Force
Force is pushing or pulling that can change the state of rest or the state of motion of an object.
- Force can change the direction of motion
- Force can change the shape and size of the object
- Force can change the speed of motion or magnitude of the velocity
- Force can bring a motion in a restin object
The expression of force is F = ma, where m = mass of the object and a = acceleration
Force It is a vector quantity and the S.I unit is Newton (N) and the CGS unit is dyne.Types of force
Contact force - A force exerted on a body when it is in contact with the body is called contact force. Example - Frictional force, mechanical, and muscular force.
Non-contact force - A force exerted on a body without any contact with two bodies is called contact force. Example - Gravitational force, magnetic force, and an electrostatic force.
Frictional force - Frictional force is the force caused by the relative motion of two surfaces that come in contact with each other.
Resultant force - The resultant force is a net force acting on a body along with its direction. When a body at rest or moving with a uniform velocity, the net force has to be zero.
1-Newton force
1-Newton force is defined as the amount of force that produces an acceleration of 1 m/s2 in an object of 1 kg mass.
The balanced and unbalanced force
Balanced force - The net effect produced by a number of forces on a body is zero is called balanced force
Unbalanced force - The net effect produced by a number of forces on a body is non zero and it is called unbalanced force. In an unbalanced force, two opposite forces acting on a body and the body moves in the direction of greater force.
Momentum
Momentum
The momentum of an object is the product of its mass and velocity.
- Its S.I. unit is kg m/s
- momentum has both direction and magnitude.
- it is a vector quantity
Conservation of momentum
If the external force on a system is zero, and the sum of the momentum of two objects before the collision is equal to the sum of momentum after the collision, then it is known as conservation of momentum.
Suppose A and B are two balls, they have mass mA and initial velocities uA and uB . When the two bodies collide their final velocities changes to vA and vB
Suppose A and B are two balls, they have mass mA and initial velocities uA and uB . When the two bodies collide their final velocities changes to vA and vB
The force is exerted by ball A is FAB and by the ball B is FBA.
According to the conservation of momentum
muA+ muB= mAvA + mBvB
Linear momentum
The product of the mass and velocity of a moving body is called linear momentum.
Momentum p = mv. (where = momentum, m = mass and v = velocity)
S.I unit of momentum is Kg m/s.
Prove the principle of conservation of linear momentum for two bodies moving in the same direction and coiling.
Suppose two balls A and B of masses mA and mB are moving in the same direction along a straight line at different initial velocities uA and uB, respectively. And there are no other external unbalanced forces acting on them.
Let uA is greater than uB . The two balls collide with each other. During collision ball 'A' exerts a force FAB on ball 'B' and the ball 'B' exerts a force FBA on ball 'A'.
Let uA is greater than uB . The two balls collide with each other. During collision 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 momentum of ball 'A' before the collision is mAuA
The momentum of ball 'B' after the collision is mAvA,.
The rate of change of its momentum during the collision will be
= (mA vA- mAuA) /t
= 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,
Therefore, FAB = – FBA
mA( vA - uA) / t = mB ( vB - uB) / t
or mAvA - mAuA = mBvB - mBuB
or mAuA+ mBuB = mAvA + mBvA
This proves the total momentum of the two balls remains unchanged or conserved provided no other external force acts.
The rate of change of its momentum during the collision will be
= (mA vA- mAuA) /t
= 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,
Therefore, FAB = – FBA
mA( vA - uA) / t = mB ( vB - uB) / t
or mAvA - mAuA = mBvB - mBuB
or mAuA+ mBuB = mAvA + mBvA
This proves the total momentum of the two balls remains unchanged or conserved provided no other external force acts.
Inertia
There are two types of inertia: The motion of inertia and the rest of inertia.
The tendency of undisturbed objects to stay at rest or to keep moving with the same velocity is called inertia. The physical quantity of inertia is mass and the S.I unit is Kg.
The relation between inertia and mass
The property of inertia is because of the mass of the body. The greater the mass, the greater is the inertia of the body.
Steel has the highest inertia because the mass of steel is more than the aluminum and wooden solid because the greater the mass, the greater is the inertia of the body so.
Steel has the highest inertia because the mass of steel is more than the aluminum and wooden solid because the greater the mass, the greater is the inertia of the body so.
Newton's first law that is known as the law of inertia
According to Newton's first law of motion, if a body is in rest, it will remain in the state of rest, and if it is in a state of motion, it will remain moving in the same direction with uniform velocity unless an external force is applied on it.
It is known as the law of inertia because this property of an object by virtue of which it neither changes its present state nor it tends to change the present state, is called inertia.
It is known as the law of inertia because this property of an object by virtue of which it neither changes its present state nor it tends to change the present state, is called inertia.
When a carpet is beaten with a stick it releases dust, why?
When a carpet is beaten, due to the inertia of rest, the dust remains in the state of rest and the carpet comes in motion and leaves the carpet and falls down.
Balanced and unbalanced force.
- When two equal forces acting on a body in the opposite direction, do not change the state of rest or motion of the object. These forces are called balanced forces.
- When two opposite forces of different magnitudes acting on a body, the body starts to move in the direction of the greater force. These forces are called the unbalanced force acts in the direction the body moves. An unbalanced force acting on an object brings it in motion.
Differences between mass and weight
- Mass of a body is a measure of the quantity of matter contained in the body where weight is the force by which the earth attracts the body.
- Mass is a scalar quantity, weight is a vector quantity.
- It is constant for the body and does not change by changing the place of the body, weight is not constant but varies from place to place.
Factors on which inertia depends
The factor on which inertia depends directly, are mass and acceleration.
The greater the mass, the greater is the inertia of the body.
More the mass of a body more difficult it is to move the body from rest or to stop the body if it is initially moving.
Similarly the greater the acceleration, the greater is the inertia of the body.
Newton's second law of motion.
The greater the mass, the greater is the inertia of the body.
More the mass of a body more difficult it is to move the body from rest or to stop the body if it is initially moving.
Similarly the greater the acceleration, the greater is the inertia of the body.
Newton's second law of motion.
The first law of motion indicates that when an unbalanced external force acts on an object, its velocity changes, that is the object gets an acceleration and the acceleration of an object depends on the force applied to it. Newton's second law of motion gives the quantitative value of force.
Therefore F = ma.
Newton's second law in terms of momentum.
According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the force applied on it and the change in momentum is in the direction in which the force is applied.
Newton's first law in terms of the second law.
The first law of motion can be mathematically stated from the mathematical expression for the second law of motion.
F = ma or F = m(v − u)/ t
or F= (mv – mu)/t .That is when F = 0, v = u for whatever time, t is taken. This means that the object will continue moving with uniform velocity, u throughout the time, t. If u is zero then v will also be zero. That is, the object will remain at rest. This is newtons second law.
How karate player can break a pile of tiles in a single blow with his hands.
Karate player moves his hand with high speed due to which momentum force increases and strikes the pile with his hand very fast. Thus the entire momentum of the fast-moving hand is reduced to zero in a very short time, due to this, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for breaking the pile of tiles.
Therefore F = ma.
Newton's second law in terms of momentum.
According to Newton's second law of motion, the rate of change of momentum of a body is directly proportional to the force applied on it and the change in momentum is in the direction in which the force is applied.
Newton's first law in terms of the second law.
The first law of motion can be mathematically stated from the mathematical expression for the second law of motion.
F = ma or F = m(v − u)/ t
or F= (mv – mu)/t .That is when F = 0, v = u for whatever time, t is taken. This means that the object will continue moving with uniform velocity, u throughout the time, t. If u is zero then v will also be zero. That is, the object will remain at rest. This is newtons second law.
How karate player can break a pile of tiles in a single blow with his hands.
Karate player moves his hand with high speed due to which momentum force increases and strikes the pile with his hand very fast. Thus the entire momentum of the fast-moving hand is reduced to zero in a very short time, due to this, the rate of change of momentum of the ball will be large. Therefore, a large force would have to be applied for breaking the pile of tiles.
When a tree is shaken, its fruits and leaves fall down
It is due to the inertia of rest in which 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 force.
When a tree is shaken, it brings a motion in the tree but its fruits and leaves tend to continue in the same state of rest because of its inertia which causes the leaves and fruits to separate from its branch and fall down.
When a tree is shaken, it brings a motion in the tree but its fruits and leaves tend to continue in the same state of rest because of its inertia which causes the leaves and fruits to separate from its branch and fall down.
The action and reaction forces for a man walking on the road
According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction. when we push the road below backward, the road exerts an equal and opposite reaction force on our feet to make us move forward.
Derivation of the relation between force and acceleration
The mathematical formulation of the second law of motion:
If the mass of an object is 'm' and moving along a straight line with an initial velocity u.
If the mass of an object is 'm' and moving along a straight line with an initial velocity u.
It is uniform velocity is v in time 't' and the constant force is F,
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
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
According to Newtons second law
The applied force F ∝ m (v−u ) /t
F= km (v- u)/ t
F = kma : Here [a (acceleration)= (v – u)/t ]
The quantity, k is a constant of proportionality. If the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces an acceleration of 1 m/s2 in an object of 1 kg mass.
That is, 1 unit of force = k × (1 kg) × (1 m/s2).
Thus the value of k becomes 1.
From Eq. F = ma
The unit of force is kg m/s2 or Newton N.
The applied force F ∝ m (v−u ) /t
F= km (v- u)/ t
F = kma : Here [a (acceleration)= (v – u)/t ]
The quantity, k is a constant of proportionality. If the value of the constant, k becomes one. For this, one unit of force is defined as the amount that produces an acceleration of 1 m/s2 in an object of 1 kg mass.
That is, 1 unit of force = k × (1 kg) × (1 m/s2).
Thus the value of k becomes 1.
From Eq. F = ma
The unit of force is kg m/s2 or Newton N.
How a force can change the velocity of a body?
According to newtons 2nd law, F = ma, therefore, a force can cause acceleration on a moving body and acceleration means a change in velocity at a constant rate i.e, a force can change the velocity of a body E.g., a moving ball comes to rest
The frictional force acting in the opposite direction of motion between the moving body and floor.
The frictional force acting in the opposite direction of motion between the moving body and floor.
Newton’s third law of motion
According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously exerts a force back on the first. These two forces are always equal in magnitude but opposite in direction.
If we are standing at rest and intend to start walking on a road. we must accelerate, and this requires a force in accordance with the second law of motion. We push the road below backward. The road exerts an equal and opposite reaction force on our feet to make us move forward.
If we are standing at rest and intend to start walking on a road. we must accelerate, and this requires a force in accordance with the second law of motion. We push the road below backward. The road exerts an equal and opposite reaction force on our feet to make us move forward.
Action and reaction forces
Action and reaction forces act on different bodies. According to Newton's third law of motion when one object exerts a force on another object, the second object instantaneously 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 the same object. These two opposing forces are also known as action and reaction forces.
The physical principle on which jet aircraft work
Newton's third law is the physical principle on which jet aircraft work. According to Newton's third law, when jet air crafts exert force on the air, air gives equal and opposite reaction force on the jet, due to which jet aircraft can move in the forward direction.
Recoil
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. 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.
Factors on which solid and liquid pressure depends
Factors of solid pressure: The pressure exerted on a surface depends on
(i) Force or thrust and - Larger the force on the surface, larger is the pressure exerted on it
(ii) Area on which thrust is applied- Larger the area, less is the pressure exerted on it.
Factors of liquid pressure : The pressure at a point inside the liquid depends on
(i) depth of the point below the surface- Larger the depth of the point, the larger is the pressure exerted on it
(ii) the density of the liquid- Larger the density of the liquid, larger is the pressure exerted on it
(iii) acceleration due to gravity- Larger the acceleration due to gravity larger is the pressure exerted on it.
(i) Force or thrust and - Larger the force on the surface, larger is the pressure exerted on it
(ii) Area on which thrust is applied- Larger the area, less is the pressure exerted on it.
Factors of liquid pressure : The pressure at a point inside the liquid depends on
(i) depth of the point below the surface- Larger the depth of the point, the larger is the pressure exerted on it
(ii) the density of the liquid- Larger the density of the liquid, larger is the pressure exerted on it
(iii) acceleration due to gravity- Larger the acceleration due to gravity larger is the pressure exerted on it.
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