Module 2 Flashcards
Definition of density?
mass per unit volume
Units of density?
kg m^-3
Hookes Law?
Extension is proportional to the force applied, up to the limit of proportionality
What are the features of graph force against extension confirming Hooke’s Law?
There is a straight line through the origin of the graph.
Units of spring constant?
Nm^-1
Rules of springs in series
- Both springs experience the dame Force (F)
- The total extension (of both springs together) is the sum of the extension of each spring individually.
Rules of (identical) springs in parallel
- The Force (F) applied to the spring combination is shared across each of the springs individually (if there are two identical springs, each spring experiences a force of 1/2F).
- All the springs have the same extension (and equals the extension for the spring combination.
Definition of Elastic Limit?
The maximum amount a material can be stretched by a force and still return to its original length when the force is removed.
Definition of Limit of Proportionality
Point beyond which force is no longer proportional to extension
Definition of elastic behaviour?
Material will return to its original length (when force removed) with no permanent extension.
Definition of plastic behaviour?
Material will be permanently extended (when force is removed)
What does area under a force/extension graph show you?
- Area under a graph of force against extension is work done on spring and hence the energy stored, as it is loaded.
OR - Area under a graph of force against extension is the work done by the spring, and hence energy released, as it is unloaded.
What does the area between the loading and unloading curves of an elastic band?
Internal energy retained, e.g. as heat, within the elastic band.
Explain the derivation of energy stored = ½ FL?
- Energy stored in a stretched spring = work done stretching spring
- Work done = Force x distance (moved in the direction of the force)
- As spring is stretched, the force gets bigger (and so isn’t constant)
- Force is proportional to extension, so, the average force = F/2 which = 1/2F
- The work done = average force x distance moved
- energy stored = work done = ½ FL
- This is the area under the graph of Force against Extension (1/2base x height)
Explain the Derivation of energy stored = ½ FL from a graph of force against extesion
- W=Fs, so the area beneath the line from origin to L represents the work done to compress/extended spring.
- Work done (on spring) equals the energy it stores.
- Area under graph = area of triangle = 1/2base x height, therefore energy stored = ½ F x L.
What is the definition of tensile stress?
Tensile (stretching) force divided by its cross-sectional area
What are the units of stress?
Pa or Nm^-2
What is the definition of tensile strain?
It’s the extension of material divided by its original length
What are the units of strain?
None
What is the definition of breaking stress?
Stress needed to break a solid material.
What is the description of stiffness?
Requires a large force (or stress) for a small deformation (or extension)
What is the description of fracture?
- Non-brittle fracture: Material necks which reduces the cross-sectional area so increases stress at that point until the wire breaks.
- Brittle fracture
No plastic deformation, usually snaps suddenly without any noticeable yield.
What is the description of brittle?
A material that fractures without any plastic deformation.
What is the description of ductile?
When a material can be draw into a wire (exhibits a lot of plastic deformation)
Description of strength (or weakness)?
Material with a higher (or lower) breaking stress.
What is the definition of the Young Modulus?
It’s the ratio of tensile stress to tensile strain.
What is the unit of the Young Modulus?
Pa or Nm^-2
What is the use of stress/strain curves to find young modulus?
From a graph of stress against strain, Young Modulus is the gradient of the linear section of the graph (the region where the stress and strain are directly proportional).
What does the area under the graph of stress against strain show?
The energy stored per unit volume.
Explain one simple method of measuring Young Modulus
- Measurements to make
+ Original length of wire,L, with a ruler
+ Diameter of wire with a micrometer
+ Mass attached to end of wire
+ Length of stretched wire with a ruler - Reducing Uncertainty in each measurement
+ Repeat measurements of length
+ Repeat measurements of diameter of wire at different points
+ Check for zero error on electronic scales
+ Check for zero error on micrometer - How measurements are used to determine Young Modulus
+ F=weight=mg
+ Extension L = stretched length - original length
+ Cross sectional area of wire A = d2 / 4
+ Stress = F/A; Strain = L/L
+ Plot a graph of stress (y-axis) against strain (x-axis)
+ Young Modulus is gradient of linear section of the graph
What is the difference between a scalar and a vector?
Vector has magnitude and direction, whereas scalar only has magnitude.
What are some examples of scalar quantities?
- Speed
- Mass
- Time
- Energy
- Power
What are some examples of vector quantities?
- Displacement
- Velocity
- Acceleration
- Force
- Weight
How do you add perpendicular vectors by calculation?
- You draw the vectors a a right angled triangle.
- Then use the pythagoras theorem to find the magnitude of resultant vector
- Use trigonometry to calculate the angle of resultant vector.
How to add vectors by scale drawing?
- Write down scale eg 1cm=2N
- Draw the vectors to correct length and angle to each other “tip to tail”
- The add the resultant vector line
- Measure the length and angle of resultant vector
- Convert length into appropriate quantity to find magnitude of resultant vector.
`What are the conditions for equilibrium of two or three coplanar forces acting at a point?
- Total resultant equals zero
OR - If the vectors representing the forces are added together they will form a closed triangle.
What are the two conditions for a body to remain in equilibrium?
- Resultant force acting on body is zero
2. Resultant moment about any point is zero.
What is the definition of a moment?
Force multiplied by the perpendicular distance between the line of action of the force and the pivot.