4: Mechanics & Materials Flashcards
(74 cards)
1
Q
Scalar Quantity
A
A quantity with only magnitude
2
Q
Vector Quantity
A
A quantity with magnitude and direction
3
Q
Vector Examples (4)
A
- Velocity
- Force / Weight
- Acceleration
- Displacement
4
Q
Scalar Examples (3)
A
- Speed
- Mass
- Distance
5
Q
Addition of Vectors
A
Combining two vectors by calculation (for right angles) or scale drawings (any angles)
6
Q
Resolution of Vectors
A
Splitting vectors into two component vectors at right angles to each other (e.g., forces along and perpendicular to an inclined plane)
7
Q
Moment
A
Force x perpendicular distance from the pivot to the line of action of the force
8
Q
DELETE
A
moment = F d
F is force in N
d is perpendicular distance from the pivot to the line of action of the force in m
9
Q
Couple
A
A pair of equal and opposite coplanar forces
10
Q
Principle of Moments
A
An object is at equilibrium if the total anticlockwise moment acting about any point / axis of the object is equal to the total clockwise moment acting about that point / axis
11
Q
Centre of Mass (2)
A
- The point, through which the line of action of a force causes no rotation
- Where the mass of the body can be considered to be concentrated
12
Q
The Centre of Mass is at the Centre of a _____
A
Uniform regular solid
13
Q
Displacement
A
The distance an object has travelled from its starting point in a given direction
14
Q
Speed
A
How fast an object is moving, regardless of direction
15
Q
Velocity
A
The rate of change of an object’s displacement (speed in a given direction)
16
Q
Acceleration
A
The rate of change of velocity
17
Q
Velocity Formula
A
v = Δs / Δt
v is velocity in ms⁻¹
Δs is change in displacement in m
Δt is change in time in s
18
Q
Acceleration Formula
A
a = Δv / Δt
a is acceleration in ms⁻²
Δv is change in velocity in ms⁻¹
Δt is change in time in s
19
Q
Area & Gradient of Velocity-Time Graph
A
Area: Change in displacement
Gradient: Acceleration
20
Q
Gradient of Displacement-Time Graph
A
Velocity
21
Q
Area of Acceleration-Time Graph
A
Change in velocity
22
Q
Constants in Equations for Uniform Acceleration (5)
A
- s is displacement in m
- u is initial velocity in m s⁻¹
- v is final velocity in m s⁻¹
- a is acceleration m s⁻²
- t is time in s
23
Q
Define g
A
Acceleration due to gravity
24
Q
Projectile Motion in Horizontal Direction
A
Projectile travels at constant velocity: there is no resultant force acting on it
25
Projectile Motion in Vertical Direction
There is a resultant force acting downwards on the projectile due to gravity. The projectile has an initial velocity so decelerates upwards until it reaches maximum displacement with velocity 0 (vertex of parabola). Then, it accelerates downwards
26
Friction
A frictional force that acts in the opposite direction to the motion of an object. It occurs between solid surfaces and converts kinetic energy to heat
27
Drag (3)
- A frictional force that acts in the opposite direction to the motion of an object through a fluid
- It depends on the viscosity of the fluid and the shape of the object
- The force increases with speed and converts kinetic energy to heat
28
Lift (3)
- An upward force on an object moving through a fluid
- It happens when the shape of an object causes the fluid flowing over it to change direction
- The force acts perpendicular to the direction in which the fluid is flowing
29
Terminal Speed (3)
- An object accelerates uniformly from rest using a constant driving force
- As speed increases, frictional forces increase, reducing the resultant force
- Eventually, all forces are balanced so the object travels at a maximum, constant velocity
30
Air Resistance Increases with ____
Speed
31
Effect of Air Resistance on Trajectory of a Projectile
Cause a deceleration in the horizontal direction. It increases the deceleration in the vertical direction when the projectile travels upwards but reduces the projectile's downward acceleration. Thus, it reduces the horizontal and vertical displacements of the projectile
32
Factors Affecting Maximum Speed of Vehicle (2)
- Increasing driving force increases maximum speed
- Increasing frictional forces reduces maximum speed
33
Newton's 1st Law of Motion
The velocity of an object will not change unless a resultant force acts on it
34
Newton's 2nd Law of Motion
The acceleration of an object is proportional to the resultant force acting on it
35
Newton's 3rd Law of Motion
If an object A exerts a force on object B, then object B exerts a force of equal magnitude but opposite direction on object A
36
Force Equation
F = m a = Δ(m v) / Δt
F is force in N
m is mass in kg
a is acceleration in ms⁻²
Δ(mv) is change in momentum in kg m s⁻¹
Δt is change in time in s
37
momentum = ____
mass x velocity
38
Principle of Linear Momentum
Assuming no external forces act, linear momentum is conserved (e.g., collisions & explosions)
39
Force is Rate of ____
Change of momentum
40
Impulse
Change in momentum
41
Area of Force-Time Graph
Impulse
42
Elastic Collision
Collisions where both momentum and kinetic energy are conserved
43
Inelastic Collision
Collisions where momentum is conserved but kinetic energy isn't
44
Work Equation
W = F s cos θ
W is work done in J
F is force in N
s is displacement in m
θ is angle at which the force acts from the direction of motion
45
Work Done is ____
Energy transferred
46
Rate of Doing Work = ____
Rate of energy transfer
47
Power Equation
P = ΔW / Δt = F v
P is power in W
ΔW is work done in J
Δt is change in time in s
F is force in N
v is velocity in m s⁻¹
48
Area under a Force-Displacement Graph
Work done
49
Efficiency Equation
efficiency = useful power output / input power
50
Principle of Conservation of Energy
The amount of energy in a closed system will not change
51
Gravitational Potential Energy Equation
ΔE_p = m g Δh
ΔE_p is change in gravitational potential energy in J
m is mass in kg
g is gravitational field strength in N kg⁻¹
Δh is change in height in m
52
Kinetic Energy Equation
E_k = ½ m v²
E_k is kinetic energy in J
m is mass in kg
v is velocity in m s⁻¹
53
Density
The mass per unit volume of a material
54
Density Equation
ρ = m / V
ρ is density in kg m⁻³
m is mass in kg
V is volume in m³
55
Hooke's Law
The extension of a stretched wire is proportional to the load or force
56
Hooke's Law Equation
F = k ΔL
F is force in N
k is stiffness and spring constant in N m⁻¹
ΔL is extension in m
57
Limit of Proportionality
The point, beyond which a material no longer obeys Hooke's law – where force is no longer proportional to extension
58
Elastic Limit
The point, after which the material is permanently stretched
59
Elastic Strain Energy
The potential energy stored in a material from the work done deforming the material elastically
60
Energy Stored Equation
E = ½ F ΔL
E is energy stored in J
F is force in N
ΔL is extension in m
61
Energy Stored =
Area under a force-extension graph
62
Tensile Stress
The force applied divided by the cross-sectional area
63
Tensile Strain
The change in length divided by the original length of the material
64
Tensile Stress Equation
tensile stress = F / A
tensile stress in Pa
F is force in N
A is area in m²
65
Tensile Strain Equation
tensile strain = ΔL / L
tensile strain is a ratio
ΔL is extension in m
L is original length in m
66
Breaking Stress
The tensile stress that breaks a material
67
Young Modulus Equation
Young modulus = tensile stress / tensile strain = F L / A ΔL
Young modulus in Pa
tensile stress in Pa
tensile strain is a ratio
F is force in N
L is original length in m
A is cross-sectional area in m²
ΔL is extension in m
68
Plastic Behaviour
Where a material is permanently stretched and doesn't return to its original shape (when the deforming force is removed). A metal stretched past its elastic limit deforms plastically
69
Brittle Behaviour
When a material obeys Hooke's law until it breaks – it doesn't deform plastically
70
Conservation of Energy in Vertical Springs (3)
- When a vertical spring suspending a mass is stretched, elastic strain energy is stored in the spring
- When the end is released, the elastic strain energy is transferred to kinetic energy (as the spring contracts) and gravitational potential energy (as the mass gains height)
- Then, the spring compresses and kinetic energy is transferred back to elastic strain energy and gravitational potential energy
71
Required Practical 3
Determination of g by a freefall method
72
Required Practical 3 Method (6)
https://docs.google.com/document/d/1hRsKv6saq_Kb4k5UDMCJaJ3lZKGEnrWiD0Gs-qRB3aQ/edit?usp=sharing
1. Measure the mass of the system
2. Place all the masses on top of the trolley
3. Incline the slope such that the trolley (and all of the masses, which you intend to use to accelerate it) is at rest on the slope and if given a small push, it travels at constant velocity
4. Whilst holding the trolley, attach a known mass from the top of the trolley to the hook
5. Release the trolley and record the acceleration shown by the light gate
6. Repeat steps 5 to 6, incrementing the accelerating masses
73
Required Practical 4
Determination of the Young modulus by a simple method
74
Required Practical 4 Method (7)
https://docs.google.com/document/d/1rbEfdTEdAUt8Vmx3ArXusU4Rd70gfD2SDuphuv_dsdw/edit?usp=sharing
1. Set up the apparatus as shown in the diagram
2. Measure the diameter and original length of the wire
3. Add a 10 g mass onto the hook
4. Measure the new length of the wire
5. Remove the mass the hook and ensure that the wire returns to its original length
6. If it doesn’t then stop the experiment and discard the last result
7. Otherwise, repeat steps 4 to 6, incrementing the mass on the hook
