Forces and Motion Flashcards
What is a distance - time graph ?
A distance-time graph shows how the distance of an object moving in a straight line (from a starting position) varies over time:
What is a constant speed on a distance - time graph ?
Distance-time graphs also show the following information:
Whether the object is moving at a constant speed
How large or small the speed is
A straight line represents constant speed:
The slope of the straight line represents the magnitude of the speed:
A very steep slope means the object is moving at a large speed
A shallow slope means the object is moving at a small speed
A flat, horizontal line means the object is stationary (not moving)
What is the changing speed on a distance-time graph?
Objects might be moving at a changing speed
This is represented by a curve
In this case, the slope of the line will be changing
If the slope is increasing, the speed is increasing (accelerating)
If the slope is decreasing, the speed is decreasing (decelerating)
The image below shows two different objects moving with changing speeds
How to calculate speed from a distance-time graph?
The speed of a moving object can be calculated from the gradient of the line on a distance-time graph:
How do you calculate average speed ?
The speed of an object is the distance it travels every second
Speed is a scalar quantity because it has a magnitude but not a direction
Average speed
The speed of an object can vary throughout its journey
Therefore, it is often more useful to know an object’s average speed
What is the average - speed formula
The equation for calculating the average speed of a moving object is:
average space speed space equals fraction numerator space distance space moved over denominator time space taken end fraction
Average speed considers the total distance moved and the total time taken
Core practical 1: investigating motion
Aim of the experiment
The aim of this experiment is to investigate the motion of some everyday objects, by measuring their speed
Examples of objects that could be used are:
a paper cone
a tennis ball
Measuring speed directly is difficult to do; therefore, by measuring distance moved and time taken, the average speed of the object can be calculated
This is just one method of measuring the speed of different objects - some methods involve the use of light gates to measure speed and acceleration, e.g. for a toy car moving down a slope
Variables
Independent variable = Distance, d
Dependent variable = Time, t
Control variables:
Use the same object (paper cone, tennis ball etc.) for each measurement
What is the method of this investigation ?
- Measure out a height of 1.0 m using the tape measure or metre ruler
- Drop the object (paper cone or tennis ball) from this height, which is the distance travelled by the object
- Use the stop clock to measure how long the object takes to travel this distance
- Record the distance travelled and time taken
- Repeat steps 2-3 three times, calculating an average time taken for the object to fall a certain distance
- Repeat steps 1-4 for heights of 1.2 m, 1.4 m, 1.6 m, and 1.8 m
What are the results ?
Analysis of results
The average speed of the falling object can be calculated using the equation:
average space speed space equals fraction numerator space distance space moved over denominator time space taken end fraction
Where:
Average speed is measured in metres per second (m/s)
Distance moved is measured in metres (m)
Time taken is measured in seconds (s)
Therefore, calculate the average speed at each distance by dividing the distance by the average time taken
Evaluating the experiment
Systematic errors
Make sure the measurements on the tape measure or metre rule are taken at eye level to avoid parallax error
The average human reaction time is 0.25 s, which is equivalent to half a second per when starting and stopping the timer
This is likely to be significant when small intervals of time are measured
To reduce this systematic error, larger distances could be used resulting in larger time intervals
Using a ball bearing and an electronic data logger, like a trap door, is a good way to remove the error due to human reaction time for this experiment
Consider using an electronic sensor, such as light gates, to obtain highly accurate measurements of time
The timer on a light gate starts and stops automatically as it passes the sensors positioned at the start and stop points
Random errors
Ensure the experiment is done in a space with no draft or breeze, as this could affect the motion of the falling object
Safety considerations
Place a mat or a soft material below any falling object to cushion its fall
What is acceleration ?
Rate of change in velocity
Acceleration is defined as the rate of change in velocity
In other words, it describes how much an object’s velocity changes every second
The equation below is used to calculate the average acceleration of an object:
acceleration space equals fraction numerator space change space in space velocity over denominator time space taken end fraction
a space equals space fraction numerator increment v over denominator t end fraction
Where:
a = acceleration in metres per second squared (m/s2)
increment v = change in velocity in metres per second (m/s)
t = time taken in seconds (s)
What happens when a object speeds up or slow downs ?
An object that speeds up is accelerating
An object that slows down is decelerating
The acceleration of an object can be positive or negative, depending on whether the object is speeding up or slowing down
If an object is speeding up, its acceleration is positive
If an object is slowing down, its acceleration is negative (also known as deceleration)
What are velocity time graphs ?
A velocity time graph, or velocity-time graph, shows how the velocity of a moving object varies with time
Velocity-time refers to the fact that velocity is plotted against time on the graph
The red line represents an object with increasing velocity
The green line represents an object with decreasing velocity
What is acceleration on a velocity - time graph ?
Velocity-time graphs also show the following information:
Whether the object is moving with a constant acceleration
The magnitude of the acceleration
A straight line represents constant acceleration (or deceleration)
The slope of the line represents the magnitude of acceleration
A steep slope means large acceleration
The object’s speed changes very quickly
A gentle slope means small acceleration
The object’s speed changes very gradually
A positive gradient shows increasing velocity
The object is accelerating
A negative gradient shows decreasing velocity
The object is decelerating
A flat line means the acceleration is zero
The object is moving with a constant velocity
What is the gradient of a velocity - time graph ?
The acceleration of an object can be calculated from the gradient of a velocity-time graph
How do you find the area under a velocity-time graph?
If the area beneath the velocity-time graph forms a triangle (i.e. the object is accelerating or decelerating), then the area can be determined by using the following formula:
Area = ½ × Base × Height
If the area beneath the velocity-time graph forms a rectangle (i.e. the object is moving at a constant velocity), then the area can be determined by using the following formula:
Area = Base × Height
How do you find distance from a velocity-time graph?
Enclosed areas under velocity-time graphs represent total displacement (or total distance travelled) in a time interval
How to calculate uniform acceleration ?
Uniform acceleration is constant acceleration
The following equation applies to objects moving with uniform acceleration:
(final speed)2 = (initial speed)2 + (2 × acceleration × distance moved)
v2 = u2 + 2as
Where:
s = distance moved in metres (m)
u = initial speed in metres per second (m/s)
v = final speed in metres per second (m/s)
a = acceleration in metres per second squared (m/s2)
This equation is used to calculate quantities such as initial or final speed, uniform acceleration, or distance moved in cases where the time taken is not known
Exam Tip
This is an example of an equation that cannot be rearranged with a formula triangle. It is really important that you learn to rearrange equations without the help of a triangle for your exam.
To rearrange any equation, follow these simple rules:
What ever you do to the equation, you must do to both sides
To undo an operation, perform the opposite operation
To undo a subtraction, you must add (and vice versa)
To undo a multiplication, you must divide (and vice versa)
To undo a square, you must square root (and vice versa)
Always show your working out, there is usually a mark awarded for rearranging an equation in an exam question.
How do you find the area under a velocity-time graph?
The area under a velocity-time graph represents the displacement (or distance travelled) by an object
If the area beneath the velocity-time graph forms a triangle (i.e. the object is accelerating or decelerating), then the area can be determined by using the following formula:
Area = ½ × Base × Height
If the area beneath the velocity-time graph forms a rectangle (i.e. the object is moving at a constant velocity), then the area can be determined by using the following formula:
Area = Base × Height
How do you find distance from a velocity-time graph?
Enclosed areas under velocity-time graphs represent total displacement (or total distance travelled) in a time interval
If an object moves with constant acceleration, its velocity-time graph will consist of straight lines
In this case, calculate the distance travelled by working out the area of enclosed rectangles and triangles
The area of each enclosed section represents the distance travelled in that particular interval of time
The total distance travelled is the sum of all the individual enclosed areas
What are the different type of forces ?
Gravitational force (weight)
There is a gravitational force of attraction between all objects with mass
The more massive the object, the greater the gravitational force exerted by it
When a football is thrown (or kicked), the gravitational pull of the Earth on the football pulls it toward the (centre of the) Earth
Reaction force
When an object rests on a surface, the surface exerts a push force on the object
This reaction force acts at right angles (perpendicular) to the surface
When a football rests on the horizontal surface of the grass, the grass exerts a push force (reaction force) vertically upwards on the football
What is friction ?
Frictional forces always oppose the motion of an object, causing it to slow down
Friction occurs when two surfaces move over one another
When a box is pushed across a carpet, the carpet exerts a frictional force on the box, slowing its motion
What is drag force ?
Drag force is a type of frictional force that occurs when an object moves through a fluid (a gas or a liquid)
The particles in the fluid collide with the object moving through it and slow its motion
When a pebble is thrown into water, the water molecules flow against its solid surface, causing it to slow down
What is air resistance ?
Air resistance is a specific type of drag force and is therefore also a frictional force
Air resistance occurs when particles of air collide with an object moving through it and slows its motion
When a skydiver opens their parachute, air resistance opposes their motion and reduces their speed so it is safe to land
What is thrust ?
Thrust is a force produced by an engine that speeds up the motion of an object
The engine of a car exerts a thrust force and increases its speed
What is up thrust ?
When an object is fully or partially submerged in a fluid, the fluid exerts an upward-acting push force on the object
A boat floats on a lake due to the upthrust exerted by the water on the boat
A ball held underwater will shoot upwards when released due to the upthrust exerted by the water pushing it back to the surface
What is electrostatic force ?
Electrostatic force
There is an electrostatic force between two objects with charge
Like charges repel one another, and opposite charges attract one another
When an electron gets close to a positively charged ion, the ion exerts a pull force on the electron (attraction)
When an electron gets close to another electron, the electrons experience a push force from one another (repulsion)
What is a magnetic force ?
Magnetic force
There is a magnetic force between objects with magnetic poles
Like poles repel one another, opposite poles attract one another
When a north pole gets close to a south pole, they experience a pull force from one another (attraction)
When a north pole gets close to a north pole, they experience a push force from one another (repulsion)
What is tension ?
Tension occurs in an object (like a rope or spring) that is stretched
When a pull force is exerted on each end of an object, tension acts across the length of the object
When two people pull a rope in opposite directions, tension
acts along the rope and pulls back on each person
Exam Tip
The force of gravitational attraction on an object is called its weight. Remember not to refer to this force as simply ‘gravity’, as this term can mean several different things, and examiners will probably mark it as wrong.
Similarly, when referring to air resistance, avoid using terms like ‘wind resistance’ (there is no such thing!) or ‘air pressure’, which is a different concept. Drag is an acceptable alternative to the force of air resistance because air resistance is a special type of drag.
What are effects of forces ?
When a force acts on an object, the force can affect the object in a variety of ways
The object could:
change speed
change direction
change shape
The effects of forces on an object often depend on the type of force acting
The push force (thrust) of an engine can cause a car to speed up, whilst the force exerted by the brakes (friction) can cause it to slow down
The gravitational pull of the Sun on a comet causes the comet to change direction
When two opposing forces push on each end of a spring, the spring changes shape (it compresses)
What are scalars ?
Scalars are quantities that have magnitude but not direction
For example, mass is a scalar quantity because it has magnitude but no direction
What are vectors ?
Vectors are quantities that have both magnitude and direction
For example, weight is a vector quantity because it is a force and has both magnitude and direction
What is distance and displacement
Distance is a measure of how far an object has travelled, regardless of direction
Distance is the total length of the path taken
Distance, therefore, has a magnitude but no direction
So, distance is a scalar quantity
Displacement is a measure of how far it is between two points in space, including the direction
Displacement is the length and direction of a straight line drawn from the starting point to the finishing point
Displacement, therefore, has a magnitude and a direction
So, displacement is a vector quantity
What is speed and velocity ?
Speed is a measure of the distance travelled by an object per unit time, regardless of the direction
The speed of an object describes how fast it is moving, but not the direction it is travelling in
Speed, therefore, has magnitude but no direction
So, speed is a scalar quantity
Velocity is a measure of the displacement of an object per unit time, including the direction
The velocity of an object describes how fast it is moving and which direction it is travelling in
An object can have a constant speed but a changing velocity if the object is changing direction
Velocity, therefore, has magnitude and direction
So, velocity is a vector quantity
What are forces as vectors ?
Vector quantities can be represented by arrows
The length of the arrow represents the magnitude
The direction of the arrow indicates the direction
Force is a vector quantity because force has magnitude and direction
When using arrows to represent forces:
the length of the arrow represents the magnitude of the force
the direction of the arrow indicates the direction of the force
the scale of the arrows should be proportional to the relative magnitudes of the forces
an arrow for a 4 N force should be twice as long as an arrow for a 2 N force
the arrows should be labelled with the names of the forces, or a description of the forces
for example, weight, W, or the gravitational pull of the Earth on the object
Not all forces are directed perfectly horizontally or vertically and so need to have an angle described for the direction
It is useful to describe an angle with respect to the vertical or the horizontal
How do you add forces to find the resultant force ?
Resultant forces can be calculated by adding all of the forces acting on the object
Forces working in opposite directions are subtracted from each other
Forces working in the same direction are added together
If the forces acting in opposite directions are equal in size, then there will be no resultant force – the forces are said to be balanced
Imagine the forces on the boxes as two people pushing on either side
In the first scenario, the two people are evenly matched - the box doesn’t move
In the second scenario, the two people are pushing on the same side of the box, it moves to the right with their combined strength
In the third scenario, the two people are pushing against each other and are not evenly matched, so there is a resultant force to the left
What are balanced forces ?
Balanced forces mean that the forces have combined in such a way that they cancel each other out and no resultant force acts on the body
For example, the weight of a book on a desk is balanced by the normal force of the desk
As a result, no resultant force is experienced by the book, the book and the table are equal and balanced
A car salesperson claims that their best car has a mass of 900 kg and can accelerate from 0 to 27 m/s in 3 seconds.
Calculate:
a) The acceleration of the car in the first 3 seconds.
b) The force required to produce this acceleration.
How to calculate stopping distance ?
For a given braking force, the speed of a vehicle determines the size of the stopping distance
The greater the speed of the vehicle, the larger the stopping distance
How do you reach terminal velocity?
At the instant the skydiver steps out of the plane, the support force of the plane is no longer acting on the skydiver, but they are not yet falling, so the only force exerted them is the weight force
There is a downward acting resultant force on the skydiver
The resultant force is equal to the weight force
The skydiver accelerates downward at maximum acceleration
As the skydiver begins to fall, the force of air resistance is very small because the skydiver’s speed is small
There is a downward acting resultant force on the skydiver
The resultant force is equal to the weight force minus the force of air resistance
The skydiver accelerates downward but the acceleration decreases
As the skydiver accelerates, their speed increases, so the force of air resistance increases
There is a downward acting resultant force on the skydiver
The resultant force is equal to the weight force minus the force of air resistance
The skydiver accelerates downward but the acceleration continues to decrease
As the skydiver’s acceleration decreases, their speed increases at a slower and slower rate
Eventually, the skydiver reaches a speed at which the force of air resistance is equal to the force of weight
The forces are balanced, so the resultant force is zero
The skydiver no longer accelerates and a constant velocity is reached
This is terminal velocity
Core Practical: Investigating Force & Extension
Experiment 1: investigating force and extension for springs and rubber bands
The aim of this experiment is to investigate the relationship between force and extension for a spring and a rubber band:
Variables
Independent variable = Force, F
Dependent variable = Extension, e
Equipment
What is the method ?
- Align the marker to a value on the ruler with no mass added, and record this initial length of the spring / rubber band
- Add the 100 g mass hanger onto the spring / rubber band
- Record the mass (in kg) and position (in cm) from the ruler now that the spring / rubber band has extended
- Add another 100 g to the mass hanger
- Record the new mass and position from the ruler now that the spring / rubber band has extended further
- Repeat this process until all masses have been added
- Remove the masses and repeat the entire process again, until it has been carried out a total of three times, and an average length (for each mass attached) is calculated
What is the example result table for this investigation ?
Experiment 2: investigating force and extension for metal wires
he aim of this experiment is to investigate the relationship between force and extension for a metal wire
Variables
Independent variable = Force, F
Dependent variable = Extension, e
What is the method of this investigation ?
- Set up the apparatus so the wire is taut with no masses added
- Measure the original length of the wire using a metre ruler and mark a reference point with tape preferably near the beginning of the scale eg. at 1 cm
- Record the initial length of the wire to the marker
- Add a 100 g mass onto the mass hanger
- Read and record the new reading of the tape marker from the meter ruler now that the metal wire has extended
- Repeat this process until all masses have been added
- Remove the masses and repeat the entire process again, until it has been carried out a total of three times, and an average length (for each mass attached) is calculated
What are the results ?
Analysis of results
The force, F added to the spring / rubber band / metal wire is the weight of the mass
The weight is calculated using the equation:
W = m × g
Where:
W = weight in newtons (N)
m = mass in kilograms (kg)
g = gravitational field strength on Earth in newtons per kg (N/kg)
Therefore, multiply each mass by gravitational field strength, g, to calculate the force, F
The force can be calculated by multiplying the mass (in kg) by 10 N/kg
The extension e of the spring / rubber band is calculated using the equation:
e = average length – original length
The final length is the length of the spring / rubber band recorded from the ruler after the masses were added
The extension e of the metal wire is calculated using the equation:
e = new marker reading − reference point reading
The original length is the length of the spring / rubber band / metal wire when there were no masses attached
- Plot a graph of the force against extension for the spring / rubber band / metal wire
- Draw a line or curve of best fit
- If the graph has a linear region (is a straight line), then the force is proportional to the extension
Evaluating the experiments
Systematic errors
Make sure the measurements on the ruler are taken at eye level to avoid parallax error
Random errors
The accuracy of such an experiment is improved with the use of a pointer (a fiducial marker)
Wait a few seconds for the spring / rubber band / metal wire to fully extend when a mass is added, before taking the reading for its new length
Make sure to check whether the spring has not gone past its limit of proportionality otherwise, it has been stretched too far
Safety considerations
Wear goggles during this experiment in case the spring, rubber band or wire snaps
Stand up while carrying out the experiment, making sure no feet are directly under the masses
Place a mat or a soft material below the masses to prevent any damage in case they fall
Use a G clamp to secure the clamp stand to the desk so that the clamp and masses do not fall over
As well as this, place each mass carefully on the hanger and do not pull the spring so hard that it breaks or pulls the apparatus over
Exam Tip
Remember - for the spring and rubber band, the extension measures how much the object has stretched by and can be found by subtracting the original length from each of the subsequent lengths.
For the metal wire, each extension is measured by finding the difference between the new marker point and the original reference point.
A common mistake is to calculate the increase in length by each time instead of the total extension. If each of your extensions is roughly the same, then you might have made this mistake!
What is Hookes Law ?
The relationship between the extension of an elastic object and the applied force is defined by Hooke’s Law
Hooke’s Law states that:
The extension of an elastic object is directly proportional to the force applied, up to the limit of proportionality
Directly proportional means that as the force is increased, the extension increases
If the force is doubled, then the extension will double
If the force is halved, then the extension will also halve
The limit of proportionality is the point beyond which the relationship between force and extension is no longer directly proportional
This limit varies according to the material
What is the force-extension graph?
Hooke’s law is the linear relationship between force and extension
This is represented by a straight line on a force-extension graph
Any material beyond its limit of proportionality will have a non-linear relationship between force and extension
What is inelastic deformation ?
Inelastic deformation is when the object does not return to its original shape after the deforming forces are removed
Inelastic deformation results in a change in the object’s shape that is permanent
Examples of materials that undergo inelastic deformation are:
Plastic
Clay
Glass
How will the momentum of a object change ?
The momentum of an object will change if:
it’s velocity increases or decreases (acceleration)
it’s direction changes (acceleration)
it’s mass changes
Exam Tip
Remember the units of momentum as kg m/s which is the product of the units of mass (kg) and velocity (m/s).
Which direction is taken as positive is completely up to you in the exam. In general, forwards, to the right, and upwards are taken as positive, and backward, to the left, or down are taken as negative.
What is a collision ?
For a collision between two objects:
The total momentum before a collision = the total momentum after a collision
In the example below:
Before the collision:
The momentum is only generated by mass m because it is the only moving object
If the right is taken as the positive direction, the total momentum of the system is m × u
After the collision:
Mass M also now has momentum
The velocity of m is now -v (since it is now travelling to the left) and the velocity of M is V
The total momentum is now the momentum of M + the momentum of m
This is (M × V) + (m × -v) or (M × V) – (m × v) written more simply
Since momentum is a vector quantity, a system of objects moving in opposite directions (e.g. towards each other) at the same speed will have an overall momentum of 0 since they will cancel out
Momentum is always conserved over time
What is Newton’s third law?
Newton’s third law of motion can be defined as follows:
Whenever two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction
Newton’s third law explains the forces that enable someone to walk
The foot exerts a push force on the ground
The ground exerts a push force force on the foot
The forces are equal in magnitude and opposite in direction
What is newtons third law in collision ?
According to Newton’s Third Law:
When two objects collide, both objects will react, generally causing one object to speed up (gain momentum) and the other object to slow down (lose momentum)
Consider the collision between two trolleys, A and B:
When trolley A exerts a force on trolley B, trolley B will exert an equal force on trolley A in the opposite direction
In this case:
FB–A = –FA–B
While the forces are equal in magnitude and opposite in direction, the accelerations of the objects are not necessarily equal in magnitude
From F = ma, acceleration depends upon both force and mass, this means:
For objects of equal mass, they will have equal accelerations
For objects of unequal mass, they will have unequal accelerations
What are safety feats ?
Vehicle safety features are designed to absorb energy upon an impact by changing shape
The main vehicle safety features are crumple zones, seat belts and airbags
For a given force upon impact, these absorb the energy from the impact and increase the time over which the force takes place
This, in turn, increases the time taken for the change in momentum of the passenger and the vehicle to come to rest
The increased time reduces the force and risk of injury on a passenger
The usefulness of safety features depends on two main factors: mass and velocity
If the impact is from a large mass, for example, a truck travelling very fast and colliding with a wall, the momentum will be very large
The change in momentum (ie. from a high speed to rest) will also be very large
This means that a very long contact time is needed to reduce the force of impact .
Seat belts
These are designed to stop a passenger from colliding with the interior of a vehicle by keeping them fixed to their seat in an abrupt stop
They are designed to stretch slightly to increase the time for the passenger’s momentum to reach zero and reduce the force on them in a collision
Airbags
These are deployed at the front on the dashboard and steering wheel when a collision occurs
They act as a soft cushion to prevent injury on the passenger when they are thrown forward upon impact
Crumple zones
These are designed into the exterior of vehicles
They are at the front and back and are designed to crush or crumple in a controlled way in a collision
This is why vehicles after a collision look more heavily damaged than expected, even for relatively small collisions
The crumple zones increase the time over which the vehicle comes to rest, lowering the impact force on the passengers
What are the benefits of crash mats ?
Crash mats used in gymnasiums help reduce the risk of injury for falls in gymnastics and climbing
They are thick and soft to offer shock absorption of the force created by the person landing on the mat
When a person lands on a crash mat with a large force, for example, after jumping, the soft landing means their body is in contact with the mat for a longer period of time than if it were otherwise not there
This increases the contact time over which their momentum is reduced, creating a smaller impact force and a lower chance of injury
In a similar way, playgrounds utilise cushioned surfaces as children will often fall onto these with a large force
The cushioned surface reduces the risk of a severe injury by increasing their contact time with the ground
Meanwhile, a child in a gymnasium can use a thinner crash mat than an adult due to having a lower mass
This is the same for activities where a person/adult will fall with a low velocity such as falling from lower heights
Therefore, thin crash mats are suitable for low-impact activities
Safety features are intended to reduce the chance of serious injury but do not completely prevent it in all cases
What is the moment of a force ?
The moment of a force is the turning effect produced when a force is exerted on an object
Examples of the rotation caused by the moment of a force are:
A child on a see-saw
Turning the handle of a spanner
A door opening and closing
Using a crane to move building supplies
Using a screwdriver to open a tin of paint
Turning a tap on and off
Picking up a wheelbarrow
Using scissors
Forces can cause the rotation of an object about a fixed pivot
This rotation can be clockwise or anticlockwise
What is the principal of moments ?
The principle of moments states that:
If an object is balanced, the total clockwise moment about a pivot equals the total anticlockwise moment about that pivot
For a balanced object, the moments on both sides of the pivot are equal
clockwise moment = anticlockwise moment
Clockwise and anticlockwise moments
How can you support a light beam?
A light beam is one that can be treated as though it has no mass
The supports, therefore, must exert upward forces that balance the downward acting weight of any object placed on the beam
What is the centre of gravity ?
The centre of gravity of an object is defined as:
The point through which the weight of an object acts
For a symmetrical object of uniform density, the centre of gravity is located at the point of symmetry
For example, the centre of gravity of a sphere is at the centre
Finding the centre of gravity of symmetrical objects
How can you find the centre of gravity in a irregular object ?
The centre of gravity of an irregular object can be found using suspension
The irregular shape is suspended from a pivot and allowed to settle
A plumb line (weighted thread) is then held next to the pivot and a pencil is used to draw a vertical line from the pivot (the centre of mass must be somewhere on this line)
The process is then repeated, suspending the shape from two additional points
The centre of mass is located at the point where all three lines cross
Exam Tip
Since the centre of gravity is a hypothetical point, it can lie inside or outside of a body. The centre of gravity will constantly shift depending on the shape of a body. For example, a human body’s centre of gravity is lower when learning forward than when standing upright
However, when you are drawing force diagrams, always draw the weight force as if it were acting from the centre of gravity of the object!
