materials and mechanics Flashcards
vector calculation way 1
only if vectors are perpendicular
- add 2 vectors a and b
- link the vectors head to tail
- form the resultant vector from linking the tail of A to the head of B
- Calculate R using pythagorus’ theorum
vector calculation way 2
what to do if they’re not perpendicular
SCALE DRAWING
Describe an elastic deformation
Material returns to its ORIGINAL SHAPE and SIZE once the forces are removed
Explain an elastic deformation
1) when material is under a lot of TENSION, the ATOMS of material are PULLED APART from one another.
2) Atoms can MOVE small distances relative to their EQUILIBRIUM POSITIONS, without actually changing position in the material.
3) Once the LOAD is REMOVED, the atoms RETURN to their EQUILIBRIUM distance apart
When does elastic deformation happen
As long as the ELASTIC LIMIT of the object isn’t reached
Describe plastic deformation
The material is PERMANENTLY STRETCHED
Explain plastic deformation
1) some atoms in the material move position relative to one another
2) when the load is removed, the ATOMS DON’T RETURN to their original positions
3) An object stretched PAST ITS ELASTIC LIMIT shows plastic deformation
What happens to the energy when an object is stretched
It’s conserved.
If elastic: work done is stored in ELASTIC STRAIN ENERGY
If plastic: work done to SEPARATE ATOMS, and energy is NOT stored as elastic strain energy (but dissipated as heat)
What is a moment
The turning effect of a force
Formula for moment of a force
Moment (N m) = Force (N) × perpendicular distance from the pivot (m)
State 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)
Define the centre of mass
the point at which the weight of the object may be considered to act
Centre of gravity vs centre of mass in a uniform gravitational field
the centre of gravity is identical to the centre of mass
How does an object reach terminal velocity
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 the maximum velocity that the object can have and is called the terminal velocity
4.3.7 Required Practical: Determination of g
- Set up the apparatus by attaching the electromagnet to the top of a tall clamp stand. Do not switch on the current till everything is set up
- Place the glass tube directly underneath the electromagnet, leaving space for the ball-bearing. Make sure it faces directly downwards and not at an angle
- Attach both light gates around the glass tube at a starting distance of around 10 cm
- Measure this distance between the two light gates as the height, h with a metre ruler
- Place the cushion directly underneath the end of the glass tube to catch the ball-bearing when it falls through
- Switch the current on the electromagnet and place the ball-bearing directly underneath so it is attracted to it
- Turn the current to the electromagnet off. The ball should drop
- When the ball drops through the first light gate, the timer starts
- When the ball drops through the second light gate, the timer stops
- Read the time on the timer and record this as time, t
- Increase h (eg. by 5 cm) and repeat the experiment. At least 5 – 10 values for h should be used
- Repeat this method at least 3 times for each value of h and calculate an average t for each
4.3.7 Required Practical: Determination of g
Systematic errors
Residue magnetism after the electromagnet is switched off may cause t to be recorded as longer than it should be
4.3.7 Required Practical: Determination of g
Random errors
Large uncertainty in h from using a metre rule with a precision of 1 mm
Parallax error from reading h
The ball may not fall accurately down the centre of each light gate
Random errors are reduced through repeating the experiment for each value of h at least 3-5 times and finding an average time, t
What is the young modulus
the measure of the ability of a material to withstand changes in length with an added load
This gives information about the stiffness of a material
This is useful for engineers to make sure the materials they are using can withstand sufficient forces
Define the young modulus
ratio of tensile stress and tensile strain
F = force (N)
L = original length (m)
A = cross-sectional area (m2)
ΔL = extension (m)
The young modulus from stress-strain graphs
The Young Modulus is equal to the gradient of a stress-strain graph when it is linear (a straight line)
This is the region in which Hooke’s Law is obeyed
The area under the graph in this region is equal to the energy stored per unit volume of the material
Required Practical: The Young Modulus
- Measure the diameter of the wire with a micrometre screw gauge or digital callipers. Take at least 3 readings and find an average
- Set up the apparatus so the wire is taut. No masses should be on the mass hanger just yet
- 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 initial reading on the ruler of the reference point
- Add a 100 g mass onto the mass hanger
- Read and record the new reading of the tape marker from the meter ruler
- Repeat this method by adding a 100 g mass (at least 5 – 10 times) and record the new scale reading from the metre ruler
Required Practical: The Young Modulus
Aims
to measure the Young Modulus of a metal in the form of a wire
Required Practical: The Young Modulus
Variables
Independent variable = Force (or load) (N)
Dependent variable = Extension (m)
Control variables:
The original length of wire
The thickness of the wire
The metal used for the wire
State the principle of conservation of linear momentum
The total momentum before a collision = the total momentum after a collision provided no external force acts
- it is an object that only moves in one dimension
Define impulse
The change in momentum
I = FΔt = Δp = mv – mu
I = impulse (N s)
F = force (N)
t = time (s)
p = momentum (kg m s–1)
m = mass (kg)
v = final velocity (m s–1)
u = initial velocity (m s–1)
Impulse of a force-time graph
the impulse is equal to the area under the force-time graph
What are elastic collisions
where objects colliding do not stick together and then move in opposite directions
What are inélastic collisions
those where objects collide and stick together after the collision
Designing safety features - 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
Designing safety features - 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
Designing safety features - 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
Define work
The amount of energy transferred when an external force causes an object to move over a certain distance
Equation for work (if the force is parallel to the direction of the object’s displacement)
W = Fs
Describe energy transfers when a person moves a block
give the box kinetic energy to move
The kinetic energy is transferred to other forms of energy such as heat and sound
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
Formula for work if the direction of motion of an object is NOT parallel to the direction of the force
W = Fs cos θ
Define power
Power is the rate of doing work or the rate of energy transfer
Define efficiency
the ratio of the useful power output from a system to its total power input
State the principle of conservation of energy
Energy cannot be created or destroyed, it can only be transferred from one form to another
Define kinetic energy
Kinetic energy is the energy an object has due to its motion (or velocity)
Define gravitational potential energy
energy stored in a mass due to its position in a gravitational field
State hooke’s law
The extension of the material is directly proportional to the applied force (load) up to the limit of proportionality
Key features of hooke’s law graph
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
Define tensile stress
the force exerted per unit cross-sectional area of a material
Define tensile strain
extension per unit length
Define yield stress
The force per unit area at which the material extends plastically for no / a small increase in stress
Define breaking point
The stress at this point is the breaking stress. This is the maximum stress a material can stand before it fractures
Define 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
Define 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
How is all the work stored before a material reaches its elastic limit
Elastic strain energy
Whats the equation for elastic strain energy when a material DOES obey hooke’s law
E = elastic strain energy (or work done) (J)
F = average force (N)
ΔL = extension (m)
Define the breaking stress
maximum stress a material can stand before it fractures (breaks)
A material with high breaking stress is considered 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
Define ultimate tensile stress
maximum stress that the material can withstand
Describe brittle materials
have very little to no plastic region e.g. glass, concrete
The material breaks with little elastic and insignificant plastic deformation
Define ductile materials
have a larger plastic region e.g. rubber, copper
The material stretches into a new shape before breaking
