Newton's Second Law

Defintion

The acceleration 'a' of an object in the direction of a resultant force F,
is directly proportional to the magnitude of the imposed force and
inversely proportional to the mass m of the object.

See below illustration regarding the two scenarios when the forces are unbalanced:
newton-law-2
Newton’s second law is about the relationship between: force, mass, and acceleration.

1 Newton 1 kg • m/s2

Question: What happens when a force F acts on a mass m?
newton-second
Such relation can be expressed by the following formula:
Acceleration a = net force / mass = Fnet / m
Basically,

Example

Question: Calculate the acceleration of a 3000-kg, single-engine airplane as it begins its takeoff with an engine thrust of 1000 N.
Solution:
a = Fnet / m = 1000 / 3000 = 0.33 m/s2

Exercise

Based on the given table; Find the corresponding acceleration.

Check your answers here: Solution

Example: Net force and the object's acceleration
If there is more than one vector acting on an object, the forces are added together as vectors,
taking into account their directions. See example below:
newton-second2
Fto the right = 9 N
Fto the left = 4 N
Fnet = 9 N - 4 N = 5 N (to the right)
a = Fnet / m = 5 N / 10 kg = 0.5 m/s2 (to the right)

Forces acting in opposite directions

As per the below figure, let's calculate the mass m of the box if its acceleration a is 5 m/s2

newton-second3
Solution:
The net force is 30 N - 10 N = 20 N, directed to the right.
Using the formula F = m×a, the mass m = F/a = (20 N)/(5 m/s2) = 4 kg.


Exercise

Click here to access a similar exercise.
Check your answers here: Solution

Mass, Weight, and Inertia

Example:

Assume a ball hangs from a string attached to the ceiling as per the illustration below:
hanging-ball
Question: What would be the net force acting on the ball?
  1. The net force is upward
  2. The net force is zero
  3. The net force is downward
Answer: The net force is zero.
Explanation: Since the ball is hanging from the ceiling at rest, it is not accelerating hence the net force becomes zero.
There are two following forces acting on the ball canceling each other: Tension from the string and force due to gravitation:


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Date of last modification: Summer , 2019