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Net Force
The vector sum of all forces acting on an object (Newtons, N)
Net Force Equation
F=ma
net force= mass x acceleration
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 90o 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
Speed
Surface area (less surface area= less drag)
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)
Fnet=W-D so net force decreases and acceleration decreases (mass remains the same)
Journey of Drag: Part 3
Drag force equals the weight
Fnet=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
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
May have to resolve vectors with equations:
Fx=Fcosθ
Fy=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
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
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
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
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
F= upthrust (N)
ρ= density of fluid (kgm-3)
g= acceleration due to gravity (ms-2)
V= volume displaced (m3)
Note
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