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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 velocity. This means that dynamics implies change and statics implies changelessness, where change in both cases is associated with acceleration.            …

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# Statics and Dynamics

Statics and Dynamics
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Nie wieder prokastinieren mit unseren Lernerinnerungen. 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 velocity. This means that dynamics implies change and statics implies changelessness, where change in both cases is associated with acceleration.

## 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.

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

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

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

## Statics and Dynamics Quiz - Teste dein Wissen

Question

What is friction?

Friction is the force that opposes the relative motion between two surfaces in contact.

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Question

An object with a mass of 8 kg rests on a rough horizontal plane. The coefficient of friction between the object and the plane is 0.5. Find the minimum horizontal force required to get the object to move. (g=9.8 m/s²)

39.2N

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Question

What is the unit for the coefficient of friction?

The coefficient of friction is a unitless quantity

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Question

True or false : The coefficient of friction between ice and ice is the same as the coefficient of friction between ice and water.

False

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Question

What two equilibrium conditions are necessary to classify a situation under statics?

• A body will remain at rest (zero displacement)
• A body will remain in uniform motion

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Question

What is statics in mechanics?

Statics deals with objects at rest and ones that are moving with constant velocity.

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Question

The branch of mechanics that deals with the analysis of physical bodies in motion is..

Dynamics

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Question

Are forces considered vectors?

Yes, they possess both magnitude and direction.

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Question

What is a resultant force?

A resultant force is one force that provides the same effect as all those forces have on the particle

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Question

Fundamentally, acceleration, with regards to statics is always...

Zero

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Question

What is the two subdivision of dynamics?

Kinematics and Kinetics

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Question

The study of motion that relates to the forces that affect these motions is...

Kinetics

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Question

What is kinematics?

Kinematics focuses on the movement of objects, disregarding the forces that cause the movements.

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Question

Problems associated with dynamics have particles stay in equilibrium

False

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Question

The area in kinematics where acceleration changes over time is known as...

Variable acceleration

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Question

What is the derivative of displacement?

Velocity

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What is the derivative of velocity?

Acceleration

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Question

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

True

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Question

The path of a projectile is called what?

Trajectory

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Question

When two forces are broken down into two forces, the two forces are called....

Component force

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Question

Resolving forces is the process of finding two or more forces that, when combined, will produce a force with the same magnitude and direction as the original.

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Question

Vectors, when directed at an angle to the customary coordinate axis can be considered to have how many parts?

Two parts

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Question

When a force is resolved, the force directed upwards is called___

The vertical component

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When a force is resolved, the force directed to the right is called___

Horizontal component

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What mathematical functions are used to resolve forces?

Trigonometric functions

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Question

What are concurrent forces?

If the forces applied to a body are such that their lines of action meet at a single point, they are called concurrent forces

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Question

What is a truss?

A truss is a plane that takes advantage of the inherent geometric stability of triangles to distribute weight in harmony and to handle changing compressions and tension.

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What is a common example of a truss?

A roof

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Question

A force is being exerted on the particle is 12N and is at an angle of 68 degrees above the horizontal, what is the magnitude of the vertical component?

11.1N

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

Positive values

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

Negative values

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To analyse a truss, you must create a free-body diagram of the entire truss which should include all forces and ignore the individual triangles. Is this statement true or false?

True

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Question

If a force was being exerted on a particle with the magnitude of 120N and is at an angle of 56 degrees above the horizontal, what will be the component forces if resolved?

67.1N to the horizonal

99.5N to the vertical

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