Newton Second Law of Motion

(d) do calculations using the equation force = mass × acceleration.

Newton's second law of motion states:
"The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus, F = ma, where F is the net force acting on the object, m is the mass of the object and a is the acceleration of the object."

We already know about net force, or resultant force i-e the sum of all the forces acting on a body. According to newton's second law of motion, we know that the resultant force acting on a body is equal to the product of the mass and the acceleration of that body.

Let us take an example of an object falling due to the gravitational field. We know that the acceleration due to the gravitational field force is approximately 10m/s^2. Here is a scenario to prove this law right. In this scenario, we will ignore air resistance

An object of 10 Kg is falling from a height. Now from the mass, we can deduce the weight of the object, which would be 10*10 = 100 N. Now, we know that weight is a force. So, ignoring air resistance, we can say that a resultant force F of 100 N is acting on the body in the downward direction as it falls. Now putting the mass 10 Kg and the resultant force F 100N in the equation, we get:

F = ma
100 = 10 * a
a = 100/10
a = 10m/s^2

We get the exact same value of acceleration as is produced by the gravitational field!.

From this equation, we can always deduce third quantity if we are given two of three quantities from mass, resultant force and acceleration.

Let us move on to a more complex scenario.

A rocket of mass 2000 Kg accelerates upwards at a constant rate of 30 m/s. You can ignore the effects of air resistance in your answers.

i) Calculate the resultant force acting on the body.
ii) Calculate the total upwards force acting on the rocket.

Now the first part of the question is pretty easy. We can just put the values in our equation and get our answer

F = 2000 * 30

F = 60000 N

So the resultant force acting on the rocket in the upward direction would be 60000N.

ii) Now, the second part asks about the total upward force acting on the rocket. We know that the resultant force is the sum of all the forces on an object. We also know that the rocket has a mass of 2000 Kg, which equates to a weight, or lets say downward force of 2000*10 = 20000N. Our total upward force therefore, cancels out this force of 20000N as well as produce a resultant force of 60000N. From this, we can form the equation for the total upward force:

X - 20000 = 60000
X = 80000N

Therefore, we can say that the total upward force acting on the rocket is 80000N. 20000N of this force is cancelled out by the downward weight of 20000N, and the rest of 60000N acts as the resultant on the rocket.

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