Mechanics and Materials Flashcards
Scalar vs Vector
- A scalar is a quantity which only has a magnitude (size)
- A vector is a quantity which has both a magnitude and a direction
Is distance/displacement vector or scalar and explain why
- Distance is a scalar quantity because it describes how far an object has travelled overall, but not the direction it has travelled in
- Displacement is a vector quantity because it describes how far an object is from where it started and in what direction
How can vectors be represented and how does this work
by an arrow:
The arrowhead indicates the direction of the vector
The length of the arrow represents the magnitude
What are the two methods used to add vectors
- Calculation – if the vectors are perpendicular
- Scale drawing – if the vectors are not perpendicular
Describe how vectors can be found using the triangle vs parallelogram method
- To combine vectors using the triangle method:
Step 1: link the vectors head-to-tail
Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector - To combine vectors using the parallelogram method:
Step 1: link the vectors tail-to-tail
Step 2: complete the resulting parallelogram
Step 3: the resultant vector is the diagonal of the parallelogram
Describe the forces acting on an inclined plane
When are forces in equilibrium
- At rest
- Moving at constant velocity
What are coplanar forces
Forces that act in the same plane
What is a moment
the turning effect of a force
When do moments occur
when forces cause objects to rotate about some pivot
What is the equation stating the moment of a force
Moment (N m) = Force (N) × perpendicular distance from the pivot (m)
What is the unit of a moment
N m
What is the principle of moments
For a system to be in equilibrium, the sum of clockwise moments about a point must be equal to the sum of the anticlockwise moments (about the same point)
What is a couple
a pair of equal and opposite coplanar forces that act to produce rotation only
What kind of forces does a couple contain
Forces that are:
- Equal in magnitude
- Opposite in direction
- Perpendicular to the distance between them
Does an object with a couple accelerate
No- Couples produce a resultant force of zero, so, due to Newton’s Second law (F = ma), the object does not accelerate
What kind of moment system does not require a pivot
a couple
What is the moment of a couple equal to
Force × Perpendicular distance between the lines of action of the forces
Centre of mass def
the point at which the weight of the object may be considered to act
Where is the position of the centre of mass for a uniform regular solid
at its centre
Where is the position of the centre of mass for symmetrical objects with uniform density
at the point of symmetry
When is an object stable
when its centre of mass lies above its base
How is the base width, centre of mass and stability linked?
- The wider base an object has, the lower its centre of mass and it is more stable
- The narrower base an object has, the higher its centre of mass and the object is more likely to topple over if pushed
What is instantaneous speed (or velocity)
the speed (or velocity) of an object at any given point in time
How to find instantaneous velocity on a displacement-time graph
Draw a tangent at the required time
Calculate the gradient of that tangent
How is acceleration shown on a displacement-time graph
by a curved gradient
How to find average speed on a displacement-time graph
divide the total displacement (on the y-axis) by the total time (on the x-axis)
What do the features of a displacement-time graph mean
- The gradient (or slope) equals velocity
- The y-intercept equals the initial displacement
- A diagonal straight line represents a constant velocity
- A positive slope represents motion in the positive direction
- A negative slope represents motion in the negative direction
- A curved line represents an acceleration
- A horizontal line (zero slope) represents a state of rest
- The area under the curve is meaningless
What do the features of a velocity-time graph mean
- Slope equals acceleration
- The y-intercept equals the initial velocity
- A straight line represents uniform acceleration
- A positive slope represents an increase in velocity (acceleration) in the positive direction
- A negative slope represents an increase in velocity (acceleration) in the negative direction
- A curved line represents the non-uniform acceleration
- A horizontal line (zero slope) represents motion with constant velocity
- The area under the curve equals the displacement or distance travelled
What do the components of an acceleration-time graph mean
- The slope is meaningless
- The y-intercept equals the initial acceleration
- A horizontal line (zero slope) represents an object undergoing constant acceleration
- The area under the curve equals the change in velocity
Draw a displacement-time graph for a ball bouncing up and down
Draw a velocity-time graph for a ball bouncing up and down
Draw an acceleration-time graph for a ball bouncing up and down
Describe the mechanical features of a bouncing ball at its highest point (displacement, velocity and acceleration)
- The ball is at its maximum displacement
- The ball momentarily has zero velocity
- The velocity changes from positive to negative as the ball changes direction
- The acceleration, g, is still constant and directed vertically downwards
Describe the mechanical features of a bouncing ball at its lowest point (displacement, velocity and acceleration)
- The ball is at its minimum displacement (on the ground)
- Its velocity changes instantaneously from negative to positive, but its speed (magnitude) remains the same
- The change in direction causes a momentary acceleration (since acceleration = change in velocity / time)
What are the components that make up the SUVAT equations
s = displacement (m)
u = initial velocity (m s-1)
v = final velocity (m s-1)
a = acceleration (m s-2)
t = time (s)
What are the components of the trajectory of an object undergoing projectile motion
a vertical component and a horizontal component
What is the range for projectile motion
the horizontal distance travelled by the projectile
How is the time of flight and maximum height calculated for an object in projectile motion
How is the range calculated for an object in projectile motion
What are drag forces
forces that oppose the motion of an object moving through a fluid (gas or liquid)
Examples of drag forces
friction and air resistance
What are the rules of drag forces
- Are always in the opposite direction to the motion of the object
- Never speed an object up or start them moving
- Slow down an object or keeps them moving at a constant speed
- Convert kinetic energy into heat and sound
- increases with the speed of the object
What is ‘lift’ and explain an example of it
- an upwards force on an object moving through a fluid. It is perpendicular to the fluid flow
- For example, as an aeroplane moves through the air, it pushes down on the air to change its direction
- This causes an equal and opposite reaction upwards on the wings (lift) due to Newton’s third law
In what direction is a lift force
in the opposite direction to the weight
What is air resistance
an example of a drag force that objects experience when moving through the air
What factors affect the maximum speed of an object
- Cross-sectional area
- Shape
- Altitude
- Temperature
- Humidity
Why is there less air resistance at higher altitudes
because air is less dense
Draw a height/distance graph for an object in projectile motion with and without air resistance
Describe how terminal velocity is achieved
- For a body in free fall, the only force acting is its weight and its acceleration g is only due to gravity.
- The drag force increases as the body accelerates
- This increase in velocity means the drag force also increases
- Due to Newton’s Second Law, this means the resultant force and therefore acceleration decreases (recall F = ma)
- When the drag force is equal to the gravitational pull on the body, the body will no longer accelerate and will fall at a constant velocity
- This is the maximum velocity that the object can have and is called the terminal velocity
Newton’s first law
A body will remain at rest or move with constant velocity unless acted on by a resultant force
Newton’s second law
The resultant force on an object is equal to its rate of change in momentum.
(The resultant force on an object with constant mass is directly proportional to its acceleration - F=ma)
What is a resultant force
the vector sum of all the forces acting on the body
Newton’s third law
If body A exerts a force on body B, then body B will exert a force on body A of equal magnitude but in the opposite direction
(the force pairs must be the same type)
What is, and what are the components of, the linear momentum equation
Unit of momentum
kg m s−1
Principle of conservation of momentum
The total momentum before a collision = the total momentum after a collision provided no external force acts
What is linear momentum
The momentum of an object that only moves in one dimension
External vs internal forces
- External forces = forces that act on a structure from outside e.g. friction and weight
- Internal forces = forces exchanged by the particles in the system e.g. tension in a string
- Forces which are internal or external will depend on the system itself
What are systems with no external forces called
‘closed’ or ‘isolated’
Force def
the rate of change of momentum on a body
What is the equation linking force, momentum and time
What is impulse equal to
The change In momentum
What do the components of the impulse equation mean
In what direction does the impulse work in, in regards to force
In the same direction as the force
Unit of impulse
N s
What does the impulse equation say about the relationship between force over time
A small force acting over a long time has the same effect as a large force acting over a short time
What does the area under a force-time graph equate to
Impulse
How are impact forces reduced
By increasing the contact time
Examples of where reducing impact force is important
- In sport
- In packaging
What are the two types of collision (or explosion)
Elastic and inelastic
Describe the difference between elastic and inelastic collisions
- Elastic – if the kinetic energy is conserved
- Inelastic – if the kinetic energy is not conserved
What do elastic/inelastic collisions commonly look like
Elastic collisions are commonly those where objects colliding do not stick together and then move in opposite directions
Inelastic collision are commonly those where objects collide and stick together after the collision
What is the difference between collisions and explosions
- collisions are usually to do with objects striking against each other
- explosions are usually to do with recoil
Describe the function of the safety features of cars
Vehicle safety features are designed to absorb energy upon an impact by changing shape
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
Draw the differences in a time/force graph for a car collision with and without a seatbelt
Work def
The amount of energy transferred when an external force causes an object to move over a certain distance
What do the components of the work done equation mean
When does an object gain/lose energy, in regards to the direction of the force
- Usually, if a force acts in the direction that an object is moving then the object will gain energy
- If the force acts in the opposite direction to the movement then the object will lose energy
What do the components of the work done (at an angle) equation mean
Power def
the rate of doing work or the rate of energy transfer
What do the components of the power equation mean
What does the power equation show
that the power is increased if:
- There is a greater energy transfer (work done)
- The energy is transferred (work is done) over a shorter period of time
What do the components of the power, f and v equation mean
What does the area under a force-displacement graph equal to
The work done
What is the magnitude of work done, in regards to force/ displacement
The work done is equivalent whether there is:
- A small force over a long displacement
- A large force over a small displacement
What is a variable force
A force on an object which is not always constant
Can these equations be used when the force is not constant?
No
How must work done be calculated, if the force is not constant
By the area under a force-displacement graph
Efficiency def
the ratio of the useful power output from a system to its total power input
What does it mean when a system has high/low efficiency
- If a system has high efficiency, this means most of the energy transferred is useful
- If a system has low efficiency, this means most of the energy transferred is wasted
Efficiency equation
Principle of conservation of energy
Energy cannot be created or destroyed, it can only be transferred from one form to another
What is kinetic, gravitational potential, elastic, chemical, nuclear and internal energy
What is energy dissipation
Ways in which energy is wasted
Density def
Mass per unit volume of an object
Units of density
Hooke’s law
The extension of the material is directly proportional to the applied force (load) up to the limit of proportionality
(Applies to both compressions and extensions)
What do the components of the hooke’s law equation mean
What is the spring constant a measure of
The stiffness of a material. The larger the spring constant, the stiffer the material
Draw the force-extension graph for a spring
What do the features of the force-extension graph for a spring mean
- The limit of proportionality: The point beyond which Hooke’s law is no longer true when stretching a material i.e. the extension is no longer proportional to the applied force
The point is identified on the graph where the line starts to curve (flattens out) - Elastic limit: The maximum amount a material can be stretched and still return to its original length (above which the material will no longer be elastic). This point is always after the limit of proportionality
- The gradient of this graph is equal to the spring constant k
What are forces called that stretch an object
Tensile forces - they lead to tensile stress and tensile strain
What do the components of the tensile stress equation mean
Unit of tensile stress
Pascals (Pa)
What do the components of the tensile strain equation mean
Draw a labelled diagram of the features of a stress-strain graph
Describe the key points of the features of a stress-strain graph
- Yield Stress: The force per unit area at which the material extends plastically for no / a small increase in stress
- The elastic strain energy stored per unit volume is the area under the Hooke’s Law (straight line) region of the graph
- Breaking point: The stress at this point is the breaking stress. This is the maximum stress a material can stand before it fractures
- Elastic region: The region of the graph up till the elastic limit. In this region, the material will return to its original shape when the applied force is removed
- Plastic region: The region of the graph after the elastic limit. In this region, the material has deformed permanently and will not return to its original shape when the applied force is removed
Explain what elastic strain energy is
- Work has to be done to stretch a material
- Before a material reaches its elastic limit (whilst it obeys Hooke’s Law), all the work is done is stored as elastic strain energy
What is the area under a force-extension graph equal to
Elastic strain energy (true for whether the material obeys Hooke’s law or not)
What do the components of the elastic strain energy equation mean
What is the equation for elastic strain energy that is not on the formula sheet
What is the breaking stress
the maximum stress a material can stand before it fractures (breaks)
What is a material called when it has a high breaking stress, what does this mean and give an example
- ductile, which means it can extend more before breaking because of plastic deformation
- A common example of this is copper, as well as being a good electrical conductor, copper is ductile so it is a suitable material for making wires
What is the ultimate tensile stress
the maximum stress that the material can withstand
Describe the two types of deformation that materials can undergo
- Elastic deformation:
When the load is removed, the object will return to its original shape
This is shown in the elastic region of the graph - Plastic deformation:
The material is permanently deformed
When the load is removed, the object will not return to its original shape or length
This is beyond the elastic limit and is shown in the plastic region of the graph
Draw a labelled force-load graph, showing the points of deformation
Describe what brittle/ductile materials are
- Brittle materials have very little to no plastic region e.g. glass, concrete
- The material breaks with little elastic and insignificant plastic deformation
- Ductile materials have a larger plastic region e.g. rubber, copper
- The material stretches into a new shape before breaking
Draw a stress-strain graph for a brittle/ductile material
Draw a force-extension graph for a material that has undergone plastic deformation
Draw a force-extension graph for loading and unloading a rubber band (elastic material)
Describe what the features of a force-extension graph for loading and unloading a rubber band
- The graph shows the rubber band stores a greater amount of strain energy when it is loaded (stretched) than when it is being unloaded (contracted)
- The curve for contraction is always below the curve for stretching
- However, due to the conservation of energy, the difference in strain energy when loading and unloading must be accounted for
- A rubber band becomes warm when it is stretched and contracted hence some energy is transferred to heat energy
Describe how shock absorbers in a car wheel work
- Impact energy is absorbed by shock absorbers
- These are elastic objects designed to absorb or dampen the compression and rebound of the springs above a vehicle’s tires
- They help keep the tires on the road at all times
- When a vehicle hits a bump in a road, the shock absorbers dampen the movement of the springs in the suspension system
- They do this by converting kinetic energy, from the movement of the car, into thermal energy which is dissipated
- The faster the springs in the suspension system move (say, if a vehicle hits a bump at a high velocity), the more resistance the shock absorber provides
What is the Young’s modulus a measure of
- Of the ability of a material to withstand changes in length with an added load
- This gives information about the stiffness of a material
What is the Young’s modulus
the ratio of a material’s tensile stress and tensile strain
Units of Young’s modulus
Pascals (Pa)
What is the gradient of a stress-strain graph (when it is linear) equal to
the Young’s modulus
What is the moment of a force equal to
