3.2: Dynamics

Net Force

The vector sum of all forces acting on an object (Newtons, N)

Net Force Equation

F=ma

net force= mass x acceleration

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Equation only works for net force

Net Force Equation Explanation

The amount of force is directly proportional to acceleration, with mass as the constant

Weight

The weight of an object is the gravitational force acting upon it (Newtons, N)

Weight equation

W=mg

Weight=mass x acceleration of freefall

Tension

The force within a stretched cable

Normal Contact Force

The reaction force between an object and surface, acting at a 90^o angle to plane of contact

Upthrust

The upwards (buoyancy) force that a fluid applies on an object

Friction

The resistive force produced when there is a (relative) movement between the two surfaces

Drag

A frictional force experienced by an object moving through a fluid that opposes the motion of an object

What happens when a constant force acts on an object

Object experiences a constant resultant acceleration, determined with F=ma

One dimensional motion under a constant force

• Involves up and down or left and right

• On the ground

Two dimensional motion under a constant force

• Involves up and down and left and right

• On a slope

What is Drag

The frictional force experienced by an object moving through a fluid that opposes the motion of the object

Factors Affecting Drag

1. Speed

2. Surface area (less surface area= less drag)

3. Density of fluid (type of fluid)

Most crucial factor affecting drag

Speed (d∝v²)

Journey of Drag: Part 1

• Initial velocity is zero.

• Net force is the weight.

• Acceleration is g=9.81ms^-1

Journey of Drag: Part 2

• Velocity increases, and the drag force also increases (as d∝v²)

• F_net=W-D so net force decreases and acceleration decreases (mass remains the same)

Journey of Drag: Part 3

• Drag force equals the weight

• F_net=0 so acceleration=0

• Object moving at terminal velocity

Definition of terminal velocity

Terminal velocity is the constant velocity an object falls at when the drag force is equal to the gravitational pull on the body

Determining Terminal Velocity in Fluids: Step 1

Fill a vertical tube with a viscous liquid like hand sanitizer

Determining Terminal Velocity in Fluids: Step 2

Use a metre ruler, and mark regular consecutive intervals (like very 10cm) using rubber bands

Determining Terminal Velocity: Step 3

Drop a ball bearing into the tube and (with a timer) record the time for the ball bearing to reach each individual interval

Determining Terminal Velocity: Step 4

Repeat several times (at least 3) and calculate the average

Determining Terminal Velocity: Step 5

Use average values, calculate the velocity (distance of each interval / time taken)

Determining Terminal Velocity: Step 6

Plot a velocity-time graph and draw the line of best git (representative of acceleration)

Determining Terminal Velocity: Step 7

You should observe an initial linear section which eases off into a horizontal line. The velocity at the horizontal line is the terminal velocity

Exam Definition of a Moment

The turning effect of a force about a point and is the product of the force and the perpendicular distance of the line of action of force from the point of rotation (units are Nm)

Grace-Friendly Definition of a Moment

• Turning effect of a force

• They occur when forces cause objects to rotate about same pivot

Equation for Moment

moment= Fx

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F= Force (N)

x= Perpendicular distance (m)

Perpendicular force/distance with moments

Force and distance NEED to be perpendicular to each other in calculations with moments

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May have to resolve vectors with equations:

F_x=Fcosθ

F_y=Fsinθ

The Principle of Moments

For a body in rotational equilibrium, the sum of anti-clockwise moments about any point is equal to the sum of the clockwise moments about that same point

What is a couple

A pair of equal and opposite, parallel, coplanar forces that act to produce rotation only

What do coplanar forces mean

Forces that act in the same plane

What do couples consist of

A pair of forces that are…

• Equal in magnitude

• Opposite in direction

• Perpendicular to the distance between them

Resultant force of a couple

• Net force is zero (due to Newton’s Second Law)

• Object doesn’t accelerate

Moment of a couple

• Doesn’t depend on a pivot

Moment of a couple= force x perpendicular distance between the lines of action of the forces

Torque

Is the rotational effect of a couple

Equation of a torque

T=Fd

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T= Torque (Nm)

F= one of the applied forces (N)

d= perpendicular distance between the forces (m)

Centre of Mass

A point through which any externally applied force produces straight line motion but no rotation

Centre of Mass for Objects with a Uniform Density

Is located at point of symmetry

Centre of Mass and stability

Most stable objects have wide bases and low centres of masses

Centre of Gravity

An imaginary point where the entire weight of an object appears to act

Centre of Gravity in a Uniform Gravitational Field

The centre of gravity is identical to the centre of mass

Determining Centre of Mass and Gravity: Step 1

Drill a small hole in the object and hang it so it is free to swing without obstruction

Determining Centre of Mass and Gravity: Step 2

Hang a plumb line from the same suspension point, and mark the vertical line directly below the suspension point

Determining Centre of Mass and Gravity: Step 3

Drill a hole at a different location within the object

Determining Centre of Mass and Gravity: Step 4

Hang a plumb line to determine the vertical, and mark it on

Determining Centre of Mass and Gravity: Step 5

The point at which the two marked lines cross is the centre of mass and gravity

Systems in Equilibrium

All the forces are balanced in the system

Conditions for Equilibrium

• No net resultant force acting on an object

  • Net moment of zero acting on an object

Objects in Equilibrium

• Will remain at rest OR at a constant velocity

• Won’t rotate

Density

Mass per unit volume of a substance

Equation for density

ρ=m/v

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ρ= density (kgm^-3)

m= mass (kg)

v= volume (m³)

Determining Density

For liquids you can use a measuring cylinder to determine the volume. The volume of a regular-shaped solid can be calculated from measurements taken with a ruler, digital callipers or a micrometre. The volume of irregular solids cam be determined by displacement

Pressure

How a force presses on a surface

Pressure and area

Inversely proportional

Equation for pressure

p= F/A

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P= pressure (Pa)

F= force (N)

A= area (m²)

Type of quantity: Pressure

Scalar

Pressure in Fluids

Fluids exert a pressure on surfaces because of constant bombardment by their molecules

Equation for pressure in fluids

p=hρg

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p= pressure (Pa)

h= height of fluid column (m)

ρ= density of fluid (kgm^-3)

g- acceleration due to gravity (ms^-2)

Upthrust

The upward force that a liquid or gas exerts on a body floating in it

Archimede’s Principal

An object submerged in a fluid at rest has an upward buoyancy force (upthrust) equal to the weight of the fluid that the body displaces

It will sink!

The upthrust is less than the weight of the object

It will float!

The upthrust is equal to the weight of the object

How to find the magnitude of upthrust

F=ρgV

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F= upthrust (N)

ρ= density of fluid (kgm^-3)

g= acceleration due to gravity (ms^-2)

V= volume displaced (m³)