Mechanics and Materials Flashcards
(99 cards)
1
Q
What is a scalar quantity?
A
A quantity that is fully defined by a magnitude or size .
e.g. speed, distance, time, work done etc.
2
Q
What is a vector quantity?
A
A quantity that is fully defined by a magnitude and a direction.
e.g. velocity, displacement, weight, etc.
3
Q
Seven forces?
A
- Pushes and pulls
- Weight
- Friction
- Drag
- Upthrust
- Contact force
- Tension
4
Q
Pushes and pulls?
A
- An object accelerates when you push or pull on it.
- The engine of a car provides a force to push backwards on the road.
- Frictional forces from the road on the tyre push the car forwards.
5
Q
Weight?
A
-Force of gravity acting on an object.
6
Q
Friction?
A
- Force that arises when two surfaces rub against each other.
- If an object is sliding along the ground, friction acts in the opposite direction to its motion.
- If an object is stationary, but tending to slide i.e. on a slope, the force of friction acts up the slope to stop it from sliding down.
- Always acts along a surface, never at an angle to it.
7
Q
Drag?
A
- When an object moves through the air, friction is present between it and the air.
- The object has to push aside the air as it moves along.
- These effects combine to produce drag.
- When an object moves through a liquid, it experiences a drag force.
- Drag acts to oppose the motion of an object; it acts in the opposite direction to the object’s velocity.
- Can be reduced by giving an object a streamlined shape.
8
Q
Upthrust?
A
- An object placed in a fluid such as water or air experiences an upwards force - this makes floating possible.
- It arises from the pressure which a fluid exerts on an object.
- The deeper you go, the greater the pressure. Thus, there is more pressure on the lower surface of an object, pushing it upwards.
- If upthrust>weight, the object will float.
9
Q
Contact force?
A
- A force always pushes against your weight and supports you so you don’t fall.
- It is also known as the “normal reaction” of a surface - as in perpendicular.
- The contact force always acts at right angles to the surface which produces it.
10
Q
Tension?
A
- Force in a rope or string when it is stretched.
- If you pull on a rope, it tend to stretch.
- The tension in the rope pulls back against you, trying to shorten the rope.
- Tension also acts in springs.
- If you stretch a spring, the tension pulls back to try and shorten the spring.
- If you compress a spring, the tension acts to expand the spring.
11
Q
What is equilibrium?
A
- When an object is in equilibrium, the resultant force acting on it is zero
- The vector diagram always closes the loop. Thus, the final point is always the same as the initial point.
12
Q
How does length of rope affect tension?
A
The weight on the rope remains constant. If the rope is made shorter, the vertical side of the vector triangle will remain the same. The other two sides will be longer as the angles will be greater.
Thus, the tension will be increased.
13
Q
What is a moment?
A
-The turning effect of a force.
moment (Nm) = force (N) x perpendicular distance from force to pivot (m)
14
Q
Triangle of forces?
A
If three forces are acting on a point object that is in equilibrium, they can be represented in magnitude and direction by the sides of a triangle taken in order.
15
Q
Principle of moments?
A
For any object that is in equilibrium, the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about that same point.
16
Q
What is a couple?
A
- Formed when two forces that are equal in size and opposite in direction are acting not along the same straight line.
- Every couple has a moment.
- The torque (turning effect) due to a couple is equal to the magnitude of one of the forces multiplied by the perpendicular distance between them.
- Torque: M=Fd
17
Q
What is the centre of mass?
A
The point on an object where the entire mass is thought to be concentrated.
18
Q
COM (Symmetrical Objects) ?
A
- Always lies along line of symmetry.
- When there’s more than one line of symmetry, COM is where they intersect.
19
Q
COM (Non-Symmetrical Objects) ?
A
-When an object swings freely, when it stops, the COM is always on a vertical line passing through the pivot (which is drawn using a plumb line).
20
Q
What is the centre of gravity?
A
The point at which we consider an object’s entire weight to act.
21
Q
Conditions for equilibrium?
A
For an object to be in equilibrium:
-There’s no net (resultant) force.
-There’s no turning effect (moment) about any point.
THUS, resultant force = 0 and resultant torque = 0.
22
Q
Are couples in equilibrium?
A
NO.
Although resultant force = 0, resultant moment (Fd) ≠ 0.
23
Q
What is speed?
A
average speed = distance/time
The speed of an object tells the distance moved per second. It is scalar.
24
Q
What is velocity?
A
average velocity = displacement/time
Velocity measures rate of change of displacement. It is vector.
25
What is acceleration?
acceleration = change in velocity/time taken
The change in velocity may be a change in speed or direction or both.
If an object is slowing down, its change in velocity is negative. This gives a negative acceleration (deceleration).
26
s-t?
gradient = velocity
27
v-t?
```
gradient = acceleration
area = displacement
```
28
a-t?
```
gradient = rate of change of acceleration
area = velocity
```
29
Equations of motion?
- A set of equations describing motion.
| - Can only be used if acceleration, a, is constant.
30
SUVAT?
```
s - displacement (m)
u - initial velocity (ms^-1)
v - final velocity (ms^-1)
a - acceleration (ms^-2)
t - time (s)
```
31
5 equations?
```
v = u + at
s = vt - 0.5at^2
s = ut +0.5at^2
s = 0.5(u+v)t
v^2 = u^2 + 2as
```
32
What is the acceleration due to gravity?
9.81ms^-2
33
What is a projectile?
An object that it projected or thrown through the air at an angle.
For example, a ball thrown at velocity, v, at an angle, θ, to the ground.
34
What happens to the initial velocity?
It can be resolved into two components:
initial horizontal velocity = vcosθ
initial vertical velocity = vsinθ or vcos(90-θ)
35
What forces act on a projectile?
Ignoring air resistance, the only force acting is gravity.
36
What is the motion of a projectile?
Horizontal: Constant velocity thus a=0ms^-2.
Vertical: Constant acceleration thus a=9.81ms^-2.
-The horizontal and vertical components of an object's motion are independent and can be treated separately in calculations.
37
When calculating time it takes for projectile to reach ground?
```
Use vertical component.
s=ut+0.5at^2
s=vertical distance
u=0
a=9.81
```
38
When calculating the horizontal distance traveled by projectile?
```
Use horizontal component.
s=ut(+0.5at^2) but a=0
u=velocity given in question
v=velocity given in question
t=previously calculated
```
39
When calculating projectile's velocity when it hits the ground?
```
Use vertical component.
v^2=u^2+2as
v=u+at
Then use Pythagoras - a^2+b^2=c^2
thus v=√v(vertical) + v(horizontal)
```
40
Does mass affect g?
```
No.
W=ma
mg=ma
g=a
g=9.81N/kg
g=9.81ms^-2
```
41
If projectile starts and ends on ground?
s(vertical) = 0
a=-9.81
s(max)=v=0 and t=0.5t - v^2=u^2+2as
42
If u(general) isn't given?
Calculate using s=d/t.
43
If projectile starts above ground?
```
Horizontal:
u=xcosθ
v=xsinθ
a=0
Vertical:
s=-vertical height
u=xsinθ
a=-9.81
NB: FOR MAX HEIGHT ADD TO S
```
44
To calculate max height and time when reached?
s(max)=v=0 and a=-9.81 - v^2=u^2+2as
| t=0.5t
45
Resultant force?
A single force that has the same effect as all the forces combined.
46
Newton's first law?
An object will remain at rest or continue to move with a constant velocity as long as the forces acting on it are balanced.
In terms of momentum:
Any object's momentum is constant unless their is a resultant unbalanced force acting on it.
47
Inertia?
- Newton's first law tells us that any object has a built-in resistance to any change in their motion.
- This reluctance to change velocity is inertia.
- The inertia of an object depends on its mass.
- A bigger mass needs a bigger force to overcome its inertia and change its motion.
e. g inertia when travelling in a car
48
Momentum?
momentum/kgms^-1 or Ns = mass/kg x velocity/ms^-1
p=mv
The greater an object's momentum, the greater the force required to change its velocity.
Objects can have no momentum (VECTOR) when stationary, but still have inertia (SCALAR).
49
Newton's second law?
The rate of change of momentum of an object is directly proportional to the RF acting on it.
The change in momentum takes place in the direction of the force.
Δp=mv-mu (if mass is constant)
F∝ Δp/Δt
If F is in Newtons, F=Δp/Δt thus F=mv-mu/Δt
If the mass of an object doesn't change, this is simplified to:
F=m(v-u/t) = mass x change in velocity/time taken
So if mass is constant, F=ma.
50
Rules of F=ma?
F=T-mg
| T=ma+mg
51
Newton's third law?
When two objects interact, they exert equal and opposite forces on each other.
The pair of forces act on different objects and are always the same type of force (e.g. friction and friction).
Forces can't exist in isolation, they always act in pairs.
The two forces act on different objects so can't cancel each other out.
52
Conservation of momentum (using Newton)?
When A and B interact, they exert equal and opposite forces.
From Newton's third law, F1=-F2.
From Newton's first law, A has an unbalanced force acting on it so it will accelerate to the left and B has an unbalanced force acting on it so it will accelerate to the right.
Newton's second law: F=Δp/Δt
thus F1=Δp(A)/Δt(A) and F2=Δp(B)/Δt(B)
but F1=-F2, therefore Δp(A)/Δt(A)=-Δp(B)/Δt(B)
but Δt(A)=Δt(B)
Δp(A)=-Δp(B) therefore Δp(A)+Δp(B)=0.
53
Conservation of momentum?
Th principle of conservation of momentum states that when bodies in a system interact, the total momentum remains constant provided no external forces act on the system.
total momentum before=total momentum after
(provided no external forces act)
54
Collisions?
When objects collide, the total momentum is always conserved:
total momentum before=total momentum after
When we consider kinetic energy, the result may be different. It depends on whether the collision is elastic or inelastic.
55
Elastic collision?
```
Kinetic energy is conserved.
total Ek before=total Ek after
e.g.
Collisions between snooker balls.
Collisions between molecules in a gas. Otherwise, repeated collisions would slow down the gas molecules, so they would eventually settle at the bottom of the container.
```
56
Inelastic collisions?
Most collisions are inelastic.
Some of the initial kinetic energy is 'lost'.
It is transferred to other forms, usually internal (heat) energy.
total Ek before>total Ek after
e.g.
Crash barriers and crumple zones of cars are specifically designed to collide in elastically, to absorb the kinetic energy in a crash.
57
Explosions?
The principle of conservation of momentum can also be applied to explosions.
total momentum before=total momentum after
Initially, all objects involved in an explosion are stationary.
Therefore, initial total momentum is zero.
58
Impulse?
'Following through' in sports keeps the force acting on the ball for a longer time.
resultant force = change in momentum/time
force x time = change in momentum
The greater the force on an object and the longer it acts for, the greater the change in the object's momentum.
So, by following through, you increase the time the force acts on the ball, producing a greater change in the ball's momentum .
Similarly, by drawing your hands backward when catching a ball, you reduce the string, as the change in momentum occur over a longer time, reducing the force on your hand.
Impulse = fΔt = Δp
p=mv (momentum conserved)
59
Force-time graph?
AREA = impulse or Δp (change in momentum)
60
If system is wider?
Any external force is now an internal force. Therefore, momentum is still conserved.
61
Force-distance graph?
AREA = work done or ΔEk (change in kinetic energy)
62
Equation for work done?
```
Work done (J) = Force (N) x Displacement (m)
W=Fs
NB: Although force and displacement are both vector quantities, work is a scalar quantity.
```
63
Resolving the force?
If force and displacement aren't in the same direction, the force needs to be resolved to find the component acting in the direction of the displacement.
W=fxcosθ.
64
Work done and the joule?
Work done = Energy transferred
Both work and energy have the same unit, the joule, J:
1J is the work done (energy transferred) when a force of 1N moves through a distance of 1m (in the direction of the force).
65
Power?
```
A measure of how fast work is done.
Power (W) = Work done (J) / Time taken (s)
P = ΔW/Δt
The unit of power is the Watt, W.
1W = 1Js^-1
```
66
Power (other equation)?
P=W/t
P=F x s/t
P=Fv
67
Rotational kinetic energy?
The kinetic energy due to the rotation of an object and contributes to the total kinetic energy.
Therefore the total Ek of the moon is the kinetic energy of its orbit + its rotational kinetic energy.
68
If friction and air resistance are negligible?
mgh=0.5mv^2
69
Inclined ramp v varying slope ramp?
- Acceleration is constant.
| - Acceleration is greatest at top and decreases down the slope.
70
Types of energy?
Heat, light, sound, kinetic, chemical, electrical, nuclear, elastic potential and gravitational potential.
71
Proving gpe?
```
Work done = F x distance moved parallel to force
= Weight x Δh
W = Ep gain
thus Ep = Weight x change in height
Ep=mgh
```
72
Proving epe?
```
F=kx (Hooke's law)
When a spring is stretched, work is done.
av. force = 0.5ke
W=Fd
=0.5kx x x
=0.5kx^2
```
73
Proving ke?
```
Any object gains kinetic energy if a constant force does work on it.
W=Fs
Newton's second law F=ma thus W=mas
If F and a are constant, SUVAT can be used:
a=v-u/t and s=(u+v/2)t
W=mas
W=m x v-u/t x (u+v/2)t
W=0.5m(v^2-u^2)
ΔEk = 0.5mv^2 - 0.5mu^2
ΔEk = new Ke - old Ke
```
74
Principle of conservation of energy?
Energy can be transferred from one form to another, but it can't be created or destroyed.
The total amount of energy always remains the same.
75
Efficiency?
The proportion of energy that is usefully transferred is called the efficiency of the machine.
efficiency = useful energy output/total energy input
efficiency = useful power output/total power input
76
Density?
The density of a substance is defined as its mass per unit volume.
For a certain amount of a substance of mass m and volume V, its density ρ is calculated using:
ρ=m/v where ρ=kgm^-3
77
Ice and water?
Ice floats on water as it is less dense.
Mass of displaced water = Mass of ice
ρW x VW = ρI X VI
VW/VI = ρI/ρW = 920/1000 = 92%
78
Behavior of springs?
A pair of forces are required to change the shape of a spring.
If the spring is being squashed/shortened, we say the forces are compressive.
If the spring is being stretched/lengthened, we say the forces are tensile.
79
Hooke's law?
The force needed to stretch a spring is proportional to the extension of the spring from its natural length, provided the elastic limit is not exceeded.
F=kΔL where:
F = Force/N
k = spring constant/Nm^-1
If a spring is stretched beyond its elastic limit, it doesn't regain its initial length when the force applied to it is removed.
80
What is the spring constant?
The greater the spring constant, the stiffer the spring.
81
The graph?
Graph of F against ΔL:
P = limit of proportionality
E = elastic limit
In the middle, the material displays plastic behavior.
82
Calculating stiffness?
```
Series:
F1 + F2 = W
kΔL1 + kΔL2 = W
(k1+k2)ΔL = W
k = k1+k2
Parallel:
ΔL = ΔL1+ΔL2
W/k = W/k1+W/k2
1/k = 1/k1+1/k2
```
83
Force-extension graph?
Area = energy stored in a stretched spring/ work done
Area = 0.5FΔL
thus strain energy = work done stretching a spring
Ek = 0.5FΔL
if F=kΔL
Ep=0.5kΔL x ΔL
Ep=0.5kΔL^2 (only if Hooke's law is obeyed)
84
What does stiffness depend on?
Material, length and cross-sectional area.
| k=EA/l (E= Young Modulus)
85
Stress?
The stress on a material is the force acting per unit cross-sectional area.
stress (Pa) = force (N) / cross-sectional area (m^2)
σ = F/A
86
More on stress?
The breaking stress (a.k.a ultimate tensile strength) of a material is the maximum stress it can withstand without fracture.
Some materials get a thinner section when they stretch. This increases stress so this is where the material breaks.
87
Strain?
The strain of a material is the extension produced per unit length.
strain = extension (m) / length (m)
e = x/l
88
Young Modulus?
Young Modulus, E = tensile stress, σ/ tensile strain, e
E = (F/A) / (ΔL/L) = FL/AΔL = (F/ΔL) x (L/Δ) = kL/A
thus k=EA/l
89
Properties of materials?
Materials that are hard to stretch are said to be stiff.
| Materials that are easy to stretch are said to be flexible.
90
Elastic materials?
An elastic material returns to its original shape when the forces deforming it are removed (as long as it has not been stretched beyond its elastic limit).
Rubber is elastic but doesn't obey Hooke's law.
91
Plastic materials?
Materials that permanently deform.
Strain is increased when forces deforming it are removed.
-Ductile - they can be drawn into wires.
-Malleable - They can be hammered into sheets.
e.g. Polythene
92
Tough materials?
Malleable materials e.g. lead are tough.
| When you try and break lead, it deforms plastically. It gives way gradually, absorbing a lot of energy before it snaps.
93
Brittle materials?
This is the opposite of tough.
Brittle materials, e.g. glass, do not deform plastically. It doesn't absorb much energy before it breaks; it cracks or shatters suddenly.
94
Brittle materials graph?
Straight line through origin with set breaking point.
95
Rubber band?
- Area under loading curve is the work done to stretch the rubber band.
- Area under unloading curve is the work done by the rubber band when it is unloaded.
- The area between the two curves represents the difference between energy stored in the rubber band when it is stretched and the useful energy recovered from it when it is unstretched.
- The difference occurs because some of the energy stored in the rubber band becomes the internal energy of the molecules when the rubber band unstretches.
96
Polythene?
- It doesn't regain its initial length.
- The area between the loading and unloading curves represents work done to deform the material permanently, as well as internal energy retained by the polythene when it unstretches.
97
How stress varies with strain in a wire?
Recall graph:
| P, E, Y1 (wire weakens), Y2, UTS and B (wire snaps).
98
F-E?
- Usually for objects e.g. a particular spring.
- Gradient: k, spring constant in Nm^-1
- Area: work done=0.5FΔL or 0.5kΔL^2
- Unit: J
99
S-S?
-Usually for materials (of any size).
-Gradient: E, Young Modulus in Nm^-2 or Pa
-Area: 0.5 x stress x strain
= 0.5 x (F/A) x (ΔL/L) = 0.5FΔL/AL = W/V
= work done per unit volume
-Unit: Jm^-3
