Mechanics And Materials Flashcards
What is a scalar quantity?
Magnitude but no direction
Name some scalars
Distance, speed, mass, temperature
Name some vectors
Displacement, Velocity, force/weight, acceleration
How do you find the resultant force of 2 perpendicular vectors?
Pythagoras or trig
What is a vector quantity?
Has magnitude and direction
How would you calculate the component of the wave acting perpendicular to the slope?
W=Wsin x
How would you calculate the component of the weight acting perpendicular to the slope?
W=Wcos x
How are F and g related?
F=mg
What is a moment?
The force x perpendicular distance from the pivot
Define the centre of mass
The point where the resultant moment due to the pull of gravity is 0
What is a couple?
A pair of forces that provide turning effect but there is no translational movement. Act parallel in opposite directions e.g twisting a lid of a bottle
How do you find the moment of a couple?
Force x Perpendicular distance between the lines of action of forces
How can you find velocity from a displacement time graph?
The gradient
How do you get acceleration from a velocity time graph?
The gradient
How do you get displacement from a velocity time graph?
The area underneath
What is drag?
The resistive forces experienced by an object moving through a fluid such as air of water
What is terminal speed?
The speed reached when the weight of an object in free fall is balanced by drag forces acting upwards on the object
What does the size of the drag on a falling object increase with?
Speed
Surface area
State Newton’s first law
When the resultant force on an object is 0 it has constant velocity
State Newton’s second law
The force equals the mass of the object x the acceleration
State Newton’s third law
2 objects in contact will exert equal and opposite forces on eachother
What are the conditions for Newton’s third law?
They act on separate bodies
The same type of force
Same magnitude
They act along the same line
They act in opposite directions
What is the relation between work done and GPE?
Work done=GPE
What is the relation between work done and kinetic energy?
Work done=Kinetic energy
What is the area underneath a force disaplcement graph?
The work done
What is the law of conservation of energy?
Energy cannot be created or destroyed, only transferred
How are power and work done related?
Work done= power x time
How are power and force related?
Power= Force x velocity
What is the law of conservation of momentum?
Momentum before= momentum after providing there are no external forces
What is momentum?
The product of mass and velocity
What is impulse?
The product of force and time
How do you calculate the change in momentum?
The area under a force time graph
In collisions and explosions, what is conserved and what is not conserved?
Total energy and momentum are conserved
Kinetic energy is not conserved
Define an elastic collision
Kinetic energy is conserved
Define an inelastic collision
Kinetic energy is not conserved
Define density
Mass per unit volume
What is a compressive force?
Forces that squeeze objects and reduce their size in the direction the force is applied
What is a tensile force?
Forces that act to stretch or pull an object
What is the spring constant?
A measure of how hard it is to bend or stretch a spring
What are the units of spring constant?
Nm>-1
What is the limit of proportionality?
The end point of the linear section of a force-extension graph
When Hooke’s law is no longer obeyed
What is the elastic limit?
The load above which the material is permanently deformed
What is elastic deformation?
When it returns to its original shape when the force is removed
What is plastic deformation?
When the material doesn’t return to its original shape once the force has been removed
What makes a material ductile?
It can be formed into wires by stretching them
What makes a material brittle?
One that show little or no plastic deformation before breaking
What is elastic strain energy?
The energy stored in stretched materials
What is Young’s modulus?
The measure of stiffness of an elastic material
What is the unit of Young’s modulus?
Pascals or N/m2
How can you calculate the energy stored in an object from a stress strain graph?
The area underneath
Define angular velocity?
The angle an object moves through per unit time
What is the unit of angular velocity?
radians per second
What letter represents angular velocity?
ω
When does circular motion occur?
When the resultant force acts towards the centre
What is centripetal acceleration?
When a particle moves in a circular path of radius r at a constant speed, there is constant acceleration towards the centre of the circle
Define centripetal force
When an object moves in a circular path, there must be a centripetal force acting towards the centre of the circle
What is simple harmonic motion?
A repetitive motion about an equilibrium position e.g a pendulum
When does an object experience simple harmonic motion?
When its acceleration is directly proportional to the displacement and in the opposite direction
Over what angle is it no longer Simple harmonic motion?
10°
In a swinging pendulum, when is kinetic energy a maximum?
At the equilibrium position
In a swinging pendulum, when is kinetic energy a minimum?
At the Maximum displacement as velocity is 0
In a swinging pendulum, when is potential energy a maximum?
At maximum displacement as all kinetic energy has been transferred to potential energy
In a swinging pendulum, when is potential energy a minimum?
At the equilibrium position
In terms of energy, what remains constant and what remains the same in a pendulum?
Total energy remains constant
Potential and kinetic energy change
what is damping?
When friction or wind resistance takes energy out of the oscillation
What is natural frequency?
The frequency it vibrates naturally when it is disturbed
What is resonant frequency?
The same s it’s natural frequency
Define resonance
When the driving frequency= natural frequency, the oscillator undergoes high amplitude oscillations
What effects does damping have on a resonance curve?
The peak is lower
The peak is broader
Peak occurs at a frequency lower than the natural frequency
What means that an object is in equilibrium?
The sum of all the forces acting on the object is 0
Describe the motion of an object in equilibrium?
Because it has no resultant force it is either at rest or moving with a constant velocity according to newtons first law
Describe 2 methods to show that the an object is in equilibrium
- Add the horizontal and vertical components of the force acting on it showing they equal 0
- In a scale diagram, if the forces form a closed triangle
What is the principle of moments?
For an object in equilibrium the sum of clockwise moments = the sum of anti clockwise moments
How is a uniform object indentified?
Its centre of mass it at its physical centre
How can average velocity be found?
Dividing final displacement by time taken
Define free fall?
Where an object experiences an acceleration of g
What is friction?
A force which opposes the motion of an object and it is also known as drag or air resistance when considering friction experienced in a fluid
How do frictional forces cause resistance?
Because they convert kinetic energy into other forms of energy e.g. heat and sound
What happens to the magnitude of air resistance as the speed of object increases?
It increases
What is lift?
An upwards force which acts on objects travelling in a fluid and is caused by the object creating a change in direction of fluid flow and it acts perpendicular to the direction of fluid flow
What is impulse?
The change of momentum
What is the work done?
The force causing a motion multiplied by the distance travelled in the direction of the force
What is efficiency?
A measure of how efficiently a system transfers energy
What is Hooke’s law?
extension is directly proportional to the force applied given environmental conditions are kept constant
What is tensile stress?
Force applied per unit cross sectional area
What is tensile strain?
Caused by tensile stress and is defined as extension over original length
What does the area under a force-extension graph represent?
The elastic strain
What is breaking stress?
The value of stress at which the material will break.
This does depend on conditions of the material e.g. temp
Describe a loading unloading curve for an object that is stretched above its elastic limit
It will not return to the origin but rather the loading and unloading curves will be parallel as the stiffness of the material is constant
What does the area under a loading unloading curve represent?
The work done to permanently deform the material
What do stress-strain graphs represent?
the behaviour of a material
What is the ultimate tensile stress of an object?
the highest point on the graph as it shows the maximum stress the material can withstand
How do you find the youngs modulus from a stress strain graph?
The gradient
Describe the velocity of an object moving in circular motion
Constantly changing
What does the displacement-time graph for an object in SHM look like?
A sine or cosine curve with maximum of A and minimum of -A
How do you get Acceleration from a displacement-time graph?
The gradient of the second derivative
Describe the energy transfers in kinetic energy
Kinetic energy is transferred to potential energy and back as the system oscillates.
What is light damping/ under-damping?
When the amplitude gradually decreases by a small amount each oscillation
What is critical damping?
It reduces the amplitude to 0 in the shortest possible time without oscillating
What is heavy damping7over-damping?
Where the amplitude reduces slower than with critical damping but also without any additional oscillations
When do free vibrations occur?
When no external force is continuously acting on the system therefore the system will oscillate at its natural frequency
What are forced vibrations?
Where the system experiences an external driving force which causes it to oscillate
What is the frequency of the driving force?
The driving frequency
What happens when the driving frequency equals the natural frequency?
resonance occurs
Name some things that have resonance
Instruments e.g. Flute- air resonates and a stationary wave is formed
radio- Their electric current resonates at the same frequency as the desired broadcast
What effect does Damping have on resonance?
It decreases the effect of damping
