Speed and graphs
Solving questions
Vector A quantity that is represented by direction and
magnitude
●
Formula ●
Distance is m
●
Substitution ●
Speed is m/s
Scalar A quantity that is represented solely by magnitude ●
Calculation ●
Rate of change
●
Units of speed is m/s2
Retardation Negative acceleration
Graphs
Equations
●
The slope of a distance-time graph = speed
Average speed = initial speed + final speed ●
The slope/gradient of a speed-time graph = the rate of
2 change of speed
●
The area under a speed-time graph = the distance moved
Or distance moved
time taken
Rate of change of speed = final speed – initial speed
At rest
time taken
Same for velocity and acceleration (vector), just
replace distance with displacement and speed with
velocity
●
Velocity can be 0 if you return to starting position
●
Distance-time – negative gradient = going back, negative distance =
going other way
●
Velocity-time – negative gradient = decelerating, negative velocity =
going back
Newton’s laws Newton’s first law: In the absence of
unbalanced forces and object will continue to move in a straight
Practical 1 line at constant speed or remain at rest
Newton’s second law: A resultant force will cause an object
to accelerate and acceleration is proportional to the size of
the resultant force
Forces on moving objects
Ramp length known, measure height of support then release
marble from top and measure time taken to go to B. Write this All forces can be classified as pushes or pulls, but
down into a table and repeat 3 times for reliability. Find many are given different names. e.g:
average time, and then use S = D/T to find average speed. ●
WEIGHT acts straight down
●
DRAG (air resistance or friction) slows things
Examples of forces down
A force is any influence
●
TENSION is in a rope or cable
A force has both size and ●
LIFT is due to an airplane wing
that causes a free body direction. The size of the force is
to undergo:
●
THRUST speeds something up
measured in newtons (N), and is REACTION acts straight up on a horizontal
1) A change in speed or represented by an arrow in
●
velocity plane
diagrams. The length of the arrows
2) A change in shape represents the size of the force. All forces are
3) A change in direction measured in
NEWTONS and
The movements of an object
are represented
depends on the forces acting on it: Thrust = drag =
●
If they are equal and opposite
●
on diagram by
constant drawing lines
the forces acting are balanced
or in equilibrium, with these the speed/stationary with arrows
object will either be
●
Thrust > drag = pointing in the
stationary/at rest or moving accelerating direction of the
with a constant speed ●
Thrust < drag = force
●
If they are not equal and decelerating
opposite then an unbalanced
(resultant) force acts
, Resultant force Newton’s second law
Acceleration of an object is directly proportional to the
When calculating resultant force of
size of an unbalanced force, while acceleration is
an object you must add and
inversely proportional to the mass of an object.
subtract forces vectorially – you
must take into account direction.
F = ma
All movement has opposite forces ●
M is the mass in kg
●
A is the acceleration in m/s2
Therefore, regardless ●
F is the unbalanced or resultant force acting on
G = 10m/s , u = 0 2 of mass objects hit
ground at same time the object in newtons
Investigating Newton’s Laws Relationship between resultant force and acceleration
DV – acceleration
CV – weight of trolley
Tilted – friction
IV – weight of pulley
compensated
●
Weight attached to string attached to trolley
●
Trolley released and acceleration calculated using light
gates
●
Force increased by attaching more weights and new
acceleration calculated
●
Done for 5 different weights and repeated for accuracy
●
Graph – acceleration (y axis) against force (x axis)
Directly proportional – F/A will always be the same – constant
F/A = const
Relationship between force and acceleration
DV – acceleration
CV – mass of trolley, trolley starting point, distance
between light gates
IV – masses
●
Trolley with known length of card placed on friction-
compensated runway – air track here
●
When masses released, pulled through light, first light
gate records time it takes for card to pass through
Tilted – friction ●
First velocity calculated using v = d/t
compensated ●
Card will accelerate due to force produced by
masses, velocity at next light gate should therefore be
greater
●
Time taken to move through second light gate
recorded. Velocity can be worked out.
●
Acceleration calculated by finding change in velocity
divided by time taken
●
Masses can be varied to investigate the effect force
will have on acceleration
Relationship between mass and acceleration Dependant
DV – acceleration
CV – weight of pulley Direct
IV – weight of trolley
●
Weight attached to string attached to trolley
●
Trolley released and acceleration calculated using
light gates
●
Mass is added to trolley and new acceleration
calculated
●
Done for 5 different masses and repeated for y = kx
accuracy
●
Graph – acceleration (y axis) against mass (x axis)
y = k/x
Inversely proportional – 1/m x a will always be the same – Inverse
constant
am = const Independent
, “The extension of a spring is directly proportional to
the force applied, provided that the limit of
Hooke’s law When no force or mass is attached
proportionality is not exceeded” to a spring the length of the spring
is called its natural length, l0
F = ke
To measure extension – stretched
●
F is the force in newtons (N) length – natural length
●
k is the 'spring constant' in newtons per
metre (N/m) (stiffer spring – greater/smaller e = l – l0
spring constant)
●
e is the extension in metres (m)
Hooke’s law practical 1) Measure the original length of the
Meaning spring using a ruler.
2) Attach a known weight (approximately
Investigate the relationship 0.5N) to the spring.
between the extension of a spring 3) Measure the new length of the spring.
and the force applied to that spring. 4) Calculate the extension of the spring by
subtracting the original length from the
Variables new length of the spring.
5) Repeat steps 2-4 up to around 5N.
●
Independent Variable: The 6) Plot a scatter graph with the force of
force applied to the spring. weight on the x-axis and the extension
●
Dependent Variable: The on the y-axis. The gradient of line of best
extension of the spring. fit will be the spring constant of the coil
●
Control Variables: The spring.
spring being used.
Improving Accuracy
More Hooke’s ●
Calculate the weight added by measuring its
Forces can cause object to deform (i.e. change their mass using an electronic balance on a flat, level
shape). The way in which an object deforms depends on: surface each time and using the equation W=mg
●
Its dimensions
●
with g=9.8. This will give a more accurate
●
The material it is made from knowledge of the weight rather than relying on
●
The size of the force the number printed on the weights.
●
The direction of the force
●
Add a fiduciary marker to the bottom of the
coil spring to prevent any error caused by not
Because the force acting on the spring (or any object) reading the ruler from eye level.
causes stretching, it is sometimes called tension or
●
Ensure the spring is not moving when taking
tensile force. measurements of it's length.
Limit of proportionality In this short version of the Pressure
equation:
●
F represents force which
is measured in newtons
●
a represents area which
is measured in m2
●
p represents pressure
which is measured in
pascals (usually used)
●
1 pascal = 1 N/m2 Pressure in solids acts on
●
1 cm2 = 0.0001m2 the point of contact
●
1mm2 = 0.000001m2 between the object on
which the force is being
exerted on and the solid
which will experience the
Up to P, when the force is removed, the spring returns pressure. Reducing
to its natural length, l0. In this part of the graph the surface area or increasing
spring is elastic. In the section of the graph where the force will increasing
line starts to curve (after P), the force on the spring pressure.
permanently deforms it. At this point it is plastic.
Not only springs follow this – many materials will obey
Hooke’s Law for at least a small range of applied force.
Solving questions
Vector A quantity that is represented by direction and
magnitude
●
Formula ●
Distance is m
●
Substitution ●
Speed is m/s
Scalar A quantity that is represented solely by magnitude ●
Calculation ●
Rate of change
●
Units of speed is m/s2
Retardation Negative acceleration
Graphs
Equations
●
The slope of a distance-time graph = speed
Average speed = initial speed + final speed ●
The slope/gradient of a speed-time graph = the rate of
2 change of speed
●
The area under a speed-time graph = the distance moved
Or distance moved
time taken
Rate of change of speed = final speed – initial speed
At rest
time taken
Same for velocity and acceleration (vector), just
replace distance with displacement and speed with
velocity
●
Velocity can be 0 if you return to starting position
●
Distance-time – negative gradient = going back, negative distance =
going other way
●
Velocity-time – negative gradient = decelerating, negative velocity =
going back
Newton’s laws Newton’s first law: In the absence of
unbalanced forces and object will continue to move in a straight
Practical 1 line at constant speed or remain at rest
Newton’s second law: A resultant force will cause an object
to accelerate and acceleration is proportional to the size of
the resultant force
Forces on moving objects
Ramp length known, measure height of support then release
marble from top and measure time taken to go to B. Write this All forces can be classified as pushes or pulls, but
down into a table and repeat 3 times for reliability. Find many are given different names. e.g:
average time, and then use S = D/T to find average speed. ●
WEIGHT acts straight down
●
DRAG (air resistance or friction) slows things
Examples of forces down
A force is any influence
●
TENSION is in a rope or cable
A force has both size and ●
LIFT is due to an airplane wing
that causes a free body direction. The size of the force is
to undergo:
●
THRUST speeds something up
measured in newtons (N), and is REACTION acts straight up on a horizontal
1) A change in speed or represented by an arrow in
●
velocity plane
diagrams. The length of the arrows
2) A change in shape represents the size of the force. All forces are
3) A change in direction measured in
NEWTONS and
The movements of an object
are represented
depends on the forces acting on it: Thrust = drag =
●
If they are equal and opposite
●
on diagram by
constant drawing lines
the forces acting are balanced
or in equilibrium, with these the speed/stationary with arrows
object will either be
●
Thrust > drag = pointing in the
stationary/at rest or moving accelerating direction of the
with a constant speed ●
Thrust < drag = force
●
If they are not equal and decelerating
opposite then an unbalanced
(resultant) force acts
, Resultant force Newton’s second law
Acceleration of an object is directly proportional to the
When calculating resultant force of
size of an unbalanced force, while acceleration is
an object you must add and
inversely proportional to the mass of an object.
subtract forces vectorially – you
must take into account direction.
F = ma
All movement has opposite forces ●
M is the mass in kg
●
A is the acceleration in m/s2
Therefore, regardless ●
F is the unbalanced or resultant force acting on
G = 10m/s , u = 0 2 of mass objects hit
ground at same time the object in newtons
Investigating Newton’s Laws Relationship between resultant force and acceleration
DV – acceleration
CV – weight of trolley
Tilted – friction
IV – weight of pulley
compensated
●
Weight attached to string attached to trolley
●
Trolley released and acceleration calculated using light
gates
●
Force increased by attaching more weights and new
acceleration calculated
●
Done for 5 different weights and repeated for accuracy
●
Graph – acceleration (y axis) against force (x axis)
Directly proportional – F/A will always be the same – constant
F/A = const
Relationship between force and acceleration
DV – acceleration
CV – mass of trolley, trolley starting point, distance
between light gates
IV – masses
●
Trolley with known length of card placed on friction-
compensated runway – air track here
●
When masses released, pulled through light, first light
gate records time it takes for card to pass through
Tilted – friction ●
First velocity calculated using v = d/t
compensated ●
Card will accelerate due to force produced by
masses, velocity at next light gate should therefore be
greater
●
Time taken to move through second light gate
recorded. Velocity can be worked out.
●
Acceleration calculated by finding change in velocity
divided by time taken
●
Masses can be varied to investigate the effect force
will have on acceleration
Relationship between mass and acceleration Dependant
DV – acceleration
CV – weight of pulley Direct
IV – weight of trolley
●
Weight attached to string attached to trolley
●
Trolley released and acceleration calculated using
light gates
●
Mass is added to trolley and new acceleration
calculated
●
Done for 5 different masses and repeated for y = kx
accuracy
●
Graph – acceleration (y axis) against mass (x axis)
y = k/x
Inversely proportional – 1/m x a will always be the same – Inverse
constant
am = const Independent
, “The extension of a spring is directly proportional to
the force applied, provided that the limit of
Hooke’s law When no force or mass is attached
proportionality is not exceeded” to a spring the length of the spring
is called its natural length, l0
F = ke
To measure extension – stretched
●
F is the force in newtons (N) length – natural length
●
k is the 'spring constant' in newtons per
metre (N/m) (stiffer spring – greater/smaller e = l – l0
spring constant)
●
e is the extension in metres (m)
Hooke’s law practical 1) Measure the original length of the
Meaning spring using a ruler.
2) Attach a known weight (approximately
Investigate the relationship 0.5N) to the spring.
between the extension of a spring 3) Measure the new length of the spring.
and the force applied to that spring. 4) Calculate the extension of the spring by
subtracting the original length from the
Variables new length of the spring.
5) Repeat steps 2-4 up to around 5N.
●
Independent Variable: The 6) Plot a scatter graph with the force of
force applied to the spring. weight on the x-axis and the extension
●
Dependent Variable: The on the y-axis. The gradient of line of best
extension of the spring. fit will be the spring constant of the coil
●
Control Variables: The spring.
spring being used.
Improving Accuracy
More Hooke’s ●
Calculate the weight added by measuring its
Forces can cause object to deform (i.e. change their mass using an electronic balance on a flat, level
shape). The way in which an object deforms depends on: surface each time and using the equation W=mg
●
Its dimensions
●
with g=9.8. This will give a more accurate
●
The material it is made from knowledge of the weight rather than relying on
●
The size of the force the number printed on the weights.
●
The direction of the force
●
Add a fiduciary marker to the bottom of the
coil spring to prevent any error caused by not
Because the force acting on the spring (or any object) reading the ruler from eye level.
causes stretching, it is sometimes called tension or
●
Ensure the spring is not moving when taking
tensile force. measurements of it's length.
Limit of proportionality In this short version of the Pressure
equation:
●
F represents force which
is measured in newtons
●
a represents area which
is measured in m2
●
p represents pressure
which is measured in
pascals (usually used)
●
1 pascal = 1 N/m2 Pressure in solids acts on
●
1 cm2 = 0.0001m2 the point of contact
●
1mm2 = 0.000001m2 between the object on
which the force is being
exerted on and the solid
which will experience the
Up to P, when the force is removed, the spring returns pressure. Reducing
to its natural length, l0. In this part of the graph the surface area or increasing
spring is elastic. In the section of the graph where the force will increasing
line starts to curve (after P), the force on the spring pressure.
permanently deforms it. At this point it is plastic.
Not only springs follow this – many materials will obey
Hooke’s Law for at least a small range of applied force.
