Section 4: Mechanics Flashcards
1
Q
What is a vector?
A
Vectors are quantities with both a size and a direction
2
Q
What is the difference between scalers and vectors?
A
- a scaler quantity has no direction - it’s just an amount of something e.g. The mass of a sack of carrots
- a vector quantity has magnitude (size) and direction e.g. The velocity of a car is it’s speed and direction
3
Q
What are some examples of scalers?
A
- length/distance
- speed
- mass
- temperature
- time
- energy
4
Q
What are some examples of vectors?
A
- displacement
- velocity
- force(including weight)
- acceleration
- momentum
5
Q
What is adding two or more vectors known as?
A
Finding their resultant
6
Q
How can you find resultant vectors using scale diagrams?
A
You can draw a scale drawing of them ‘tip-to-tail’ then measuring the length and angle of the resultant vector
IT MUST BE TO SCALE!!
1. Measure the side with a ruler
2. Measure the missing angle with a protractor
7
Q
What is a bearing?
A
A three digit angle measured clockwise from north in degrees
8
Q
How can you find resultant vectors using trigonometry?
A
If the two sides are perpendicular to each other you can use trigonometry.
You can calculate the resultant vectors using the formula R^2 = a^2+b^2 (Pythagoras’s theorem)
You can calculate the size of the angle theta using the formula
Theta=(tan to the -1/ cos to the -1/sin to the -1) x (b➗a)
9
Q
How do you work out
- Sin theta?
- Cos theta?
- Tan theta?
A
Sin theta = opp/hyp
Cos theta = adj/hyp
Tan theta = opp/adj
10
Q
What is the opposite of finding the resultant?
A
Resolving vectors
11
Q
What is resolving vectors?
A
You start from the resultant vector and split it into two components at right angles to each other.
Basically the opposite of finding resultant vectors.
12
Q
How can you find the horizontal component Vx?
A
Sin/cos/tan theta = Vx/V
Vx = V (sin/cos/tan) theta
13
Q
How can you find the vertical component Vy?
A
Sin/cos/tan theta = Vy/V
Vy = V (sin/cos/tan) theta
14
Q
What is Cos60 equal to?
A
Cos60 = Sin30 = 0.5
15
Q
In resolving vectors, what is theta measure by?
A
Theta is measured anti clockwise from the horizontal
16
Q
Why is resolving vectors useful?
A
Because two perpendicular components of a vector don’t effect each other. You can deal with the two directions completely separately.
17
Q
What can all the forces acting on an object be shown as?
A
A free-body force diagram
18
Q
When is a body in equilibrium?
A
When all the forces are balanced and cancel each other out. There is no resultant force. It can only be in equilibrium if the forces are equal and opposite.
19
Q
When can an object be in equilibrium?
A
When it is at rest or moving with a constant velocity
20
Q
When do force vectors form a closed loop?
A
When you draw them tip to tail. Sometimes called a vector triangle/vector polygon(more than three forces)
21
Q
How do you resolve forces in two perpendicular directions?
A
If an o next is in equilibrium, the sum of the components in each direction must be equal to zero. Just use trigonometry to find the forces.
22
Q
What can you use force boards for?
A
Investigating equilibrium
You can use them to apply forces to an object and vary the forces and directions they act in to find different conditions for equilibrium.
23
Q
What is a moment?
A
A moment is the turning effect of a force around a point.
24
Q
What is a couple?
A
A couple is two moments of equal size acting parallel to each other
25
What is the mass of an object?
The amount of stuff(matter) in it.
26
What is mass measured in?
Kg
27
What does a greater mass on an object mean?
The greater an objects mass, the greater it's resistance to a change in velocity (its inertia)
28
What is weight?
* weight is a force
| * measured in newtons
29
How can you calculate weight?
Weight = mass x gravitational field strength
W = mg
30
What is g usually taken as in w = mg?
g is usually taken as -9.81 ms^-2 because it acts downwards
31
What does the moment of a force depend on?
* the size of the force
| * how far the force is applied from the turning point
32
What is the equation of work out a moment?
M = F x d
* M = moment of a force (Nm)
* F = size of the force (N)
* d = perpendicular distance between the line of action of the force and the turning point (m)
33
What is the principle of moments?
The principle of moments states that for a body to be in equilibrium, the sum of the clockwise moments about any point equals the sum of the anti clockwise moments about the same point. (If the moments aren't balanced, the object will turn)
34
What does perpendicular distance mean?
The perpendicular distance means the distance along a line that makes a right angle with the line of action of the force
35
What happens in a lever?
In a lever, an effort of force acts against a load force by means of a rigid object rotating around a pivot
36
When are levers useful?
When you need a large turning effect
37
Name some examples of levers.
* spanners
* wheelbarrows
* scissors
38
How do levers work?
They increase the distance from the pivot a force is applied, so you need less force to get the same moment. You can use the principle of moments to work it out.
39
How do you work out the moment of a couple?
M = F x d
* M = moment of a couple (Nm)
* F = size of the force (N)
* d = perpendicular distance between the lines of action of the forces (m)
40
What is the center of mass?
The centre of mass of an object is the single point that you can consider its whole weight to act through (whatever its orientation)
41
Where is the centre of mass on a uniform regular solid?
The centre of the object
42
How can you find the centre of mass by experiment?
* Hang the object freely from a point
* Draw a vertical line downwards from the point of suspension. Use a plumb bob to get the line exactly vertical
* Hang the object from a different point and draw another vertical line
* The centre of mass is where the lines cross
43
When will an object topple over?
An object will topple over if the line of action of ta weight (drawn down from the centre of mass) falls outside its base area. This is because a resultant moment occurs which provides a turning force
44
When will an object be least stable?
The higher the centre mass and the smaller the base area
45
What can be deduced from forces on supports?
If an object is being held up by supports, the force acting on each support won't always be the same. The closer the objects centre of mass to its support, the stronger the force on the support. A support closer to the centre of mass will experience a larger force.
46
What is speed?
How fast something is moving, regardless of direction
47
What is Displacement?
How far an objects travelled from its starting point in a given direction
48
What is velocity?
The rate of change of an objects displacement (speed in a given direction)
49
What is acceleration?
The rate of change of an objects velocity
50
What do the letters in suvat stand for?
* s = displacement (m)
* u = initial velocity (ms^-1)
* v = final velocity (ms^-1)
* a = acceleration (ms^-2)
* t = time (s)
51
Equation for acceleration?
a = (v-u) / t So....
v = u + at
52
Displacement = average velocity x time.
| If acceleration is constant the average velocity is just the average of the initial and final velocities so...
s = ( (u+v) / 2 ) x t
53
3rd equation?
s = ut +1/2at^2
54
4th equation?
V^2 = u^2 + 2as
55
What is deceleration the same as?
Negative acceleration
56
What do displacement time graphs show?
An objects position, relative to its starting point over a period of time. They can be used to describe an objects motion as well as find its velocity at a given point.
57
What do you plot on the axis of a displacement time graph?
Y axis - displacement
| X axis - time
58
What do you use to work out the points you need to plot?
SUVAT
59
What does the gradient of a displacement time graph show?
Velocity
60
What is acceleration on a distance time graph?
The rate of change of the gradient
61
What shape does a displacement time graph make for an accelerating object?
A curve
62
What is velocity defined as?
Velocity = change in displacement / time taken
V = delta s / delta t
63
What does it mean if the displacement time graph has a horizontal section (gradient 0)
That the velocity is zero and it's not moving
64
What does a negative gradient on a displacement time graph mean?
That the object is moving backwards
65
What is an objects instantaneous velocity?
It's velocity at a particular moment in time. To find the instantaneous velocity at a certain point you need to draw a tangent to the curve
66
What is the average velocity?
The total change in the displacement of the object divided by the total time taken.
67
What do velocity time graphs show?
Velocity over time
68
What does the gradient of a velocity time graph represent?
Acceleration
69
How do you work out acceleration?
Acceleration = change in velocity / time taken
Acceleration = delta v / delta t
70
What can be seen on the velocity time graph if the acceleration is uniform?
A straight line
71
What does it mean if the velocity time graph has a steep gradient?
That it has a greater acceleration than one with a less steep slope
72
How do you work out displacement of a velocity time graph?
The area under the graph
73
What is average velocity x time equal to?
S = ((u+v)/2) x t = average velocity x time
74
How can you calculate the distance traveled?
Average speed x time
75
What does the graph look like if the object starts moving in the opposite direction?
It will have negative regions.
76
What can show constant velocity?
U=V
77
If a ball is dropped from table height, what does the graph look like?
Negative slope till it hits the floor, vertically upwards to the positive version and then a repeating pattern.
78
What happens to the velocity time graph of the acceleration is non uniform (changing)?
The gradient will also change. Increasing acceleration is shown by an increasing gradient. A decreasing acceleration is shown by a decreasing gradient
79
How can you find the acceleration if it's changing on a velocity time graph?
By working out a tangent to the curve at a particular point
80
What high tech equipment can you use to gather distance and time data?
An ultrasound position detector. It's a data logger that automatically records the distance of an object from the sensor several times a second.
81
What are the advantages of data loggers over traditional methods?
* data is more accurate
* much higher sampling rate than humans
* you can see the data displayed in real time
* used to obtain medical images
82
What do acceleration time graph show?
Acceleration over time
83
What does the height of an acceleration time graph at any pony show?
The objects acceleration at that time.
84
What does positive acceleration mean?
That the object is speeding up where as negative shows it's slowing down.
85
What does it mean if a=0?
That the object is moving with constant velocity
86
What does a straight horizontal line show?
Uniform acceleration or uniform deceleration
87
What does the area under a acceleration time graph represent?
The velocity
Delta V = a x t
88
What do Newtons Laws of Motion show?
They describe the relationship between the forces acting on an object and its motion.
89
What is Newtons 1st Law of Motion?
The velocity of an object will not change unless a resultant force acts on it.
90
What does Newtons 1st Law mean?
That a body will stay still it move in a straight line at a constant speed unless there's a resultant force acting on it. If the forces aren't balanced the object will end up accelerating
91
What is the reaction like of an apple sitting in a table?
Reaction R = Weight mg
92
What is Newtons 2nd Law of Motion?
The acceleration of an object is proportional to the resultant force acting on it.
F = m x a
Resultant Force (N) = mass (kg) x acceleration (ms^-2)
93
What does Newtons 2nd Law actually show?
That the larger the force you have the more acceleration you get. For a given force the more mass you have the less acceleration you get.
94
What direction is the acceleration always in?
The same direction as the resultant force
95
What is Newtons 3rd Law of Motion?
If an object A exerts a force on object B, then object B exerts an equal but opposite force on objects A
96
What is freefall?
Free fall is when there is gravity acting on an object and nothing else. It's the motion of an object undergoing an acceleration of 'g'
97
What is the only force acting on an object in free fall?
It's weight
98
What is Galileos method of investigating free fall?
Rolling a ball down a smooth groove in an inclined plane. Rolling the ball reduced the effect of air resistance and slowed it down.
99
Why do all objects fall at the same rate?
It can be explained by Newtons 2nd Law. Acceleration is independent of the mass. It makes no difference whether the ball is heavy or light
100
Free fall and motion equation with no initial velocity?
```
U = 0
a = g = -9.81 ms^-2
```
v=gt v^2 = 2gs
s = 1/2gt^2 s = (vt)/2
101
Free fall and motion equation with initial velocity upwards?
It's the same it just means it's projected into the air.
a = g = -9.81 ms^-2
102
How can you determine g using free fall?
Dropping a ball bearing onto a trap door using an electromagnet.
•measure height from the bottom of the ball bearing to the trap door
•flick the switch to start the timer and disconnect the electromagnet
•the ball bearing falls, knocking the trap door and breaking the circuit and stopping the timer - record the time
•repeat 3 times get an average use different heights
•find g using a graph
103
How can you identify and reduce errors of determining g by free fall?
* There will be a random error from measuring the height
* use a small and heavy ball so you can ignore air resistance
* the computer will greatly reduce the uncertainty of measuring the time it takes for the ball to drop
104
What are the axis of determining gravity by free fall?
Height (m) against time taken to fall squared (s^2)
105
What is the equation of determining gravity by free fall?
1/2g = s/t^2
The acceleration is due to gravity so the gradient delta S / delta t^2 is equal to 1/2 g
106
What is a projectile?
Any object with a given initial velocity that is then left to move freely under gravity
107
What is the horizontal and vertical components like in projectile motion?
Completely independent. The horizontal velocity remains constant whilst the vertical velocity is affected by the acceleration due to gravity
108
What method do you need to use if the projectile motion is at an angle?
* resolve initial velocity into horizontal and vertical components
* use the vertical component to work out how long it's in the air and how high it goes
* use the horizontal component to work out how far it goes in the horizontal direction whilst it's in the air
109
How are projectile motions effected by air resistance?
It affects the trajectory as it acts in the opposite direction to the motion. It reduces speed and distance abled to travel
110
What is friction?
A force that opposes motion
111
What is contact friction?
When friction happens between solid surfaces
112
What is fluid friction?
When it happens between a liquid or gas. - known as drag or air resistance
113
What are the 3 things that affect fluid friction?
* thickness : viscosity of the fluid
* shape of the object moving through it
* the speed of the object
114
What are the 3 things you need to remember about frictional forces?
* always act in the opposite direction to the motion of the object
* they can never speed up or start something moving
* they convert kinetic energy into heat
115
What is lift?
An upward force in an object moving through a fluid
116
What is terminal speed and when does it occur?
Happens when frictional forces are equal to the driving force.
117
What are the two ways of increasing a vehicles maximum speed?
* increase the driving force
| * reduce the frictional force
118
What is the terminal velocity like in a fluid test?
Ball bearing through a thick(viscous) liquid
•mark fixed distances and time how long it takes the ball to pass each one
•repeat to reduce random errors
•calculate times taken for the ball to travel between each marked area
•calculate average velocity
•you should find that it increases at first then stays at the same speed
119
What is momentum?
Momentum = mass x velocity
P = m x v
Kgms^-1 = kg x ms^-1
120
What is the principle of linear momentum?
With no external forces, momentum is always conserved
Momentum before = momentum after
121
What is an elastic collision?
It is one where momentum is conserved and kinetic energy is conserved
122
What is the equation for kinetic energy?
Ek = 1/2mv^2
123
What is an inelastic collision?
Some of the Ek is converted into other forms during the collision
124
How can Newton's second law also be written in terms of momentum?
F = m x a
F = m x a = m x delta v / delta t
F = delta (m x v) / delta t
Delta (m x v) = (m x v) - (m x u)
125
What is impulse?
The product of force and time. It's equal to the change in momentum of a body and measured in Ns
F delta t = delta (m x v)
Impulse = change in momentum
126
How can you calculate impulse on a force time graph?
The area under the graph
127
How can the force of an impact be reduced?
By increasing the time of the impact
128
What is work?
Work is done whenever energy is transferred
129
What are some examples of work being done?
Lifting up a box - against gravity
Pushing a chair across a level floor - friction
Putting two north poles together with two magnets - magnetic force
Stretching a spring - stiffness of a spring
130
What does the word work mean in physics?
The amount of energy transferred from one form to another
131
How can you calculate work done?
```
W = F x s
Work done (j) = force (N) x distance moved (m)
```
132
What does the equation for work done assume?
That the direction of the force is the same as the direction of movement
133
What is the definition of the joule?
One joule is work done when a force of 1 N moves an object by 1 m
134
How can you work out the work done at an angle?
W = f x s x cos theta
Cos theta = the angle at which the force acts from the direction of motion
135
What is power?
Power is the rate of doing work
The amount of energy transferred from one form to another per second
136
What is the equation to work out power?
P = delta w / delta t
137
What is a watt defined as?
A rate of energy transfer equal to 1 joule per second
138
What does the area under a force displacement graph show?
The work done
139
What is the equation for power on moving objects?
```
P = F x V
Power = force x speed in direction of motion
```
140
What can you put in the equation p = Fv if the force and motion are in different directions?
P = Fvcos theta
141
What is the conservation of energy?
Energy cannot be created or destroyed. Energy can only be transferred from one form to another but the total amount of energy in a closed system will not change
142
What is the equation for efficiency?
Efficiency = useful energy output / energy input
143
How can you write efficiency in terms of power?
Efficiency = useful output power / input power
144
What is the equation for change in gravitational potential energy?
Delta Ep = m x g x delta h
145
What is the equation for elastic potential energy?
E = 1/2 k (delta L)^2
146
What is the equation for the sum of kinetic energy if you ignore friction?
1/2mv^2 = mg delta h
