 # Newton's Second Law of Motion  View Notes

### What is Newton’s Second Law of Motion?

Newton's second law of motion is related with the first law of motion. It gives the quantitative definition of force. Mathematically, it describes the causes and effects of force and changes in motion of an object. Before understanding the equation of Newton's second law of motion which deals with force, mass and acceleration of an object, let’s have a look upon the three laws of motion.

### The Three Laws of Motion:

1.Newton's 1st law: It is also called the law of inertia. The statement depicts, “if a body is in the state of absolute rest, or in uniform motion, it will continue to remain likewise, provided it is acted upon by a foreign force.”

2.Newton's 2nd law: The statement depicts, “the rate of change of momentum of a body is directly proportional to the external force applied to the body. Further, the momentum of the body happens to be in the direction where the force is exerted.”

3.Newton's 3rd law: The statement depicts, “no matter what is the action, according to this phenomenon, always an equal & opposite reaction abides for it”.

### Newton’s Second Law Statement

Newton’s first law statement, “unless a body is acted by a foreign force, it abides in its state of rest, or of uniform motion.” So, the question arises, what happens to your body when an external force is applied to it? This answer is provided by Newton's second law of motion.

According to Newton's second law of motion, force acting on a body is equal to the rate of change of momentum. For a body with a constant mass ‘m’, force is given by,

F = ma

Where,

a = acceleration produced in the body.

The above equation describes that, if the force is doubled, the acceleration also gets doubled, and if mass is doubled, acceleration becomes half.

Sir Issac Newton published his works about the laws of motion in 1687, in his book "Philosophiæ Naturalis Principia Mathematica" (Mathematical Principles of Natural Philosophy), in which he described how objects with different masses move under the influence of applied force.

The first study regarding the laws of motion was done by Galileo Galilei. Based on Galileo's experiments, all objects accelerate at the same rate regardless of their size and mass. Rene Descartes has also published some laws regarding the motion of objects in 1644. Later Sir Issac Newton expanded the works of both these scientists and formulated his laws of motion.

### Acceleration and Velocity

Newton's second law of motion describes that, when a force is applied to an object, it produces acceleration in the object (i.e rate of change of velocity). For an object at rest, the applied force produces acceleration in the object and makes the object move in the direction of applied force.

For an object which is already in motion, the direction of the applied force matters to determine its state. If external force is applied in the direction in which the object is moving, the acceleration of the object increases. If external force is applied in the direction opposite to the motion of the object, the acceleration of the object decreases and finally comes to stop.

Force and acceleration are vector quantities, i.e they have both magnitude and direction. Multiple forces can also act in a body at a time.

Hence,

∑F = ma

Where;

Σ = vector sum of all the forces acting on a body (net force).

### Application of Newton’s Second Law of Motion

Some applications of Newton's second law of motion are mentioned below:

1. Kicking a Ball

When we kick a ball we apply some force in it, and in a specific direction. The ball moves in this direction. If the applied force is more the distance covered by the ball will be more, and if the applied force is less the distance covered by the ball will be less.

1. Pushing a Cart

Pushing an empty card is easy as compared to pushing a loaded cart; this is because if the mass of an object is more, a large amount of force will be needed to move it.

1. Two People Walking

If two people of different masses work together, the one with the heavier mass will walk slower as compared to the one with the lighter mass. This is because more acceleration is produced by the lightweight person.

### Second Law Of Motion Examples

Some of Newton’s second law of motion examples is mentioned below:

●  Pushing or pulling an empty cart is easy as compared to a loaded cart because the loaded cart has more mass.

●  If the same amount of force is applied to move a car and a bike, the acceleration of the bike will be more because it has less mass than the car.

●    When a ball drops on the ground, it exerts a downward force on the ground, and in reaction to it the ground exerts an equal upward force on the ball, thus making it bounce.

●      Stopping a moving ball requires force.

1. How Much Horizontal Net Force Is Required To Accelerate A 500 Kg Car At 5 m/s2?

Newton’s 2nd Law of motion describes the relationship between mass, force and acceleration of an object: Therefore, we can calculate the force by the equation:

Fnet = ma

Substituting the values of mass and acceleration, we get:

500 kg × 5 m/s2 = 2500 N

Therefore, 2500 N of horizontal net force is required to accelerate the car.

Newton’s second law of motion is applied in daily life at many places. For instance, in Formula One racing, the mass of the cars are kept as low as possible so that they can generate a higher acceleration, and their chance to win the race becomes high.

2. Which Of The Following is/Are True About Force?

1. Force will always change the magnitude of velocity

2. S.I unit of force is Newton

3. Force will always change the direction of the velocity

4. All of the above

Ans- 2

Force doesn't always change the magnitude of velocity of the object. Example: Centripetal force, It changes the only direction of motion of the object, but it doesn't change the magnitude of velocity.

Force doesn't always change the direction of motion of an object. Example: Linear motion, the frictional force only reduces the velocity of the object but it doesn't change the direction of the object.

SI unit of force is Newton.

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