4. 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 magnitude as well asdirection.
Is acceleration a vector or scalar quantity?
Vector
Is mass a scalar or vector 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.
W = mg
If an object is in equilibrium the sum of the anti clockwise moments would be …
Equal to the sum of the clockwise moments (principle of moments).
If an 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 a object be shown to be in equilibrium?
● Adding the horizontal and vertical components of the forces acting on it, showing they equal zero.
● Or if there are 3 forces acting on the object you can draw a scale diagram, if the scale diagram forms a closed triangle, then the object is in equilibrium.
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
If you have a uniform object, where would its centre of mass be?
At the centre of the solid
What can be described as ‘the change in displacement per unit of 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 and acceleration-time graph?
The displacement travelled and the velocity respectively
As speed increases, air resistance ….
Increases (proportional to the square of the speed)
A ball if projected off a castle at 6m/s, 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 that that all objects fall at the same rate?
Mass is not included in the SUVAT equations, showing that the mass of an object does not affect its speed or acceleration.
In projectile motion, what is the vertical acceleration?
The vertical acceleration is equal to gravitational field strength (g).
What is meant by terminal velocity?
When the forces acting on the falling object become balanced, the acceleration becomes zero and 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. Friction 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 the 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 an elastic collision the kinetic energy before is equal to the kinetic energy afterwards.
In an inelastic collision the kinetic energy at the end is not equal to the kinetic energy at the start.
Give an equation that can be used to calculate momentum.
momentum = mass × velocity
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.
F∆t = ∆mv
What does the area underneath a force time graph represent?
Impulse, the change in momentum
Fscos(𝜽) = ?
The work done / the energy transferred
What’s the rate of work done is equal to?
The power
What is efficiency?
Efficiency = The useful output power / input power
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 will always remain the same.
A river flowing to the right acts on a crossing boat with force 19N, the boat provides a perpendicular thrust of 45N, what is the resultant force on the boat?
Forces are perpendicular so use pythagoras’s theorem. Resultant force^2=19^2+45^2 Resultant force = 48.84669897 N Resultant force= 49N (2sf) Direction, tanθ= 45/19 θ= tan-1(45/19) θ=67° above the horizontal
A ball is fired at a velocity of 10 m/s, at
an angle of 30° from the horizontal, find
the vertical and horizontal components of
velocity.
x = 10 cos 30° = 8.7 m/s
y = 10 sin 30° = 5 m/s
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 and acts perpendicular to the direction of fluid flow.
What is Hooke’s law?
Extension (∆L) is directly proportional to force applied (F), given that the environmental conditions are kept constant.
F= k∆L k is the stiffness constant in Nm^-1
What equation is used to calculate density?
Density = Mass / Volume
Density units: kgm^-3
Mass: kg
Volume: m^3
What is meant by tensile stress?
The force applied per unit cross sectional area. Stress = force / CSA Stress units: Nm-2 Force units: N Cross sectional area units: m2
What is tensile strain?
A measure of how the material stretches: the extension (ΔL) divided by the original length (L), strain has no units.
Strain = ΔL / L
What is the difference between elastic and plastic deformation?
Elastic deformation: when the force is removed the object will return to its original shape.
Plastic deformation: 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
Which of these two graphs represents a brittle material? A Stress/Nm-2 | . . . .ヘ | . . ./ | . ./ | ./ |/\_\_\_\_\_\_\_ Strain
B Stress/Nm-2 | . . . . . . .ヘ | . . . . ./ . . . . \ | . . ./ . . . . . . . . \ | . / |/\_\_\_\_\_\_\_\_\_\_\_\_\_ Strain
A Stress/Nm-2 | . . . .ヘ | . . ./ | . ./ | ./ |/\_\_\_\_\_\_\_ Strain
What is meant when a material is described as brittle?
It doesn’t 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 (permanently stretched)
What does the area underneath a force - extension graph represent?
The work done to deform the material.
Work done= ½ x F x ΔL
State the equation to calculate elastic strain energy from the spring constant and extension.
E = ½ kΔL^2
What is Young’s modulus?
Young’s modulus (E) = tensile stress/ tensile strain.
E = FL / ΔLA
(by substituting stress and strain equations).
It describes the stiffness of a material.
How do you find the Young’s modulus from a stress-strain graph?
The gradient of the line
Which of these graphs would represent a wire which has plastically deformed? A Force/N | . . . . . . . \_\_---フ |. . . . . ̷ . . . ̷ | . . . / . . . ̷ | . . / . . ./ | . / . . ̷ |∠_ ̷\_\_\_\_\_\_\_\_\_ Extension/m
B Force/N | . . . . . . . \_\_---7 |. . . . . ̷ . . . . . / | . . ./ . . . . . . / | . ./ . . . . . . / | ./ . . . . . . / |/\_\_\_\_\_\_/\_\_\_\_\_ Extension/m
B Force/N | . . . . . . . \_\_---7 |. . . . . ̷ . . . . . / | . . ./ . . . . . . / | . ./ . . . . . . / | ./ . . . . . . / |/\_\_\_\_\_\_/\_\_\_\_\_ Extension/m
The unloading line doesn’t go through the origin as the material is permanently extended (stretched)
How can a force-extension graph show Hooke’s Law is being obeyed?
When it is a straight line through the origin ie. 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, it is shown by the line beginning to curve on a force-extension graph.
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) hasn’t changed, the forces between the atoms are the same when loading and unloading.
Why isn’t 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 of energy in plastic deformation used to design safer vehicles?
● Crumple zones deform plastically in a crash using the car’s kinetic energy so less is transferred to the 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 it) is stored as elastic strain energy, when the spring is released this is converted to kinetic energy which is converted to gravitational potential energy as the spring rises
Do stress-strain graphs show the behaviour of a material or a specific object?
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.
What would the stress-strain graph for a ductile material look like?
A ductile material can undergo a large amount of plastic deformation before fracturing.
Stress/ Pa | . Brittle . . ._ -- _ Ductile | .. ̸ . . . . ̷ \ ̷ | . ̸ . . / |. ̸ . / . . . . . \_\_----- Plastic | ̸ / \_\_---- |̸\_\_\_\_\_\_\_\_\_\_\_\_\_ Strain
