F = ma

Physics Questions Answers

This is the equation of Newton’s Second Law of Motion. Here F is the force applied on the body, m is the mass of the body which is inversely proportional to the applied force and a is the acceleration produced in the body by the force and it is directly proportional to the applied force.

Examples of Newton’s Second Law of Motion

Example No. 1

Suppose a body of Mass 20 kg is moving by applying a Force of 40 N, then what is the acceleration of the body?

We know that:

F = ma

a = F / m

a = 40 / 20 =2

a = 2m/s²

Hence Acceleration is 2ms^-2 and it is produced in the body when a force of 40 N is applied on the mass of 20 Kg.

Example No. 2

Suppose a body of Mass 20 kg is moving by applying a Force. The body is moving with an acceleration of 2ms^-2, then what Force (F) was applied on body?

We know that:

F = ma

F = 20 x 2

F = 40 N

Hence Force is 40 N and it is applied on the body of mass 20 Kg to produce an acceleration of 2ms^-2 in the direction of force.

Example No. 3

Suppose a body of Mass m is moving by applying a Force of 40 N. The force produces an acceleration of 2ms^-2, and then what is the mass of the body?

We know that:

F = ma

m = F / a

m = 40 / 2 = 20

m = 20 kg

Hence mass is 20 kg and the force of 40 N is applied on body to produce an acceleration of 2ms^-2 in the direction of the force.

Another Numerical Question

Suppose that two Eskimos named as X and Y exert a force of 400 (N) Newton to carry on their vehicles across a frozen lake. The mass of Vehicle carried by X’s Eskimos is 120 kg while the mass of vehicle carried by Y’s vehicles is only 40 Kg. Assuming there is no friction force between two vehicles on the ice. Now, find out the acceleration of two vehicles and their separation after 10 seconds.

According To Newton’s Second Law of Motion:

F = ma

For Vehicle’s X, F = 400 N and m = 120 Kg.

F = ma

a = F / m

a = 400 / 120 = 3.33 ms^-2

a = 3.33m/s²

For Vehicle’s Y, F = 400 N and m = 40 Kg.

F = ma

a = F / m

a = 400 / 40 = 10 ms^-2

a = 10 m/s²

Hence, the vehicle Y has greater acceleration than Vehicle B.

Now to find separation between two vehicles, let us firstly find the distance travelled by both vehicles in 10 seconds:

According To Newton’s Second’s Law of Motion:

S = 1 / 2 at²

For Vehicle X:

S = 1 / 2 at²

= 1 / 2 x 3.33 (10)²

S = 166.6 m

For Vehicle Y:

S = 1 / 2 at²

= 1 / 2 x 10 (10)²

S = 500 m

Now the separation between two vehicles X And Y will be written as:

S_x – S_y

333.3m

Hence, there is 333.3m difference between two vehicles or in other words Vehicle Y reached to a greater distance of 333.3m in 10 seconds than Vehicle X.

So it is all about Examples of F = ma or Newton’s Second Law of Motion.