity u1 and B is made to move with a velocity u2 in the direction AB. Also, suppose that u1 > u2. The linear momentum of A is m¹u¹ and that of B is m²u². The total linear momentum of the system is
Pi = m1u1 + m2u2
As u1 > u2 the object A will collide with B at some point of time. The two objects will remain in contact for a short time to and then they will separate. When they separate, the velocities of the objects are different from their velocities before the collision. Let the velocity of A becomes v1 and that of B becomes v2 after the collision
During the collision, A will push B towards the right, and B will push A towards the left. By Newton's third law, the magnitudes of these forces will be equal. As we are taking the direction towards AB as positive, write the force on B by A as F, and the force on A by B as -F. We assume that the force F remains constant during the collision.
If we consider A and B together to be a system, the forces F and -F are internal forces. There are some external forces which also act on A and B. Consider the object A. The earth is pulling it down by the force
m1g. This is an external force. The table is pushing it up by a normal force N1. This is also an external force. But A is neither going down nor going up. This is because m1g and N, are equal in magnitude and opposite in direction. These two forces balance each other so that the total external force on A is equal to zero. Similarly, the total external force on B is also zero. Hence the net external force on the system is zero.
The force -F acting on A (due to B) produces an acceleration in it, which changes its velocity from u1 to v1. Using Newton's second law, the acceleration is
a¹ = -F/m
Or v1-u1/t0
= -F/m1.............(1) eq
The force on B is F. This produces an acceleration in B, changing its velocity from u² to v² in the same time interval t0. Again using Newton's second law, the acceleration is
a² =F/m2 or v2-u2/t0 = F/m2
Or m2v2 - m2u2 = Ft0............. (2) eq
Adding equations (1) and (2)
m1 v1 - M1u1+ m2v2 - m2u2 = 0
Or m1v1 +m2v2 = m1u1 + m2u2
Or P2=P1
where p2 is the linear momentum of the system after the time interval to and p1 before the collision. Thus the linear momentum of the system remained constant, although the linear momentum of each of the two particles got changed.
Example:
Jet engines and rockets : Just before the launching of the rocket its momentum is zero as it is at rest. When the jet of hot gases passes out in downward direction with tremendous velocity, the rocket moves up with a velocity which makes the total momentum of the system (rocket + emitted gases) zero again.
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