Newton's law

 

 Newton's First Law of Motion:

Definition: An object at rest will stay at rest, and an object in motion will stay in motion unless acted upon by a net external force.

Example: Imagine you're playing hockey on an ice rink. When you hit the puck with your hockey stick, it slides across the ice until it eventually stops. Why does it stop? It's because of friction between the puck and the ice. If there were no friction, the puck would keep sliding forever due to its inertia, which is its resistance to change in motion, as described by Newton's first law.

Question:

A car is moving along a straight road at a constant velocity of 20 m/s. Suddenly, the driver applies the brakes, bringing the car to a stop in 5 seconds. Calculate the net force acting on the car according to Newton's first law.

Solution:

According to Newton's first law of motion, an object will remain at rest or in uniform motion unless acted upon by an external force. When the car is brought to a stop, it means there must be a net external force acting on it to change its state of motion.

Given:

- Initial velocity, u = 20 m/s

- Final velocity, v = 0 m/s since the car comes to a stop

- Time taken, t = 5s 

First, let's find the acceleration using the formula:

 a = v – u/t

 a = 0 – 20/5

 a = -4, m/s²

The negative sign indicates that the acceleration is in the opposite direction to the initial velocity, as the car is decelerating.

Now, according to Newton's second law F = ma, the net force acting on the car can be calculated by multiplying the mass of the car by its acceleration.

Let's assume the mass of the car m = 1000kg you can change this value if provided in the question:

 F = m times a

 F = 1000 times -4

 F = -4000 N

So, the net force acting on the car, according to Newton's first law, is -4000N. The negative sign indicates that the force is acting in the direction opposite to the car's initial motion, which is necessary to bring it to a stop.

Newton Second Law of Motion :-

Definition: The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. In simple terms, force equals mass times acceleration (F = ma).

Example: Imagine you're pushing a shopping cart in a supermarket. If you push it lightly, it moves slowly. But if you push it harder, it moves faster. Why? Because the force you apply (your push) causes the cart to accelerate. And the heavier the cart (more mass), the harder you need to push (more force) to make it move at the same speed.

Question :- A car of mass 1000 kg accelerates from rest to a velocity of 20 m/s in 10 seconds. Calculate the force exerted by the engine.

Solution:

To solve this problem, we can use Newton's second law equation, F = ma, where F  is the force,  m is the mass of the object, and  a is the acceleration.

Given:

- Mass of the car,  m = 1000 kg

- Initial velocity,  u = 0 m/s since the car starts from rest)

- Final velocity,  v = 20  m/s

- Time taken,  t = 10 s

First, let's find the acceleration using the formula:

a = v – u/t

a = 20 – 0/10

 a = 2 , m/s²

Now, we can use Newton's second law to find the force:

F = ma

F = 1000 * 2

F = 2000 N

So, the force exerted by the engine is 2000 Newtons.

Newton's Third Law of Motion :

Definition: For every action, there is an equal and opposite reaction. This means that whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.

Example: Consider a rocket launching into space. As the rocket engines expel gas downward, the gas pushes against the ground with an equal and opposite force. This force propels the rocket upward. The rocket exerts force on the gas, and the gas exerts an equal force on the rocket, causing it to accelerate upwards.

Question:

A rocket of mass 5000 kg is launched into space. When the rocket engines expel gas with a force of  2 times 10^5 , N  downwards, what is the force exerted by the rocket on the gas?

Answer:

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. In this case, the action is the force exerted by the rocket engines on the gas, and the reaction is the force exerted by the gas on the rocket.

Given:

- Mass of the rocket, m = 5000 kg

- Force exerted by the rocket engines, F action = 2*10⁵, N downwards

According to Newton's third law, the force exerted by the rocket on the gas F reaction is equal in magnitude but opposite in direction to the force exerted by the gas on the rocket.

 So, F_reaction = F_action = 2*10⁵, N since the magnitude is the same.

Therefore, the force exerted by the rocket on the gas is 2*10⁵, N upwards.

Understanding these laws helps us comprehend how objects move and interact with each other. They're fundamental principles in physics and are essential for understanding various phenomena in our everyday lives and the universe.