state all tree laws of motion and derive an expreesion for newtons second law
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Newton's second law of motion derivation
Newton's second law of motion states that, "The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which force acts".
NEWTONS SECOND LAW OF MOTION MATHEMATICALLY STATED
Answer:
NEWTON'S LAWS OF MOTION
Newton was the first to formulate the laws of motion known as Newton's laws of motion.
/ NEWTON'S FIRST LAW OF MOTION
First law of motion deals with bodies which are either at rest or moving with uniform speed in a straight line. According to Newton's first law of motion, a body at rest remains at rest provided no net force acts on it. This part of the law is true as we observe that objects do not move by themselves unless someone moves them. For example, a book lying on a table remains at rest as long as no net force acts on it.
Similarly, a moving object does not stop moving by itself. A ball rolled on a rough ground stops earlier than that rolled on a smooth ground. It is because rough surfaces offer greater friction. If there is no force to oppose the motion of a body, the moving body will never stop. Thus Newton's first law of motion states that:
A body continues its state of rest or of uniform motion in a straight line provided no net force acts on it.
Since Newton's first law of motion deals with the inertial property of matter, therefore, Newtons fin law of motion is also known as law of inertia.
We have observed that the passenger standing in a bus fall forward when its driver apples brakes suddenly. It is because the upper parts of the bodies tend to continue their motion, while lower pan of their bodies in contact with the bus stop with Hence, they fall forward.
NEWTON'S SECOND LAW OF MOTION
Newton's second law of motion deals with situations when a net force is acting on a body. i states that
When a net force acts on a body, It produces acceleration in the body in the direction of the net force. The magnitude of this acceleration is directly proportional to the net force acting on the body and inversely proportional to its mass.
In Si units, the value of k comes out to be 1
Thus Eq. 3 2 becomes
F = ma
Si unit of force is newton (N). According 9 Newton's second law of motion
(3.3)
One newton (1 N) is the force that produces an
acceleration of 1 ms in a body of mass of 1 kg. Thus, a force of one newton can be expressed as
IN = 1 kg x 1 ms =
or IN = 1 kg ms
(3.4)
NEWTON'S THIRD LAW OF MOTION
Newton's third law of motion deals with the reaction of a body when a force acts on it. Let a body A exert a force on another body B. the body B reacts against this force and exerts a lorce on body A. The force exerted by body A on B is the action force reaction force Newton's third law of motion states that:
To every action is always an equal but opposite reaction.
Figure 3.8: Action whereas the force exerted by body B on A is called the and reduction on t
To every action there is always an equal but opposite reaction
According to this law, action is always accompanied by a reaction force and the two forces must always be equal and opposite. Note that action and reaction forces act on different bodies.
. The weight of the book is acting on the table In the downward direction. This is the action. The reaction of the table acts on the book in the upward direction. Consider another example. Take an air-filled balloon as shown in figure 3.9. When the balloon is set free, the air inside it rushes out and the balloon moves forward. In this example, the action is by the balloon that pushes the air out of it when set free. The reaction of the air which escapes out from the balloon acts on the balloon. It is due to this reaction of the escaping air
et moves the balloon forward A rocket such as shown in figure 3.10 moves on the same principle. When its fuel burns, hot gases cape out from its tail with a very high speed. The reaction of these gases on the rocket causes it to move opposite to the gases rushing out of its tail.
