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Newton's Second Law of Motion

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4.2Newton's Second Law of Motion


In these revision notes for Newton's Second Law of Motion, we cover the following key points:

  • What is the relationship between force and acceleration in a motion?
  • What is the relationship between mass and acceleration in a motion?
  • What does the Newton's Second Law of Motion says?
  • What is the procedure used to study the motion of objects when forces acting on it are considered?
  • What advantages offers the use of a force diagram when dealing with Newton's Second Law of Motion?

Newton's Second Law of Motion Revision Notes

All objects move at constant velocity when the forces acting on them are balanced. When forces are not balanced, the resultant force at any object is different from zero. As a result, it will accelerate in the direction of the resultant force. Heavier objects accelerate less that light ones for the same acting force. On the other hand, greater the force, greater the acceleration it causes at the same object.

Newton's Second Law of Motion gives the relationship between force, mass and acceleration. It states that,

"The acceleration an object gains due to the action of a force (or the resultant of some forces) is directly proportional to the force itself and inversely proportional to the mass of the object."

Mathematically, this law is written as:

a = FR/m

where FR is the resultant force if there is more than one force acting on the object.

When several forces are acting at an object (especially when forces are at different directions), it is better to start with drawing a force diagram. This helps us understand better the situation and estimate the possible direction of motion prior of making any calculation. A force diagram includes all forces acting at an object despite some of them maybe are not involved in the motion process. When one or more forces do not lie only according one of the basic directions, we can use the components to represent them.

When the object lies on a slope, such as an inclined plane, it is better to rotate the axes in such a direction that one axis fits the plane (any possible motion occurs according this direction) and the other axis is perpendicular to the plane (it fits to the normal force). In this case, only gravitational force needs to split in directions.

Since the situations involving Newton's Second Law of Motion are a bit complicated, it is advisable to use the standard procedure shown below to solve them easier. This procedure consist in 6 steps:

  1. Plotting a force diagram in which all forces acting at the object (or the system of objects) are shown,
  2. Choosing a suitable pair of axis to show the direction of forces,
  3. Drawing the components of forces where necessary,
  4. Writing the Newton's Second law of Motion according both directions for all objects involved. The equation(s) of the perpendicular direction to the (possible) motion are used as auxiliary equation that helps to find any missing quantity that appears in the equation(s) according the direction of motion (in our previous example, we used the component Fg(y) of gravitational force to find N and then the frictional force f through it),
  5. Substituting the known values in the active equation(s), i.e. in the equations that contain the forces according the direction(s) of motion, and
  6. Making the calculations and finding the result.

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