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
