The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.
Thus, if under the action of a force F for time interval Δt, the velocity of a body of mass m changes from v to v + Δv i.e. its initial momentum p = m v changes by m Δ = Δ p v . According to the Second Law, F = k dp/dt where k is a constant of proportionality.
For a body of fixed mass m, F = m dv/dt = ma which shows that force is proportional to the product of mass m and acceleration a.
In SI unit force is one that causes an acceleration of 1 m s-2 to a mass of 1 kg. This unit is known as newton : 1 N = 1 kg m s-2.
1. In the second law, F = 0 implies a = 0. The second Law is obviously consistent with the first law.
2. The second law of motion is a vector law. It is equivalent to three equations, one for each component of the vectors : F along x axis is equal to m( a along x axis and so on).
This means that if a force is not parallel to the velocity of the body, but makes some angle with it, it changes only the component of velocity along the direction of force. The component of velocity normal to the force remains unchanged. For example, in the motion of a projectile under the vertical gravitational force, the horizontal component of velocity remains unchanged .
The second law of motion given by Eq. F= ma is applicable to a single point particle. The force F in the law stands for the net external force on the particle and a stands for acceleration of the particle.
3. The law in the same form applies to a rigid body or, even more generally, to a system of particles. In that case, F refers to the total external force on the system and a refers to the acceleration of the system as a whole. Here a is the acceleration of the centre of mass of the system. Any internal forces in the system are not to be included in F.
4 . The second law of motion is a local relation which means that force F at a point in space (location of the particle) at a certain instant of time is related to a at that point at that instant. Acceleration here and now is determined by the force here and now, not by any history of the motion of the particle .
Impulsewhen a large force acts for a very short duration producing a finite change in momentum of the body. For example, when a ball hits a wall and bounces back, the force on the ball by the wall acts for a very short time when the two are in contact, yet the force is large enough to reverse the momentum of the ball. Here the force and the time duration are difficult to ascertain separately. But the product of force and time, which is the change in momentum of the body remains a measurable quantity. This product is called impulse.
Impulse = Force × time duration = Change in momentum.
A large force acting for a short time to produce a finite change in momentum is called an impulsive force.Related posts :
Newton's First law of motion
Concept of momentum
Uniform circular motion
Projectile motion
Thus, if under the action of a force F for time interval Δt, the velocity of a body of mass m changes from v to v + Δv i.e. its initial momentum p = m v changes by m Δ = Δ p v . According to the Second Law, F = k dp/dt where k is a constant of proportionality.
For a body of fixed mass m, F = m dv/dt = ma which shows that force is proportional to the product of mass m and acceleration a.
In SI unit force is one that causes an acceleration of 1 m s-2 to a mass of 1 kg. This unit is known as newton : 1 N = 1 kg m s-2.
1. In the second law, F = 0 implies a = 0. The second Law is obviously consistent with the first law.
2. The second law of motion is a vector law. It is equivalent to three equations, one for each component of the vectors : F along x axis is equal to m( a along x axis and so on).
This means that if a force is not parallel to the velocity of the body, but makes some angle with it, it changes only the component of velocity along the direction of force. The component of velocity normal to the force remains unchanged. For example, in the motion of a projectile under the vertical gravitational force, the horizontal component of velocity remains unchanged .
The second law of motion given by Eq. F= ma is applicable to a single point particle. The force F in the law stands for the net external force on the particle and a stands for acceleration of the particle.
3. The law in the same form applies to a rigid body or, even more generally, to a system of particles. In that case, F refers to the total external force on the system and a refers to the acceleration of the system as a whole. Here a is the acceleration of the centre of mass of the system. Any internal forces in the system are not to be included in F.
4 . The second law of motion is a local relation which means that force F at a point in space (location of the particle) at a certain instant of time is related to a at that point at that instant. Acceleration here and now is determined by the force here and now, not by any history of the motion of the particle .
Impulsewhen a large force acts for a very short duration producing a finite change in momentum of the body. For example, when a ball hits a wall and bounces back, the force on the ball by the wall acts for a very short time when the two are in contact, yet the force is large enough to reverse the momentum of the ball. Here the force and the time duration are difficult to ascertain separately. But the product of force and time, which is the change in momentum of the body remains a measurable quantity. This product is called impulse.
Impulse = Force × time duration = Change in momentum.
A large force acting for a short time to produce a finite change in momentum is called an impulsive force.Related posts :
Newton's First law of motion
Concept of momentum
Uniform circular motion
Projectile motion
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