Mechanics

# Newton’s Second Law of motion: Definition, Formula & Exaamples

Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the applied force. According to Newton’s first law of motion “if no net force is acting on a body at rest, then the body remains at rest, or if the body is moving will continue to move. Common Newton’s second law of motion examples is Pushing trolly, pulling the cart by applying force.
But!
What will happen if the net force is acting on a body?
Newton perceived that the velocity of a body increased or decreased by applying a net force. If the net force is applied to the sideway of an object, its direction of velocity will change, which is called acceleration. This is called Newton’s 2nd law.

Explanation:
Newton’s 2nd law of motion deals with situations when a net force is acting on a body. It states that:
“When a net force acts on a body, it produces an 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.”

## Newton’s second law formula

If a force produces an acceleration an in a body of mass m, then we can state mathematically that as:

a ∝ F

and  a ∝ 1/m

or     a ∝ F/m

or     F ∝ ma

Putting k as a proportionality constant we get

F= k ma …..(1)

In SI units,   the value of k comes out to be one. Thus equation (1) becomes:

F =ma

SI unit of force is Newton (N). According to Newton’s second law:
“One newton (1N) is the force that produces an acceleration of 1ms-2 in a body of the mass of 1 kg. Thus, the force of one newton can be expressed as:
1N = 1kg ×1ms-2
or  1N =1kgms-2

## Newton’s second law of motion examples

Below are some cases from everyday life examples of Newton’s second law of motion can be observed:

1. What is the speed that a helicopter must have to stay in the air could be an example where the second law applies.
2. The speed that a rocket needs to acquire in order to be able to go into orbit is another example.
3. The calculation of the acceleration obtained by a stone in free fall also reflects Newton’s statement.
4. Establishing what is the movement that the planet Earth makes around the sun is another case in which the second law of motion is embodied.
5. Exerting force on a supermarket cart in order to push it is another clear example of daily life that reflects Newton’s second law.
6. The force a golfer must exert in order for his ball to hit the hole plots Newton’s Second Law statement.
7. Establishing the force as well as the angle a Gomera must acquire in order for the cast stone to hit the expected target also reflects Newton’s second law.
8. Determine the force that a cart must acquire to transport what it loads.
9. The force that must be exerted on a car for this advance is another example of Newton’s second law.
10. The force with which a soccer ball must be kicked in order for it to change its speed could be another case in which the law in question is observed.

## Practice problems for Newton’s 2nd law of motion with answers

1. 20 N force moves a body with an acceleration of 2m/s². What is its mass?

Data:

Force= F= 20 N

acceleration =a=2m/s.s

Mass=m=?

Solution:

Formula:      F =ma

m= F/a

m=20N/2ms‾²

m=10 kg

2: How much force is needed to prevent a body of mass 10 kg from falling?

Data:

Mass= 10 kg

Gravitational acceleration =g= 10 ms‾²

Force=F=?

Formula:

F = W=mg=(10 kg)(10 ms‾²)=100 N

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