PHYSICS: MECHANICS: DYNAMICS

           PHYSICS: MECHANICS: DYNAMICS

Dynamics is the study of motion and it causes. Motion is the change in position of a body with respect to time and its surrounding. The agent that change or tend to change the position of a body is known as Force.

This implies that force causes motion.

The study of the effect of this force on different systems is known as dynamics.
In this article, we are going to study dynamics under the following headings;

■Newton’s laws of motion and linear momentum

■Systems of unbalanced forces

■Systems of balanced forces

■Kinds of forces

To understand the relationship between force and the motion of a body, we will need to look into Newton’s laws of motion and the concept of linear momentum.  

Newton’s laws of motion and linear momentum

Newton’s 1st law: This is also known as the law of inertia. Inertia is the ability of a body to remain at rest or in a uniform motion.

 This law states that a body will remain at rest or uniform motion except when there is an external agent that affects this equilibrium. This law explains why a driver that jerks a car into motion seems to move backward and when the breaks are applied, it seems to continue moving forward.
That’s why we have car head rest and seat belt in vehicles to prevent accident based on this phenomena.


Newton’s 2nd law:

 This law explains the difference between the motions of two bodies of different masses moving with the same speed. It explains that the force that produces these velocities depends on the mass of the bodies.

 The collective effect of the mass and velocity of a body is known as momentum. The law states that the rate of change of momentum of a body is directly related to the force causing the motion.

Newton’s 3rd Law:

This law explains the reactions of bodies when a force acts on them. It states that the action and reaction force produced by the body are equivalent but acting oppositely.

 This explain why people bend when they wants to jump, a book resting on a table remain due to the reaction from the table to balance it weight, a balloon filled with air moves in the a direction opposite the direction from which the air is allowed to escape.


Linear Momentum

The law of conservation of linear momentum: This states that the total momentum of colliding bodies in an isolated system remains the same.

The collision can either be elastic or inelastic. The total energy is conserved for elastic collision but only the momentum is conserved for inelastic collision, energy is not conserved.

An example of inelastic collision is when two bodies stick together after collision.      

        Coefficient of restitution

The coefficient of restitution (e), is the ratio of the final to initial relative velocity between two objects after they collide.

 It normally ranges from 0 to 1 where 1 would be a perfectly elastic collision.

 A perfectly inelastic collision has a coefficient of 0, but a 0 value does not have to be perfectly inelastic. 

Newton’s laws and linear momentum find many applications in physics, some of which include;

                    Apparent weight in lift

The weight a body in a lift seems to vary with respect to the motion of the weight. When the lift accelerates while moving upward, the weight of the body seems to have increased and it becomes lighter as the lift decelerates downwards.

The apparent weight which is due to the reaction R from the floor of the lift is given to be:  R=m (g+/-a)

In a case where by the lift suddenly falls freely, the body inside the lift will experience what is known as weightlessness. This is because, R=m (g-g)=0  The apparent weight will be zero.

Systems of unbalanced forces: The idea of resultant of forces

A system of forces is said to e unbalanced it they cause the body under the action of the forces to move with an acceleration. A single force  that represents all the acting forces in both magnitude and direction is known as the resultant of the forces.                                                  

 A single force that will make this body to be at equilibrium is known as the equilibrant of the resultant force. It has same direction as the resultant force, just that they oppose each other.   

                                       

  Resultants of different systems of forces

Case3:

 Two forces acting at an acute or obtuse angle to each other.

In this case, the parallelogram law of vectors is used. This states that:

When two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the resultant of the two vectors can be represented in agni rude and direction by the diagonal of the parallelogram drawn from the point of intersection of the two vectors.

Systems of Balanced forces: The idea of Equilibrium of forces.

A system of forces is said to be in equilibrium if the forces keep the body at rest or moving in a uniform motion. This implies that the resultant acceleration is zero hence the resultant force is zero.

F=ma=m (0)=0N
            
System of concurrent forces

In this kind of system, the line of action of all the acting forces met at a point and they are not capable to cause the body to rotate

System of co-planar forces

Forces are said to be co-planar when they act on the same plane with their line of action not necessarily acting at the same point on the plane.

 These forces have the tendency to make a body to rotate, the turning effect of these forces is known as moment. 

The magnitude of the moment of a force is the product of the force and the perpendicular distance from the point of support of the body to the line of action of the force.

  Co-planar forces are either parallel or non-parallel Co-planar forces.

Conditions for equilibrium of a body under the action of parallel co-planar forces

1. The sum of the clockwise moment must be equal to the sum of the anti-clockwise moment

2. The sum of all the upward forces must be equal to the sum of all the downward forces

For non-parallel co-planar forces, the same conditions as stated above holds, just that the components of the forces are considered and also the sum of all horizontal force must be zero.


Stability of bodies

The stability of a body can either be stable, neutral or unstable.

A body is said to be in stable equilibrium if it Center of gravity (C.G) is low, that is, it's C.G is close to the ground. In this case the body tends to remain in its initial position after being slightly displaced. An example of this is a cone resting on its base. The potential energy increases after being displaced.

For Unstable equilibrium, the C.G of the body is high, far from the ground. And in this case, a slight displacement will cause the body to move farther away from its original position. A good example of this is a cone resting on its vertex. Its potential decreases after being displaced.

A body is said to be in neutral equilibrium if it tends to come to rest in its new position after a slight displacement. An example of this is a cone resting on its curved surface. In this case, the C.G remains constant. And the Potential is constant.

Kinds of forces

Laws of solid friction

1. Friction oppose motion
2. It is directly proportional to the normal reaction
3. It depends on the nature of the bodies in contact
4. It is independent on the relative velocities between the bodies
5. It is independent on the nature of the body in contact.
6. The coefficient of dynamic friction is less than the coefficient of limiting frictional force

Cases of frictional forces

There are many cases of frictional force, but we are going to be looking into three cases here.
Case1: Frictional force experienced by a body moving on a horizontal plane.

Case2: Frictional force experienced by a body on an inclined plane



To be continued... keep in touch with us.