Section 4 - Mechanics Flashcards
1
Q
What is a scalar quantity?
A
A quantity that only has a magnitude, without direction.
2
Q
What is a vector quantity?
A
A quantity that has both magnitude and direction.
3
Q
Sort these into scalar and vector: • Mass • Displacement • Velocity • Time • Force • Acceleration • Distance • Speed • Energy • Momentum
A
SCALAR • Mass • Temperature • Time • Distance • Speed • Energy VECTOR • Displacement • Velocity • Force • Acceleration • Momentum
4
Q
Is mass vector or scalar?
A
Scalar
5
Q
Is temperature vector or scalar?
A
Scalar
6
Q
Is displacement vector or scalar?
A
Vector
7
Q
Is velocity vector or scalar?
A
Vector
8
Q
Is time vector or scalar?
A
Scalar
9
Q
Is distance vector or scalar?
A
Scalar
10
Q
Is force vector or scalar?
A
Vector
11
Q
Is speed vector or scalar?
A
Scalar
12
Q
Is weight vector or scalar?
A
Vector
13
Q
Is energy vector or scalar?
A
Scalar
14
Q
Is acceleration vector or scalar?
A
Vector
15
Q
Is momentum vector or scalar?
A
Vector
16
Q
What is the term for adding two forces together?
A
Finding the resultant of them.
17
Q
What are the two methods for finding the resultant of two forces?
A
1 - Scale drawings
2 - Pythagoras + Trigonometry
18
Q
How can the resultant of two forces be found using scale diagrams?
A
- Draw the two forces tip to tail
- Draw the resultant force
- Measure the length of the resultant force and the angle from the horizontal
19
Q
A
20
Q
How can the resultant of two forces be found using Pythagoras and trigonometry?
A
- Only works if the forces are at right angles
- Draw a right angled triangle out of the forces
- Use Pythagoras to find the magnitude of the resultant
- Use trig to find the direction of the resultant
21
Q
When finding the resultant of two forces, when can Pythagoras + trigonometry be used?
A
When the forces are at right angles to each other.
22
Q
What is splitting a force into horizontal and vertical components called?
A
Resolving the force.
23
Q
When resolving a force (F) to the top right, what is the horizontal component equal to?
A
F x cosθ
Where θ is the angle from the horizontal.
24
Q
When resolving a force (F) to the top right, what is the vertical component equal to?
A
F x sinθ
Where θ is the angle from the horizontal.
25
Why is vertical and horizontal components easy to find when resolving forces?
The two components don’t affect each other, so the two directions can be dealt with separately.
26
On a free-body diagram, do the sizes of the arrows matter?
Yes, because they represent the size of the force.
27
What is a free-body diagram?
A diagram that shows all the forces acting on a single body (and NOT the forces that the body exerts).
28
What are coplanar forces?
* Forces that are all in the same plane
| * You’ll only have to deal with these types of forces
29
What are the conditions for an object to be in equilibrium?
* Forces acting on the object in each direction must be balanced.
* No resultant moment acting on the object.
30
Describe the motion of a body in equilibrium.
Either:
• At rest
• Moving at constant velocity
31
How can you demonstrate that three coplanar forces give no resultant force?
When you draw them out as a triangle, they form a closed loop.
32
When there are three forces acting on a body in equilibrium and one is unknown, how can it be calculated?
* Resolve each force horizontally and vertically
* The horizontal forces must add up to 0.
* The vertical forces must add up to 0.
* Find the missing force.
33
When resolving a force acting in an unusual direction, what is it important to do?
Choose axis that are sensible for the problem.
34
What axis should you choose when resolving a force acting on an object on a slope?
• Choose axis at right angles to the slope.
• Turning the page to be parallel with the slope will help.
(See diagram pg 41)
35
What is a moment?
* The turning effect of a force around a point.
| * Equal to the force multiplied by the perpendicular distance from the line of action to the pivot.
36
What is the equation for the moment of a force?
Moment (Nm) = Force (N) x Perpendicular distance from the point to the line of action of the force (m)
M = F x d
37
What is d in the moments equation?
Perpendicular distance from the turning point to the line of action of the force (m).
38
What is the unit for moments?
Newtonmeter (Nm)
39
State the principle of moments.
For an object in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments.
40
In a lever, what forces act against each other?
The effort force acts against the load force.
41
What is a couple?
* A pair of coplanar forces of equal size that act parallel to each other but in opposite directions.
* Produce a turning effect.
42
What is the equation for the moment of a couple?
Moment (Nm) = Size of one of the forces (N) x Perpendicular distance between the lines of action of the forces (m)
M = F x d
43
What is mass?
The amount of matter in an object.
44
What is the unit for mass?
Kilograms (kg)
45
What is inertia?
An object’s resistance to change in velocity.
46
What affects an object’s inertia?
* Its mass.
| * The greater the mass, the greater the inertia.
47
Is an object’s mass affected by the gravitational field strength?
No
48
What is weight?
The force exerted on an object due to the Earth’s gravitational field.
49
What is the unit for weight?
Newton (N)
50
What is the equation for weight?
Weight = Mass x Gravitational Field Strength
W = m x g
51
What is the value of g?
9.81 N/kg
52
What is an object’s centre of mass?
* The point through which the whole weight can be said to act through.
* Object will balance around this point.
53
Is the centre of mass always on an object?
No, sometimes it is outside the object.
54
Where is the centre of mass of a uniform, regular solid (e.g. a sphere)?
At its centre.
55
How can the centre of mass of a regular object be found?
* Look at the lines of symmetry
| * The centre of mass is where the lines cross
56
How can the centre of mass of an irregular object be found?
* Hang object from a point
* Draw vertical line downwards from point (using a plumb bob as guidance)
* Repeat with different point
* Centre of mass is where the lines cross
57
When will an object topple and why?
* When the vertical line from its centre of mass falls outside of the base area.
* Because the centre of mass causes a resultant moment around the pivot.
58
What makes an object stable?
• Low centre of mass
• Wide base
E.g racing cars won't topple over on fast corners
59
For supports:
| The closer the object's centre of mass .....
....the stronger the force on the support ...
60
What is speed?
How fast an object is moving, regardless of direction.
61
What is displacement?
How far an object has travelled from its starting point in a given direction.
62
What is the symbol for displacement?
s
63
What is velocity (in terms of displacement)?
The rate of change of an object’s displacement.
64
What is the symbol for velocity?
v
65
What is acceleration?
The rate of change of an object’s velocity.
66
What is the symbol for acceleration?
a
67
What is the equation for velocity?
v = Δs/Δt
68
What is the equation for acceleration?
a = Δv/Δt
69
What is instantaneous speed?
The speed at a given moment (as oppose to average speed).
70
Describe the displacement-time graph for an accelerating object.
* Curved graph
| * If acceleration is constant, the rate of change of the gradient is constant.
71
Remember to practice predicting different displacement-time graphs.
Pg 46 of revision guide.
72
What does the gradient and area under the curve represent in a displacement-time graph?
* Gradient = Velocity
| * Area = Nothing
73
How do you find the velocity from a displacement-time graph?
* Find the gradient.
| * You may need to draw a tangent if the graph is a curve.
74
On a curved displacement-time graph, how do you find the AVERAGE velocity?
* Divide the overall displacement by the overall time.
| * No need for tangents.
75
What is the difference between a speed-time and velocity-time graph?
A velocity-time graph can have a negative part to show motion in the opposite direction.
76
How is uniform acceleration shown on a velocity-time graph?
Straight line
77
How is a changing acceleration shown on a velocity-time graph?
Curved line
78
What does the gradient and area under the graph represent on a velocity-time graph?
* Gradient = Acceleration
| * Area = Displacement
79
How do you find the acceleration from a velocity-time graph?
Gradient of the line
80
How did you find the displacement from velocity-time graph?
Area under the graph
81
On an acceleration-time graph, what does the area under the line represent?
The change in velocity.
82
What piece of equipment can be used in motion experiments?
Ultrasound position detector
83
How does an ultrasound position detector work?
* Records distance of object from the sensor several times a second
* Connected to computer with graphing software to get graph
84
What are some advantages of data-loggers over traditional methods of recording data?
1) Data is more accurate - don't have to allow for human reaction times.
2) Higher sampling rate than humans (for example, ultrasound position detectors can take a reading ten times every second)
3) Data displayed in real time
85
What are the suvat equations used for?
4 equations that can be used to solve constant acceleration motion problems.
86
What are the 4 suvat equations?
* v = u + at
* s = (u+v)/2 x t
* s = ut + 1/2 at²
* v² = u² + 2as
87
In suvat problems for a falling object, what is the value of a?
g (9.81m/s²)
88
Remember to practice suvat equations and problems.
Pg 50/51 of revision guide.
89
What is free fall?
The motion of an object undergoing an acceleration of ‘g’ (i.e. under gravity and nothing else).
90
In free fall, what is the only force acting on an object?
Its weight.
91
Can objects with an original velocity undergo free fall?
Yes, as long as the force providing the initial velocity is no longer acting.
92
Describe the rate at which objects fall to the Earth.
All objects fall to the Earth at the same rate due to gravity (9.81m/s²).
93
Describe an experiment to calculate g.
1) Set up a circuit with a switch that controls two parallel circuits: one with an electromagnet and ball, the other with a timer and trapdoor
2) Measure the height from the bottom of the bearing to the trapdoor.
3) Flick the switch to start the timer and release the bearing.
4) Bearing falls, hits trapdoor and stops the timer. Record the time.
5) Repeat 3 times at this height and average the time.
6) Repeat at various heights.
7) Plot a graph of height (m) against time taken squares (s²).
8) a = 2 x Gradient
(See diagram pg 52)
94
In the experiment to calculate g, how is error reduced?
* Bearing is small and heavy -> Means air resistance is negligible
* Computer releasing and timing fall -> Reduces uncertainty
95
In the experiment to calculate g, what is the biggest source of error?
RANDOM error: The measurement of h (using a ruler = uncertainty of + or - 1mm).
96
In the experiment to determine g, describe what graph should be plotted and why?
```
Height (m) against time squared (s²) because:
• s = ut + 1/2 at²
• Since u = 0, s = 1/2 at²
• 1/2 a = s/t² = Gradient
• a = g = 2 x Gradient
```
97
Describe two experiments to find g.
1) Ball bearing drop with timer.
| 2) Card drop through a light gate.
98
How do you find the acceleration from a displacement-time graph?
* Find the gradient (velocity) at two separate points
| * Find the difference between these two points and divide it by the time (a = Δv/Δt)
99
Remember to revise experiments to determine g.
Pg 52/53 of revision guide.
100
When considering vertical motion, what can the acceleration be taken as?
g (-9.81m/s²)
If you use a negative for upward stay consistent
101
How do you approach projectile motion questions when an object is projected horizontally?
* Consider vertical motion separately.
* Use suvat to determine the time in the air.
* Now consider horizontal motion.
* Use distance = speed x time to find the horizontal distance travelled.
102
```
In suvat equations, what signs can these values be (can they be positive/negative)?
• g
• t
• u and v
• s
```
g = Usually negative (depends)
t = Positive
u and v = Positive or negative
s = Positive or negative
103
How do you approach projectile motion questions when an object is projected at an angle?
* Resolve the velocity into horizontal and vertical components.
* Use vertical component with suvat to work out the time in the air.
* Use the horizontal component with distance = speed x time to work out the horizontal distance travelled.
104
What is Newton’s 1st Law?
The velocity of an object will not change unless a resultant force acts on it.
105
How are the forces on an apple on a table balanced?
Reaction force of table = Weight of apple
106
What is Newton’s 2nd law?
| Written in two ways
• The force required to accelerate an object is equal to its mass times the acceleration
• F = m x a
OR
• The rate of change of momentum of an object is directly proportional to the resultant force which acts in the object.
• F = Δ(mv)/Δt
107
What is the equation for Newton’s 2nd law?
Resultant force (N) = Mass (kg) x Acceleration (m/s²)
F = m x a
108
Explain why all objects fall at the same rate.
```
Consider Newton’s 2nd Law:
• F = ma
When an object falls:
• mg = ma
• a = g
```
109
What is Newton’s 3rd Law?
* If an object A exerts a force in object B, then object B exerts an equal and opposite force on object A.
* i.e. Every action has an equal and opposite reaction
110
What must you be careful of with Newton’s 3rd Law?
* The opposite reaction is must be the EXACT reverse of the original action.
* The forces cannot both be acting on the same object!
111
What is the Newton’s 3rd Law opposite reaction of a person pushing on a wall?
The wall pushing back on the person.
112
What is the Newton’s 3rd Law opposite reaction of a person pulling a cart?
The cart pulling back on the person.
113
What is the Newton’s 3rd Law opposite reaction of a person pushing back on the water when swimming?
The water pushing the person forward.
114
What can be said about the types of forces in Newton’s 3rd Law?
The equal and opposite pairs are always of the SAME TYPE (e.g. both electrical).
115
What is a friction?
A force that opposes motion.
116
What are the two types of friction?
* Dry friction
| * Fluid friction
117
What is dry friction?
Friction between two solid surfaces.
118
What is fluid friction?
Drag or air resistance, due to a liquid or gas.
119
What is a fluid?
A liquid or a gas.
120
What factors affect the size of fluid friction (force)?
* Viscosity of liquid
* Speed of object (force increases = speed increases)
* Shape of object (larger area pushing against fluid= greater resistive force)
121
In projectile motion calculations, what is the significance of air resistance?
* Air resistance is usually ignored
| * This gives an answer which is too large
122
Can friction speed an object up or start it moving?
No
123
When energy transfers, what does friction result in?
Kinetic energy to heat and sound.
124
What is lift?
* An upwards force on an object moving through a fluid.
| * Perpendicular to the direction of fluid flow.
125
The resistive force from the fluid isn't necessarily in the same direction as...
...the direction of the movement of the fluid
| check the explanation but it should match this picture
126
How does lift happen?
When an object in a fluid causes the fluid flowing over it to change direction.
127
Give an example of when lift might happen.
* A plane wing moving through the air.
* Wing pushes down on the air, changing its direction.
* The air pushes back with an equal and opposite reaction force (Newton's 3rd)
128
When is terminal speed achieved?
When the friction force equals the driving force or weight.
129
Describe how a moving object reaches terminal speed.
1) Constant driving force causes acceleration.
2) As speed increases, so does the frictional force. This reduces the resultant force and therefore the acceleration.
3) Eventually, the frictional force equals the driving force and terminal speed is achieved.
130
What factors will cause a terminal speed in a moving object?
1) Driving force that stays constant
| 2) Frictional force that increases with speed
131
What things can be done to increase a moving object’s terminal speed?
1) Increase the driving force (e.g. bigger engine)
| 2) Reduce the frictional force (e.g. more streamlined object)
132
How does air resistance change with speed?
It increases with speed.
133
What does a v-t graph look like for terminal velocity?
134
What does an a-t graph look like for terminal velocity?
135
How can you find the terminal speed of a ball bearing in a viscous material?
Put elastic bands around the tube of viscous liquid at fixed distances using a ruler.
Drop the ball bearing into the tube.
Use a stopwatch and record the time at which it reaches each band.
…
(You could alter other variables instead of fluid velocity e.g the shape of the object)
136
Describe how and why the speed of a skydiver changes as he falls.
* Skydiver accelerates until air resistance equals weight.
* Travelling at terminal speed until parachute opens.
* Air resistance is now bigger than his weight.
* This slows him down until his speed has dropped so that the air resistance is equal to the weight again.
* This is the new terminal speed.
137
Describe the velocity-time graph of a falling skydiver.
* Velocity increases at a decreasing rate
* Until terminal speed (flat part of graph)
* Sharp drop in velocity when parachute opens
* New terminal speed (lower flat part of graph)
138
What is momentum?
The tendency of an object to keep moving in the same direction.
139
What two factors affect the momentum of an object?
* Mass
| * Velocity
140
What is the equation for momentum?
Momentum (kg m/s) = Mass (kg) x Velocity (m/s)
p = m x v
141
What is the unit for momentum?
Kilogram metres per second (kg m/s)
142
The total momentum before a collision is...
...equal to the total momentum after the collision.
143
Is momentum conserved in a system?
* Yes, assuming no external forces act.
| * Even if the collision is inelastic.
144
The total momentum before an explosion is...
...equal to the total momentum after the explosion.
145
What can be said in terms of momentum after an air rifle is fired?
The forward momentum gained by the bullet is equal to the backward momentum of the rifle.
146
What are the two types of collision?
* Elastic
| * Inelastic
147
What is an elastic collision?
* One where kinetic energy is conserved (as well as momentum).
* No energy is dissipated as heat, sound, etc.
148
What is an inelastic collision?
* One where kinetic energy is not conserved (but momentum is conserved).
* Some energy is dissipated as heat, sound, etc.
149
What two equations represent Newton’s 2nd Law?
* F = ma
| * F = Δ(mv)/Δt
150
Give the momentum definition of Newton’s 2nd Law.
The rate of change of momentum of an object is directly proportional to the resultant force which acts on the object.
151
Express force in terms of momentum and time.
Force = Change in Momentum / Time
152
What is impulse?
* Force x Time
| * It is the change in momentum
153
What is the unit for impulse?
Newton seconds (Ns)
154
What is the equation for impulse?
Impulse = Change in Momentum
Ft = mv - mu
(Note: This is derived from Newton’s 2nd Law)
155
How can impulse be found from a force-time graph?
Area under the graph (because it is equal to force x time).
156
How can the force of an impact be reduced?
Increasing the impact time.
| For example packaging takes longer to deform on impact, so absorbs shock and protects packaged object.
157
Give some ways in which vehicles have safety features to reduce the force of an impact.
* Crumple zones -> Crumple on impact and increase time of crash
* Seat belts -> Stretch slightly to increase stopping time
* Air bags -> Slow passengers down more slowly and prevent them from hitting hard surfaces
158
When work is done...
...energy is transferred.
159
What is work?
The amount of energy transferred from one form to another.
160
Why is a force needed to move an object?
You have to overcome another force to move the object.
161
What is work done against when lifting a box and what is the final energy form?
* Work done against: Gravity
| * Final energy form: GPE
162
What is work done against when pushing a chair across a level floor and what is the final energy form?
* Work done against: Friction
| * Final energy form: Heat
163
What is work done against when pushing two magnetic north poles together and what is the final energy form?
* Work done against: Magnetic force
| * Final energy form: Magnetic energy
164
What is work done against when stretching a spring and what is the final energy form?
* Work done against: Stiffness of spring
| * Final energy form: Elastic potential energy
165
What is the equation that relates work done, force and distance?
Work done (J) = Force (N) x Distance (m)
W = F x d
166
What is the unit for work done?
Joules (J)
167
When work is done on an object, is the object’s energy equal to the work done?
No, it is the CHANGE in the object’s energy that is equal to the work done.
168
When using “W = F x d” with a changing force, what value of F is used?
The average force.
169
In “W = F x d”, what is F?
The force CAUSING MOTION.
170
What is an assumption of “W = F x d”?
The direction of the force is the same as the direction of movement (otherwise you must resolve forces).
171
Define a joule.
The work done when a force of 1N moves an object through a distance of 1 metre.
172
When using the equation “W = F x d” with a force in a direction different to the direction of motion, what must you do?
* Resolve the force so that you have the component that is equal to the direction of motion.
* Now use “W = F x d”
(See page 62 of revision guide)
173
Remember, the sledge is only moving horizontally
...
174
For a force F acting to the top right at an angle θ above the horizontal causing a motion horizontally to the right, give an equation for the work done.
W = (Fcosθ) x d
175
For a force F acting to the top right at an angle θ above the horizontal causing a motion horizontally to the right, why does the vertical component not have an effect on work done?
* It is not causing horizontal motion.
| * It is only balancing out some of the weight of the object, so there is a smaller reaction force (in a sledge example).
176
On a force-displacement graph, what does the area under the graph give you and why?
* The work done
| * Because of “W = F x d”
177
What is power?
* The rate of doing work
| * P = ΔW / Δt
178
What is the equation for power?
Power (W) = Change in energy or work (J) / Change in time (s)
P = ΔW / Δt
179
What is the unit for power?
Watt (W)
180
Define a watt.
The rate of energy transfer equal to 1 joule per second.
181
What equation relates velocity, power and force?
Power (W) = Force (N) x Velocity (m/s)
P = F x v
182
Derive the equation that relates power, force and velocity.
* P = W / t
* W = Fd
* Therefore, P = Fd / t = F x (d/t)
* v = d / t
* Therefore, P = F x v
183
For a force acting at angle θ to the direction of motion, what is the equation for the work done?
W = (Fcosθ) x d
184
For a force acting at angle θ to the direction of motion, what is the equation for the power?
P = (Fcosθ) x v
185
State the principle of conservation of energy.
* Energy cannot be created or destroyed.
| * Energy can be transferred from one form or another, but the total amount of energy in a closed system will not change.
186
In a closed system, total energy in...
...equals total energy out.
187
What is the equation for efficiency in terms of power?
Efficiency = Useful output power / Input power
188
When will the principle of conservation of energy come up?
When doing questions about changes between kinetic and potential energy.
189
What is kinetic energy?
The energy of an object due to movement.
190
What is the formula for kinetic energy?
Energy (J) = 1/2 x Mass (kg) x (Velocity (m/s²))²
E = 1/2 x m x v²
191
What are two types of potential energy?
* Gravitational
| * Elastic
192
What is gravitational potential energy?
The energy something gains if you lift it up.
193
What is the equation for GPE?
ΔGPE (J) = Mass (kg) x G.F.S. (N/kg) x ΔHeight (m)
ΔE = m x g x Δh
194
What is elastic strain energy (aka elastic potential energy)?
The energy stored in a stretched rubber band or spring, for example.
195
What is the equation for elastic strain energy?
Energy (J) = 1/2 x Spring Constant x (Extension (m))²
E = 1/2 x k x (Δl)²
196
Where does the energy for human interactions come from and what energy transfers occur?
* Food
* Chemical energy is converted to other forms, such as kinetic energy
* Some is wasted in, for example, heat
197
Describe the energy transfers when a ball is thrown vertically up.
* When the ball goes up, the kinetic energy is converted into GPE
* When the ball comes down, the GPE is converted back into kinetic energy
198
Describe the energy transfers when a person slides down a slide.
The gravitational potential energy is converted into kinetic energy.
199
Describe the energy transfers when a person jumps on a trampoline.
* When bouncing up, Elastic energy -> Kinetic energy -> GPE
| * When coming down, GPE -> Kinetic energy -> Elastic energy
200
What forces are involved when jumping on a trampoline?
Weight force.
| Tension in springs and trampoline material.
201
In reality there are other energy transfers in jumping on a trampoline, what are these?
To keep jumping at the same height each time, you would have to use some force from your muscles.
Each time the trampoline stretches, some heat is generated in the trampoline material.
202
In energy conservation problems, what must you usually assume?
That frictional forces are negligible.
203
Remember to revise conservation of energy problems.
Pg 65 of revision guide.
204
Question:
Remember: the height from the ground is different from the length of string.
You need to find change in height
205
In energy transfer problems where kinetic energy and GPE are exchanged, what must you do?
* Put the kinetic energy change equal to the GPE change.
| * mgΔh = 1/2mv²
206
How can a motor lifting a mass vertically be used to investigate efficiency?
