Newtons Laws of Motion
Category : 9th Class
Newton's Laws of Motion
Newton's First Law of Motion
Everybody remains in its state of rest or of uniform motion, unless it is compelled to change its state by an unbalanced force, impressed on it.
\[F=m\times a\]
if, \[F=0\]
\[\Rightarrow \,\,a=0\,\,(m\ne 0)\]
(i) We tend to fall forward when a bus suddenly stops. When bus stops suddenly, we tend to resist the change in our state of motion and hence fall forward.
(ii) We tend to fall backward when a bus suddenly starts.
(iii) We tend to get thrown to one side when a car takes sharp turn.
Martin and Robert are arguing in the cafeteria. Martin says that if he throws the burger with a greater speed it will have a greater inertia. Robert argues that inertia does not depend upon speed, but rather upon mass. With whome do you agree?
(a) Martin
(b) Robert
(c) Both are correct
(d) Both are incorrect
(e) None of these
Answer: (b)
Why it is advised to tie the luggage with a rope on the roof of bus?
(a) Luggage might fall in forward direction
(b) Luggage might fall in backward direction
(c) To prevent fall (in both the directions) of the luggage from the roof of the bus.
(d) All of these
(e) None of these
Answer: (c)
Newton's Second Law of Motion
The rate of change of momentum of a body is directly proportional to the unbalanced force applied and takes place in the direction of the force.
Mathematical expression,
\[F=\frac{dp}{dt}=m\times a\]
\[\Rightarrow \,\,F\alpha \frac{\Delta p}{\Delta t}\]
\[\Rightarrow \,\,F=k\frac{\Delta p}{\Delta t}\]
Where, k is the constant of proportionality.
Taking the limit \[\Delta t\to 0,\] the term \[\frac{\Delta p}{\Delta t}\] becomes the derivative and is denoted by,
\[\frac{dp}{dt}=\frac{d(m\times v)}{dt}=\frac{mdv}{dt}=m\times a\]
\[\Rightarrow \,\,F=\frac{dp}{dt}\,\,\,\,\,\,=m\times a\]
(i) A cricketer gradually pulls hand backwards with the moving ball when he catches the ball. While doing so he increases the time during which the high velocity of the ball is reduces to zero and the acceleration of the ball is also reduced drastically and hence the impact of catching the ball is also reduced and it does not hurt the player.
(ii) A judo champ breaks a pile of bricks in one go. His action is too fast. In this case he needs to increase the force with which he can break the pile, so he decreases the time by fasting his action.
(iii) In a high jump athlete event, the athlete falls on a cushioned bed to increase the time of stop. This results in the decrease of the rate of change of momentum and hence force.
Newton's Third Law of Motion
It states that to each and every action there is equal and opposite reaction. Action and reaction always acts on different bodies.
Application of Newtons Third Laws
We can derive Newton's
(a) Second and third laws from the first law
(b) First and second laws from the third law
(c) Third and first laws from the second law
(d) All the three laws are independent of each other
(e) None of these
Answer: (c)
A body of mass 2 kg moving on a horizontal surface with initial velocity of \[4\,\,m{{s}^{-1}}\] comes to rest after two seconds. If one wants to keep this body moving on the same surface with a velocity of \[4\,\,m{{s}^{-1}}\], the force required is:
(a) 2 N
(b) 4 N
(c) 0 N
(d) 8 N
(e) None of these
Answer: (b)
Many people are familiar with the fact that a rifle recoils when fired. This recoil is the result of action-reaction force pairs. A gunpowder explosion creates hot gases which expand outward allowing the rifle to push forward on the bullet. Consistent with Newton's third law of motion, the bullet pushes backwards upon the rifle. The acceleration of the recoiling rifle is...
(a) Greater than the acceleration of the bullet
(b) Smaller than the acceleration of the bullet
(c) The same size as the acceleration of the bullet
(d) All of these
(e) None of these
Answer: (b)
In the picture (below), Billu is pulling upon a rope which is attached to a wall. In the bottom picture, the Billu is pulling upon a rope which is attached to an elephant. In each case, the force scale reads 500
Newtons. Billu is pulling...
(a) With more force when the rope is attached to the wall
(b) With more force when the rope is attached to the elephant
(c) The same force in each case
(d) all of these
(e) None of these
Answer: (c)
Momentum
The product of mass of a body and its velocity is called momentum of the body. It is a vector quantity. It is given by \[\overrightarrow{P}=m\times \overrightarrow{a}\]
It is the measure of the quantity of the motion possessed by a body.
Impulse
The product of force and time for which it is applied is called impulse. SI unit of impulse is Ns.
Impulse = Force x Time duration
= Change in momentum.
The momentum of a toy bus of 0.01 kg moving with a velocity of 5 m/s is:
(a) 0.005 kg m/s
(b) 0.05 kg m/s
(c) 0.005 N s
(d) 0.5 kg m/s
(e) None of these
Answer: (b)
A force of 5 Newton is applied on body of mass M produces an acceleration of \[10\,\,m/{{s}^{2}}\]. The same force when applied on another body of mass 'm' produces an acceleration of \[20\,\,m/{{s}^{2}}\]. Find the acceleration produced by the force when both the mass are combined together.
(a) \[10\,\,m/{{s}^{2}}\]
(b) \[6.6\,\,m/{{s}^{2}}\]
(c) \[0.75\,\,m/{{s}^{2}}\]
(d) \[50\,\,m/{{s}^{2}}\]
(e) None of these
Answer: (b)
Law of conservation of momentum
The total momentum of a system remains constant unless some external force acts on it.
Let us take two balls \['A'\,\And \,'B'\] having initial velocities \[{{u}_{A}}\,\And \,\,{{u}_{B}}\] respectively.
Momentum of ball A before collision is \[{{m}_{A}}{{u}_{A}}\]
Momentum of ball B before collision is \[{{m}_{B}}\,{{u}_{B}}\]
If final velocities of A & B are \[{{V}_{A}}\,\And \,{{V}_{B}}\] respectively.
Then,
Momentum of ball A after collision is \[{{m}_{A}}{{V}_{A}}\]
Momentum of ball B after collision is \[{{m}_{B}}\,{{V}_{B}}\]
The rate of change of momentum of ball A is \[{{m}_{A}}\frac{({{V}_{A}}-{{u}_{A}})}{t}\]
The rate of change of momentum of ball B is \[{{m}_{B}}\frac{({{V}_{B}}-{{u}_{B}})}{t}\]
According to third law, the force exerted by ball A on ball B is equal and opposite.
\[{{m}_{A}}{{u}_{A}}+{{m}_{B}}{{u}_{A}}={{m}_{B}}{{v}_{B}}-{{m}_{B}}{{u}_{B}}\]
\[{{m}_{A}}{{u}_{A}}+{{m}_{B}}{{u}_{B}}={{m}_{A}}{{V}_{A}}+{{m}_{B}}{{V}_{B}}\]
Momentum before collision = Momentum after collision
If the two bodies stick to each other after collision then they will move with a common velocity v given by, \[{{m}_{A}}{{u}_{A}}+{{m}_{B}}{{u}_{B}}=({{m}_{A}}+{{m}_{B}})V\]
\[V=\frac{({{m}_{A}}{{u}_{A}}+{{m}_{B}}{{u}_{B}})}{({{m}_{A}}+{{m}_{B}})}\]
A girl of mass 40 kg having velocity 2m/sec jumps on a stationary cart of mass 4 kg. Find the velocity of the girl when the cart starts moving.
(a) 2m/s
(b) 80m/s
(c) 1.81 m/s
(d) 78m/s
(e) None of these
Answer: (c)
The bullet of mass 25 gm is fired with a velocity of 125 m/s from a pistol of mass 2 kg. Find out the velocity with which the pistol will recoil.
(a) 1.25 m/s
(b) 2.5 m/s
(c) 125 m/s
(d) 130 m/s
(e) None of these
Answer: (a)
As you sit in your chair and study your science (presuming that you do), the force of gravity acts downward upon your body. The reaction force to the force of the Earth pulling you downward is __.
(a) The force of the chair pushing you upward
(b) The force of the floor pushing your chair upward
(c) The force of air molecules pushing you upwards
(d) The force of your body pulling the Earth upwards
(e) None of these
Answer: (d)
Name the property of matter due to which a body continues in its state of rest or uniform motion unless an external force acts on it.
(a) Inertia
(b) Elasticity
(c) Viscosity
(d) Density
(e) None of these
Answer; (a)
The sparks produced during sharpening of a knife against a grinding wheel leaves the rim of the wheel tangentially. This is due to ____.
(a) Inertia of rest
(b) Inertia of motion
(c) Inertia of direction
(d) Force applied
(e) None of these
Answer: (C)
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