Mechanics
(the study of movement and the forces that affect the movement)
Types of physical quantities:
1. Scalars: a physical quantity that has magnitude only (distance and speed)
2. Vectors: a physical quantity that has both magnitude and direction (displacement and
velocity)
Definitions:
Resultant vector: a single vector that has the same effect as two or more vectors added together
Displacement: the straight-line distance between an objects starting and ending position
Velocity: rate of change in displacement
Acceleration: rate of change in velocity
Normal force: the perpendicular force exerted by a surface on an object which is in contact with
the surface
Free body diagrams:
Fn= normal force
Fg= force of gravity (weight)
fk/ Ff= friction
Fa= force applied
Fth= thrust
Fair= air resistance
Ft= tension
Finding resultant vectors:
1. Graphic method (head to tail):
-Set a scale (1cm=2N)
-Draw the first vector accurately (length and angle)
-Draw remaining vectors from the head of the previously drawn vectors
-Find single resultant vector from tail of 1st to head of last vector
-Measure length and angle
2. Mathematical method:
-Work out the x and y components of each diagonal line
-Determine the sum of all horizontal (x) values – choose a direction as positive
-Determine the sum of all vertical (y) values – choose a direction as positive
-Fx= Fcos and Fy=Fsin for all x and y components
-Find the length of the hypotenuse using pythagorus
-Find the angle using trigonometry
, When any number of forces act on an object and the object is in equilibrium, there will be
no resultant force
Forces in equilibrium (closed triangle)
1. Draw weight/ normal force first
2. Calculate Fg=mg
3. Draw other 2 forces and add in angles
sinA sinB sinC
4. Use formula = =
a b c
5. Cross multiply two “sins” with each other to solve for unknown vectors
Newtons third law of motion
(when object A exerts a force on object B, object B will exert a force of equal magnitude
simultaneously on object A, but in the opposite direction)
Force pairs can never be in equilibrium because they do not act on the same object
E.g. the gravitational force between two objects and the tension force between two objects
F AB=−F BA
Frictional force:
(the force that opposes the motion of an object and which acts parallel to the surface)
Static friction: the frictional force of one contact surface on another when there is no relative
motion between the objects
Just before the object is about to move
Fs ( max ) =μsFn
μs=tanθ
Characteristics of static friction:
Independent on the area of the contact surface
Dependant on the mass and weight of the object (affects N force)
Dependant on the nature of the surfaces in contact with each other
Acts in the opposite direction that the object tries to move
Directly proportional to Normal force
Kinetic friction: the frictional force of one contact surface on another when one or both objects
are moving
Fk=μkFn
Characteristics of kinetic friction:
Independent on the area of the contact surface
Dependant on the speed of the object
Dependant on the mass and weight of the object
Dependant on the nature of the surfaces in contact with each other
Acts in the opposite direction that the object moves
Ensuring the object doesn’t move: Fapplied must be less than Fs (max)
Ensuring the object travels at a constant velocity: Fapplied=Fk
, Newtons first law of motion
(an object will continue in a state of rest or continue to travel at a constant velocity in a straight line
unless acted on by an external force)
Also known as the law of inertia
Inertia: the resistance of an object to change its state of motion or rest
Force components formulas:
Fy=Fsinθ
Fx=Fcosθ
Gravitational components formulas:
Fg(¿)=Fgsinθ
Fg ( perpendicular )=Fgcosθ
General calculations:
Make the vertical/ horizontal forces = 0 if the object is stationary/ at constant velocity
To calculate the net force, choose positive direction
Fnet =Forces∈one direction−forces ∈other direction
Newtons second law of
motion
In terms of mechanics:
(when an external net force is acted on an object, the object with accelerate in the direction of the
net force and the acceleration is directly proportional to the net force and inversely proportional to
the mass of the object)
In terms of momentum:
(the net force acting on an object is equal to the rate of change of momentum of the object in the
∆p
direction of the net force) - Fnet =
∆t
General calculations:
Fnet =ma
Vf −Vi
a=
t
Acceleration problems with one object:
Vf −Vi
Use Fnet =ma∧a=
t
Calculate accordingly
(the study of movement and the forces that affect the movement)
Types of physical quantities:
1. Scalars: a physical quantity that has magnitude only (distance and speed)
2. Vectors: a physical quantity that has both magnitude and direction (displacement and
velocity)
Definitions:
Resultant vector: a single vector that has the same effect as two or more vectors added together
Displacement: the straight-line distance between an objects starting and ending position
Velocity: rate of change in displacement
Acceleration: rate of change in velocity
Normal force: the perpendicular force exerted by a surface on an object which is in contact with
the surface
Free body diagrams:
Fn= normal force
Fg= force of gravity (weight)
fk/ Ff= friction
Fa= force applied
Fth= thrust
Fair= air resistance
Ft= tension
Finding resultant vectors:
1. Graphic method (head to tail):
-Set a scale (1cm=2N)
-Draw the first vector accurately (length and angle)
-Draw remaining vectors from the head of the previously drawn vectors
-Find single resultant vector from tail of 1st to head of last vector
-Measure length and angle
2. Mathematical method:
-Work out the x and y components of each diagonal line
-Determine the sum of all horizontal (x) values – choose a direction as positive
-Determine the sum of all vertical (y) values – choose a direction as positive
-Fx= Fcos and Fy=Fsin for all x and y components
-Find the length of the hypotenuse using pythagorus
-Find the angle using trigonometry
, When any number of forces act on an object and the object is in equilibrium, there will be
no resultant force
Forces in equilibrium (closed triangle)
1. Draw weight/ normal force first
2. Calculate Fg=mg
3. Draw other 2 forces and add in angles
sinA sinB sinC
4. Use formula = =
a b c
5. Cross multiply two “sins” with each other to solve for unknown vectors
Newtons third law of motion
(when object A exerts a force on object B, object B will exert a force of equal magnitude
simultaneously on object A, but in the opposite direction)
Force pairs can never be in equilibrium because they do not act on the same object
E.g. the gravitational force between two objects and the tension force between two objects
F AB=−F BA
Frictional force:
(the force that opposes the motion of an object and which acts parallel to the surface)
Static friction: the frictional force of one contact surface on another when there is no relative
motion between the objects
Just before the object is about to move
Fs ( max ) =μsFn
μs=tanθ
Characteristics of static friction:
Independent on the area of the contact surface
Dependant on the mass and weight of the object (affects N force)
Dependant on the nature of the surfaces in contact with each other
Acts in the opposite direction that the object tries to move
Directly proportional to Normal force
Kinetic friction: the frictional force of one contact surface on another when one or both objects
are moving
Fk=μkFn
Characteristics of kinetic friction:
Independent on the area of the contact surface
Dependant on the speed of the object
Dependant on the mass and weight of the object
Dependant on the nature of the surfaces in contact with each other
Acts in the opposite direction that the object moves
Ensuring the object doesn’t move: Fapplied must be less than Fs (max)
Ensuring the object travels at a constant velocity: Fapplied=Fk
, Newtons first law of motion
(an object will continue in a state of rest or continue to travel at a constant velocity in a straight line
unless acted on by an external force)
Also known as the law of inertia
Inertia: the resistance of an object to change its state of motion or rest
Force components formulas:
Fy=Fsinθ
Fx=Fcosθ
Gravitational components formulas:
Fg(¿)=Fgsinθ
Fg ( perpendicular )=Fgcosθ
General calculations:
Make the vertical/ horizontal forces = 0 if the object is stationary/ at constant velocity
To calculate the net force, choose positive direction
Fnet =Forces∈one direction−forces ∈other direction
Newtons second law of
motion
In terms of mechanics:
(when an external net force is acted on an object, the object with accelerate in the direction of the
net force and the acceleration is directly proportional to the net force and inversely proportional to
the mass of the object)
In terms of momentum:
(the net force acting on an object is equal to the rate of change of momentum of the object in the
∆p
direction of the net force) - Fnet =
∆t
General calculations:
Fnet =ma
Vf −Vi
a=
t
Acceleration problems with one object:
Vf −Vi
Use Fnet =ma∧a=
t
Calculate accordingly
