# Newton’s Second Law Definition and Formula

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.”

But!

What will happen if the net force is act 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 on the sideway of an object, its direction of velocity will change, which is called acceleration. This is called Newton’s 2nd law.

## Newton’s second law statement

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 2nd law of motion 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 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 of motion:

“One newton (1N) is the force that produces an acceleration of 1ms^{-2} in a body of the mass of 1 kg. Thus, a force of one newton can be expressed as:

1N = 1kg ×1ms^{-2}

or 1N =1kgms^{-2}

## Newton’s second law of motion examples

- Pushing the trolley by applying force
- Pushing or pulling the door
- Designing the racer bike or car to increase their speed by reducing weight
- Pulling a cart
- Hitting a ball

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

**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

Now!

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