Definition & Example I StudySmarter (2024)

Statics

Statics is concerned with the forces that act on bodies at rest under equilibrium conditions. This is expressed in the first part of Newton's first law of motion, where equilibrium conditions are met:

• A body will remain at rest (zero displacement).

• A body will remain in uniform motion.

Acceleration is always zero in statics, so the right-hand side of the equation of Newton's second law of motion will always amount to zero as well. This means that most statics problems are going to be associated with the analysis of force – on the left-hand side of Newton's second law of motion.$F_{net}=ma$

Force as a vector

Forces possess both magnitude and direction so they are considered Vectors. The magnitude of Vectors describes the size and strength of the force. When objects interact with each other, force is exerted on them. The force ceases to exist when the interaction stops. Force is what makes it possible for the conditions regarding objects in equilibrium to be possible. It takes force for objects to stay at rest, and it takes force for objects to be in uniform motion.

Now, let's look at resultant force. This is one force that provides the same effect as all the other forces have on the particle. In this section, we are only concerned with ones that affect particles in equilibrium.

Dynamics

Dynamics in mechanics studies the forces that cause or modify the movement of an object. It deals with the analysis of physical bodies in motion. Therefore, acceleration is a factor in these problems.

Dynamics can be subdivided into Kinematics and Kinetics. Kinematics is an area of study that focuses on the movement of objects, disregarding the forces that cause the movements. It studies motion that relates to displacement, velocity, acceleration, and time. Kinetics on the other hand studies motion that relates to the forces that affect these motions.

Kinematics

Kinematics focuses on the movement of objects, disregarding the forces that cause the movements. It deals with forces and the geometric aspects of motion, which is related to velocity and acceleration.

In kinematics, we can have problems associated with either acceleration being constant or acceleration changing over time (Variable Acceleration). Kinematic Equations associated with Constant Acceleration are only valid when acceleration is constant, and motion is constrained to a straight line. Variable Acceleration problems deal with kinematics where acceleration changes over time.

Differentiation is used to convert displacement to velocity, and velocity to acceleration. Integration is used to cover acceleration to velocity and velocity back to displacement. This makes velocity the first derivative, and acceleration the second derivative with respect to time.

• $s=f\left(t\right)$ [Location in reference to an origin]
• $v=\frac{ds}{dt}=f\text{'}\left(t\right)$ [Derivatives of displacement]
• $a=\frac{dv}{dt}=\frac{d^{2}s}{d{t}^2}=f\text{'}\text{'}\left(t\right)$ [Derivative of velocity]

The four equations of motion used in solving kinematics problems are:

1. $v=u+at$
2. $s=\frac{(u+v)}{2}t$
3. $v^2=u^2+2as$
4. $s=ut+\frac{1}{2}a{t}^2$

Let's look at an example:

Projectiles

A significant concept in kinematics is projectiles. Projectile motion occurs when objects are projected through the air and gravity acts on them. A good example is a ball being thrown. The path of a projectile is called a trajectory. Projectile problems are mostly tackled with trigonometric functions, by resolving the components of the path into x and y components.

Projectile motion

What is the difference between statics and dynamics?

Statics is concerned with the forces that act on bodies at rest under equilibrium conditions while dynamics studies the forces that cause or modify the movement of an object. It deals with the analysis of physical bodies in motion

What are the principles of statics?

The sum of the forces must be zero for the system to be in equilibrium.

How do you solve dynamic problems?

Explore what equation is involved in your problem, substitute the known values and find what is required