Mechanics and Materials Flashcards
What is meant by a scalar quantity?
A quantity that has only magnitude
What is a vector quantity?
A quantity that has both magnitude and direction, and obeys the vector law of addition
Is acceleration a vector or scalar quantity?
Vector
Is mass a vector or scalar quantity?
Scalar
What is the difference between mass and weight?
Mass is scalar and is not dependent on the gravity acting upon it. Weight is a vector and depends on the gravitational field strength
If an object is in equilibrium, the sum of the anti-clockwise moments would be …
Equal to the sum of the clockwise moments (the principle of moments)
If the object is in equilibrium it means the object is …
Not accelerating, so is either stationary or moving at a constant velocity
How can the forces acting on an object to be shown to be in equilibrium?
- Adding the horizontal and vertical components of the forces acting, showing they equal 0
- When drawn in a scale drawing, they should form a closed shape, eg. a triangle
What is a moment?
A turning force: force multiplied by the perpendicular distance from the point to the line of action of the force
What is meant by a couple?
A pair of equal and opposite coplanar forces
What is meant by the centre of mass?
The point through which all the mass of an object acts, for a uniform object the centre of mass is the centre of the object
What can be described as ‘the change in displacement per unit time’?
Velocity - instantaneous velocity can be found by measuring the gradient of a tangent to a displacement-time graph
What is the area under a velocity-time graph?
The displacement travelled
What is the area under an acceleration-time graph?
The velocity
As speed increases, air resistance …
Increases proportionally to the square of the speed
If a ball is projected off a castle at 6ms^-1, how does its horizontal velocity change from its launch until it hits the ground?
The horizontal velocity remains the same as there is no acceleration in that direction
How do the SUVAT equations reflect all objects fall at the same rate?
Mass is not included in the SUVAT equations, showing that the mass of the objects does not affect its speed or acceleration
In projectile motion, what is the vertical acceleration?
The vertical acceleration is equal to the gravitational field strength, g, which is 9.81ms^-2 on Earth
What is meant by terminal velocity?
When the forces acting on the falling object becomes balanced, the acceleration becomes zero as the object is moving at maximum velocity
What is meant by friction?
A resistance to motion between an object and a surface or an object moving through a fluid. It is a force that acts in the opposite direction to the movement
Which of Newton’s laws state ‘every action force has an equal and opposite reaction force’?
Newton’s third law
What is Newton’s second law?
F = ma
Where mass, m, is constant, F is the force applied and a is acceleration
What is Newton’s first law?
An object stays moving at a constant velocity until a force acts upon it
What is the difference between elastic and inelastic collisions?
In elastic collisions the kinetic energy before the collision equals the kinetic energy after the collision.
In inelastic collisions the kinetic energy after the collision is not equal to the kinetic energy before the collision.
Give an equation that can be used to calculate momentum.
Momentum = mass x velocity
Momentum, p: kgms^1
Mass, m: kg
Velocity, v: ms^-1
True or false: ‘Linear momentum is only conserved in elastic collisions’
False - linear momentum is always conserved
The rate of change of momentum can also be described as …
Force
What is impulse?
The change in momentum
What does the area under a force-time graph represent?
Impulse, the change in momentum
Fs cos(theta) = ?
Fs cos(theta) = work done/energy transferred
What is the rate of work done equal to?
The power
What is efficiency?
Efficiency = (useful output power/total input power) x 100
What is meant by the principle of conservation of energy?
Energy cannot be created or destroyed, only transferred into other forms of energy. Therefore the total energy in a closed system remains the same
A river flowing to the right acts on a crossing boat with force of 19N, the boat provides perpendicular thrust of 45N, what is the resultant force of the boat?
F^2 = 19^2 + 45^2 F = 48.846... = 49N
Direction: tan(theta) = 45/19 (theta) = tan^-1(45/19)
(theta) = 67º above the horizontal
A ball is fired at a velocity of 10ms^-1, at an angle of 30º from the horizontal, find the vertical and horizontal components of velocity.
x axis = 10 cos 30 = 8.7ms^-1
y axis = 10 sin 30 = 5ms^-1
What is lift?
An upward force which acts on objects travelling in a fluid, it is caused by the object creating a change in direction of fluid flow, acts perpendicular to fluid flow
What is Hooke’s law?
Extension is directly proportional to the force applied, given environmental conditions are kept constant.
F = k x (change in) L
k: stiffness constant, Nm^-1
What equation is used to calculate density?
Density = mass/volume
Density, p (rho): kgm^-3
Mass, m: kg
Volume, v: m^3
What is meant by tensile stress?
The force applied per unit cross-sectional area Stress = Force/Area Stress, (sigma, like an a shape): Nm^-2 Force, F: N Area, A: m^2
What is tensile strain?
A measure of how the material stretches: extension divided by original length
Strain = (change in) L / L
Had no units
What is the difference between elastic and plastic deformation?
Elastic: when the force is removed, the object will return to its original shape
Plastic: after the load is removed, the object will not return to its original shape
What is breaking stress?
The minimum stress needed to break a material
On a stress-strain graph, what line would show a brittle material?
A steep line with little to no plastic deformation (curve)
On a stress-strain graph, what line would show a ductile material?
A shallower line with lots of plastic deformation (lots of curvature)
What is meant when a material is described as brittle?
It does not deform plastically but breaks when the stress reaches a certain value
What is the elastic limit?
The force above which the material will be plastically deformed
What does the area under a force-extension graph represent?
The work done to deform the material
Work done = 1/2 x F x (change in) L
State the equation to calculate elastic strain energy from the spring constant and extension.
E = 1/2 x k x (change in) L
What is the Young modulus?
It describes the stiffness of a material E = (F x L) / ((change in)L x A) E: Young modulus F: Force, N L: original length, m (change in)L, m A: area, m^2
How do you find the Young modulus on a stress-strain graph?
The gradient of the line - only the straight portion
How could you tell from a stress-strain graph that a wire has plastically deformed?
The unloading line does not go through the origin, as the wire has deformed permanently
How can a force-extension graph show Hooke’s law is being obeyed?
When the graph has a straight line through the origin i.e. force and extension are directly proportional
What is the limit of proportionality and what does it look like on a force-extension graph?
The point after which Hooke’s law is no longer obeyed and the material plastically deforms and is shown by the line beginning to curve
How is the work done to stretch or compress a material stored?
Elastic strain energy
Why are the loading and unloading lines parallel on a force-extension graph for a plastically deformed material?
The stiffness constant, k, has not changes, the force between the atoms are the same when loading and unloading
Why is not all work done stored as elastic strain energy when a stretch is plastic?
Work is done to move atoms apart, so energy is not stored as elastic strain energy but is dissipated as heat
How is the dissipation in plastic deformation used to design safe vehicles?
- Crumple zones deform plastically using the car’s kinetic energy so less is transferred to passengers
- Seat belts stretch to convert the passenger’s kinetic energy into elastic strain energy
Outline the energy changes that occur when a spring fixed at the top is pulled down and released.
The work done in pulling the spring down (stretching) is stored as elastic strain energy, when released, this is converted to kinetic energy, then converted to GPE as the spring rises
Do stress-strain graphs show the behaviour of a material or a specific object?
They show the behaviour of a material
Where would you find the ultimate tensile stress on a stress-strain graph?
The highest point on a graph, it is the maximum stress a material can withstand
How does temperature change impact linear expansion?
(change in L / original L) = expansion coefficient x change in temp
What is an experimental expansion coefficient?
it measures the fractional change in size per degree change in temperature at a constant pressure
Why are there gaps between railway tracks when they are constructed?
To allow for expansion of the tracks in warm weather, otherwise the metal may buckle
What is the yield point on a stress-strain graph?
The point on the curve at which random and erratic movement occurs between planes of atoms in the material and marks the onset of plastic flow
Define what fracturing is.
A breaking of a solid mass by the growth of a small crack
What is engineering stress?
The applied load divided by the original cross-sectional area
What is the SI units for stress?
Vodka shots, wait, no, K g m^-1 s^-2
What is the SI units for strain?
There are no units
What is the area under a stress-strain curve equal to?
The work done per unit volume
What happens to the energy stored in a material when it fractures?
The stored energy is transferred to kinetic energy, so the metal recoils significantly
Why are car tyres warm after driving?
The rubber deforms due to the mass of the car, repeatedly loading and unloading and retaining energy which is stored as thermal energy
Which would be safer for slowing a vehicle: an escape lane containing gravel or an escape ramp?
Escape lane with gravel - constant gradient means deceleration would be uniform, gravel causes more deceleration
