Categorieën: Alle - distance - motion - gravity - kinematics

door Khubaib W 3 jaren geleden

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Kinematics and Dynamics

The concepts of kinematics and dynamics are central to understanding motion and forces. Kinematics deals with the description of motion, while dynamics explains the causes of motion, such as forces and torques.

Kinematics and Dynamics

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Kinematics and Dynamics

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Free Fall

Gravitational Field Strength
Weightlessness

Force of gravity is still acting but both the object and frame of reference are in free fall

Weight

Measure of the force of gravity on the object (N)

Mass

The amount of matter in an object (kg)

The force per unit mass acting on an object when placed in a gravitational field

9.80 N/kg [down]

Force field

A region of space around an object that exerts a force on the other object within that region

The motion of a falling object where only the force of gravity is acting on it
Air Resistance

Increases when speed increases

Increases as cross-sectional area increases

Type of friction

Terminal Speed

The maximum constant speed of a falling object

Uniform velocity as it has constant speed and will be falling in the same direction; downwards

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Coefficient of friction
Uk= Fk/Fn
Us= Fs/Fn
Ff= uFn
Depends on the mass of the object, type of surface, and type of material

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Kinetic Friction

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Force that acts against the motion of an object
Static Friction

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Force that acts against attempted motion to prevent the sliding of one surface relative to another

Forces

Weak Nuclear Force
Involves nuclear decay transmutation
Strong Nuclear Force
Keeps protons and neutrons together
Electromagnetic Force
Caused by electric charge
Gravitational Force
Exists between any two masses
Net Force
The sum of all forces acting on an object

Must add the x and y forces seperately

Free Body Diagram
A simple drawing representing the object and all forces acting on it
Friction
Always acts opposite to the motion or attempted motion of an object
A force of resistance
Tension
The force exerted by materials that can be stretched.

Ex: ropes, strings, cables, etc

Normal Force

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A pushing force exerted by a surface on an object

Always acts away from and perpendicular to the surface

Force of Gravity

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The force of attraction between any two objects due to their mass.

Fg= mg

g= 9.80 m/s^2

Acceleration due to gravity (kinematics)

Applied Force

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Any contact force not already described
A force that results when one object makes contact with another and pushed or pulls it

Speed

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Vav=Δd/Δt

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Speed= distance/time
The total distance travelled over a period of time

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Represented in meters per second, m/s
Scalar Quantity

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Only has magnitude

Distance

"d"= distance
Scalar quantity- quantity with only magnitude
The total length of the path travelled by an object in motion

Represented in meters, m

Displacement

Velocity- time graph
Displacement can be found by calculating the area under the curve or line of the velocity-time graph
Refers to the change in an object's position
∆d=Final displacement-intial displacement
Displacement is a vector quantity- has both magnitude and direction
Direction is represented in terms of direction in square brackets, [N], [S], [W], [E].

Represented in meters along with direction, m [direction]

Newton's Laws

Basic kinematic problems are approached using Newton's laws of motion
Newton's Third Law
For every action force there is a simultaneous reaction force that is equal in magnitude and opposite in direction
Newton's Second Law
Fnet= ma

Acceleration can also be found using the kinematic equations, when given other variables

The magnitude of the acceleration is directly proportional to the net force acting on it and inversely proportional to its mass
An object will accelerate in the direction of the net force
Newton's First Law
All objects will remain in a state of rest or continue to move with a constant velocity unless acted upon by an unbalanced force

Velocity would be linear on a velocity-time graph, indicating it is constant

Net Force= 0

Projectiles

The five kinematic equations of motion can be used to solve projectile motion problems
Projectile motion can begin and end at the same or at different heights
Objects can be projected horizontally or at an angle to the horizontal.
Projectiles undergo uniform acceleration in the vertical direction, due to gravity
Projectiles move horizontally at a constant velocity
The horizontal and vertical motions of a projectile take the same amount of time
Projectile motion consists of independent horizontal and vertical motions

Motion in 2D

Algebraic
Find the angle using tan
Find the resultant using the Pythagorean theorem
Add all x components, then add all y components
Break all vectors into x and y components
Sketch the vector diagram and label it
Diagram
To determine total displacement in two dimensions, displacement vectors can be added together using a scale diagram. To add two or more vectors together, join them tip to tail and draw the resultant vector from the tail of the first vector to the tip of the last vector
The compass rose can be used to express directions in a horizontal plane, such as [N 40° W]
Objects can move in two dimensions, such as in horizontal plane and a vertical plane

Kinematic Equations

Can be used to solve the acceleration for Newton's second law
Variables include initial and final velocity, displacement/distance, time, and acceleration
Five different equation consisting of different variables, where you are able to isolate and find an unknown variable

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∆d=v2∆t-1/2a∆t^2
v2^2= v1^2+2a∆d
∆d=v1∆t+1/2a∆t^2
∆d=1/2(v1+v2 )∆t
v2=v1+a∆t

Acceleration

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Inversely proportional to mass according to Newton's second law
Also part of Newton's second law, where it is directly proportional with the net force
Acceleration due to gravity
Any object falling freely near Earth will accelerate at 9.80m/s^2 [down]
Velocity-Time Graph

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Slope of a velocity-time graph will give you the acceleration
a=∆v/∆t= final velocity - initial velocity/∆t

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Acceleration= velocity/time
Vector quantity

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The rate of change of velocity with respect to time

Represented in meters per second squared, m/s^2 [direction]

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Velocity

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Acceleration-Time Graph
The area under the line or curve in an acceleration-time graph will give you the velocity
Position-Time Graph
When the data is not linear, draw a tangent line at a given time

Slope of the tangent line will give you the instantaneous velocity at the specific time

Slope of a position-time graph will give you the velocity
Vav= Δd/Δt= d2-d1/Δt
Velocity= displacement/time

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Vector Quantity

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The total displacement travelled over a period of time

Represented in meters per second with direction, m/s [direction]

Uniform Velocity

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Constant velocity means a net force of zero, according to Newton's first law of motion
Motion with a constant speed and constant direction