# Statics and Dynamics

The concepts of statics and dynamics are basically a categorisation of rigid body mechanics.  Dynamics is the branch of mechanics that deals with the analysis of physical bodies in motion, and statics deals with objects at rest or moving with constant velocityThis means that dynamics implies change and statics implies changelessness, where change in both cases is associated with acceleration.

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## 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.

Find the magnitude of ${F}_{1}$ and ${F}_{2}$ acting on the particle in equilibrium in the diagram below.

Concurrent force on a particle in equilibrium

Since our particle is in equilibrium

$\Sigma F=0$

We will need to write Equations for both x and y components equating them to zero.

By resolving the x component we get,

$\Sigma {F}_{x}=0$

$8+4\mathrm{cos}60°-{F}_{2}\mathrm{cos}30°=0$

${F}_{2}=\frac{20}{\sqrt{3}}N$

By resolving the y component we get

$\Sigma {F}_{y}=0$

${F}_{1}+4\mathrm{sin}60°-{F}_{2}\mathrm{sin}30°=0$

${F}_{1}+\frac{4\sqrt{3}}{2}-\frac{{F}_{2}}{2}=0$

${F}_{1}=\frac{{F}_{2}}{2}-2\sqrt{3}$

${F}_{1}=\frac{10}{\sqrt{3}}-2\sqrt[]{3}$

${F}_{1}=\frac{4}{\sqrt{3}}N$

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

Let's look at an example:

If a particle is travelling in a straight line with a Constant Acceleration of $5m{s}^{-2}$and at t = 0 s the particle has a speed of $3m{s}^{-1}$, what is the speed of the particle when t = 4 s?

This is a constant acceleration problem so we can use the equation of motion that involves the variable we are going to be working with.

$u=3m{s}^{-1}$

$v=?$

$a=5m{s}^{-2}$

$t=4s$

From the data, we can see that the equation is best suited for this problem is:

$v=u+at$

We can now substitute in what we know.

$v=3+5\left(4\right)$

$v=23m{s}^{-1}$

Speed is only the scalar quantity for velocity, therefore:

$v=23m{s}^{-1}$

### 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

## Statics and Dynamics - Key takeaways

• Statics is concerned with the forces that act on bodies at rest under equilibrium conditions.
• Dynamics in mechanics studies the forces that cause or modify the movement of an object.
• Dynamics can be subdivided into Kinematics and Kinetics.
• A resultant force is one force that provides the same effect as all those forces have on the particle.
• With respect to Newton, most statics problems are going to be associated with the analysis of forces.
• Projectile problems are mostly tackled with trigonometric functions by resolving the components of the path into x and y components.

#### Flashcards in Statics and Dynamics 33

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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

## Test your knowledge with multiple choice flashcards

Problems associated with dynamics have particles stay in equilibrium

Projectile motion occurs when objects are projected through the air and gravity acts on them. True or false?

All values of forces that are working upwards are treated as:

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