Physics
Force
Force is that quantity the application of which a stationary object start move and a body moving, with a uniform velocity change its velocity.
All objects in the universe attracts one another by a force due to their mass. This force is called the gravitational force.
An object that has mass attracts another object by the gravitational force.
Fundamental forces are actually only in number. These are:
1. Gravitational Force:
All objects in the universe attract one another by a force due to their mass. This force is called the gravitational force. Ex. The stars are revolving within the galaxy.
2. Electromagnetic Force:
The eletromagnetic force is a type of physical interaction that occurs between electrically changed particles.
3. Weak Nuclear Force:
It is called weak because it is weaker than the electromagnetic force but not at all weak like the gravitational force.
4. Strong Nuclear Force:
This is the strongest force of the universe; this is hundred times stronger than the electromagnetic force but it too acts at a very small distance (10 - 15m).
Newton's first law of motion:
A stationary object will remain stationary and an object in uniform motion will continue its uniform motion unless a force is applied to it.
(Since velocity is a vector quantity, for uniform motion the object will not change its direction of motion; it will move along a straight line at uniform speed.
We always observe that the bodies at rest remain at rest and do not move until pushed.
A body in motion keeps its perpetual motion for ever this is come from second part.
Q.1. What is inertia?
Ans: The characteristic that a stationary body wants to be stationary or a body in motion wants to keep its motion, unless a force is applied, is called inertia. Ex. When a car at rest suddenly starts moving we move backward. The lower part of the body is attached to the car. When the car starts moving, the lower part of the body moves with the car but the upper part of the body move backward. Since this inertia is due to the tendency of rest, this is called inertia of rest.
Q.1. Two graphs show the values of position and velocity with time in figure, explain where and for what period force was applied?
Ans: Both graphs are identical to look at, but they contain totally different information.
In the graph, from 0 to t1 or from t2 to the end, there is no change in position in these two time intervals, this means there is no velocity, therefore there is no question of change of velocity. This means definitely no force is acting in these two time intervals. From time t1 to t2 there is a change in position, but the change is at the same rate, that means the object is moving with a uniform velocity.
Therefore, when 0< t <t1, t1 < t < t2 and t2 < t1, there is no force. Only when t = t1 and t = t2 force is applied for a moment.
In the second graph, from 0 to t1 and from t2 to end, the object is in uniform motion, therefore no force is acting on the body in these time intervals. From time t1 to t2 the velocity is changing at a uniform rate, therefore, defenitely a force is applied on it.
Therefore, when 0 < t < t1 and t2 < t1, there is no force when, t1 < t < t2 force is applied.
Momentum:
Product of the mass of a particle and its velocity. Its a vector quantity, it has both magnitude & direction.
Isaac Newton's second law of motion states that the time rate of change of momentum is equal to the force acting on the particle.
Mass:
Quantity that designates how fast and in what direction a point is moving.
Velocity:
Quantity that designates how fast and in what direction a point is moving.
Sir Isaac Newton English physicist and mathematician, who was the calculating figure of the Scientific Revolution of the 17 th century.
Unit of momentum is kg m/s.
Newton's Second Law:
The rate of change of momentum of a body is proportional to the applied force acting on it and the change of momentum also takes place in the direction in which the force acts.
The more force, the more Acceleration.
If a body is moving with an initial velocity u and the velocity is changed ( by increasing or decreasing) from u to v after a time t.
Therefore, change of momentum:
mv - mu
So, the rate of change of momentum:
mv - mu
一一一一
t
= m (v - u) /t
= ma
Since, we considered that there is no change of mass, so we can write like this.
Further we know that acceleration is:
a = v-u/t
Therefore, if the applied force is F, then we can write Newton's second law of motion as:
F ∝ ma
But we don't want to express the law in proportional form, rather we want to write it as an equation.
Then using a proportionality constant k, we can write
F = kma
Therefore, we can write Newton's second law of motion as an equation. If the force is F and the proportionality constant is considered as 1, then
F = ma
That small and simple equation can make a revolutionary change in the world of physics is difficult to believe.
The unit of force is Newton (N).
Dimension of force is [ F ] = MLT ¯²
It has to be remembered that Newton's second law of motion is true not only for linear motion, but this is true for any type of motion. We have known about gravitational force, by using Newton's second law, we will be able to explain the motion of the planets revolving around the sun due to the gravitational force. If force is applied on an object, then by using Newton's second law, its acceleration can easily be determined.
Collision:
A collision is any event in which two or more bodies exert forces on each other in a relatively short time.
Let us consider that two objects of masses m1 and m2 are moving along a straight line in a plane. Due to the difference of their velocities they collide and hence their velocities are changed.
Now, v1 and v2 are the new velocities of masses m1 and m2 respectively.
The combined momentum of the two objects before
collision = m1u1 + m2 u2
The combined momentum of the two objects after collision = m1v1 + m2v2
Since, no force is applied from outside, hence the momentum before collision and after collision will be the same. This is the law of conservation of momentum.
Therefore, we can write, m1u1 + m2u2 = m1 v1 + m2v2
Here, we have only one equation and two unknown quantities v1 and v2, therefore we cannot calculate the values of v1 and v2.
Kinetic energy of an object can be expressed as 1/2 mu2
Where m is the mass and u is the velocity of the object.
Therefore, using the law of conservation of energy, we can write,
½ m1u1² + ½ m2u2²
Newton's Third Law:
When an object applies a force on another object, then that object also applies a force of equal magnitude on the first object but in the opposite direction.
Every action has an equal and opposite reaction.
Let us consider that a mass m is allowed to fall from a certain height. We know that due to the earth's gravitational force, the mass m experiences a force F towards the centre of the earth.
F = G mM/R2
Now Newton's third law we know that the mass m also attracts the giant earth tpwards itself. That force is also F, but in the opposite direction. Acceleration a of the earth due to this force can be determined
F = Ma
Here, M is the mass of the earth and a is the acceleration,
Therefore, a = F/M = mg/M = (m/M) g
If the mass you are standing on a totally frictionless surface. Your mass is 50 kg and there is a stone of mass 100kg in front of you. You decided that you will push the stone with a force of 50 N and will move it from one an end to the other end. What will be the velocity of the stone after 10 s?
Ans: When you will push the stone with a force of 50N, then according to Newton's third law the stone will push you also with a force of 50 N. There acceleration of the stone will be towards the right.
a = F/m = 50/100 m/s2
= 0.5 m/s2
Your acceleration will be exactly towards left,
a = F/m = 50/50 m/s2 = 1 m/s2
Therefore, the stone and you will move in different directions. By pushing the stone you cannot move it from one end to the other. Because a distance will be created between you and the stone. So, it is not possible to push the stone nonstop for 10s. But after the stone starts its movement, it will reach the other end moving by itself on the frictionless surface. You will also reach the opposite end but at an earlier time.
Q.2. Let us consider you pushed the stone for 2S, what happens then ?
Ans: In 2S the velocity of the stone will be increased to
v = u + at
= 0 + 0.5 x 2 m/s
= 1 m/s
Then the stone will move with a uniform velocity of 1 m/s
In 2 s your velocity will be:
u + at = 0 + 1 x 2 m/s = 2 m/s
Then you will move in the reverse direction with a uniform velocity of 2 m/s.
