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IB Physics HL > Topic 2: Mechanics > Flashcards

Topic 2: Mechanics Flashcards

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1
Q

Define: displacement.

A

The distance in a given direction from a fixed origin. It is a vector quantity.

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2
Q

What is the standard index unit for displacement?

A

m, metres

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3
Q

What is the symbol for displacement?

A

s

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4
Q

Define: velocity.

A

Velocity is the rate of change of displacement. It is a vector quantity.

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5
Q

What is the formula for calculating velocity?

A

v = s / t

  • v is velocity in m s-1
  • s is change in displacement in m
  • t is time in s
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6
Q

What is the standard index unit for velocity?

A

m s^-1

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7
Q

What is the symbol for velocity?

A

u = initial velocity v = final velocity

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8
Q

Define: speed.

A

Speed is the rate of change of distance. It is a scalar quantity.

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9
Q

What is the formula for calculating speed?

A

v = d/t Where: v is speed in m s^-1 d is distance in m t is time in s

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10
Q

What is the standard index unit for speed?

A

m s^-1

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11
Q

What is the symbol for speed?

A

u = initial speed v = final speed

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12
Q

How are speed and velocity different?

A

Velocity has direction and is a vector quantity whereas speed is a scalar quantity.

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13
Q

Define: acceleration.

A

The rate of change with time of the velocity vector. It is a vector quantity.

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14
Q

What is the formula for calculating acceleration?

A

a = v/t

  • a is acceleration in m s-2
  • v is change in velocity in m s-1
  • t is change in time in s
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15
Q

What is the standard unit for acceleration?

A

m s^-2

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16
Q

What is the symbol for acceleration?

A

a

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17
Q

What is an instantaneous value of speed?

A

Speed at a particular moment in time

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18
Q

What is an instantaneous value of velocity?

A

Velocity at a particular moment in time

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19
Q

What is an instantaneous value of acceleration?

A

Acceleration at a particular moment in time

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20
Q

What is an average value of speed?

A

Speed over a period of time.

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21
Q

What is an average value of velocity?

A

Velocity over a period of time

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22
Q

What is an average value of acceleration?

A

Acceleration over a period of time

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23
Q

Under which conditions can the equations for uniformly accelerated motion be applied?

A

Under conditions where the acceleration is constant.

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24
Q

What is the equation of uniformly accelerated motion that involves initial speed, final speed, acceleration and time?

A

v = u + a t

  • v is final velocity in m s-1
  • u is initial velocity in m s-1
  • a is acceleration in m s-2
  • t is time in s
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25
Q

What is the equation of uniformly accelerated motion that involves displacement, initial speed, final speed, and time?

A

s = (( u + v) / 2) t

  • s is displacement in m
  • t is time in s
  • u is initial velocity in m s-1
  • v is final velocity in m s-1
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26
Q

What is the equation of uniformly accelerated motion that involves displacement, initial speed, final speed and acceleration?

A

v2 = u2 + 2 a s

  • v is final velocity in m s-1
  • u is initial velocity in m s-1
  • a is acceleration in m s-2
  • s is displacement in m
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27
Q

What is the equation of uniformly accelerated motion that involves displacement, initial speed, acceleration and time?

A

s = u t + 1/2 a t2

  • s is displacement in m
  • u is initial velocity in m s-1
  • t is time in s
  • a is acceleration in m s-2
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28
Q

When is an object in free fall?

A

When an object is falling under the sole influence of gravity or the effects of air resistance are being ignored. In the absence of air resistance, all objects have the same acceleration of free-fall, independent of their mass.

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29
Q

Why is free fall an example of uniformly accelerated motion?

A

As the only force acting on the object is that of gravity.

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30
Q

What is terminal velocity?

A

The point by which the velocity of a falling object remains constant and acceleration is zero.

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31
Q

What effect does terminal velocity have on an object?

A
  1. At the start, the object accelerates downwards because of its weight. There is no air resistance. There is a resultant force acting downwards
  2. As it gains speed, the object’s weight stays the same, but the air resistance on it increases. There is a resultant force acting downwards.
  3. Eventually, the object’s weight is balanced by the air resistance. There is no resultant force and the object reaches a steady speed, called the terminal velocity.
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32
Q

What does the gradient of a displacement-time graph give?

A

The velocity.

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33
Q

What does the gradient of a velocity-time graph give?

A

The acceleration.

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34
Q

What does the area under a velocity-time graph give?

A

The displacement.

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35
Q

What does the gradient of an acceleration-time graph give?

A

The rate of change of acceleration.

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36
Q

What does the area under an acceleration-time graph give?

A

The change in velocity.

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37
Q

Define: force.

A

The cause of a deformation or a velocity change. A force is a vector quantity.

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38
Q

What is the standard unit for force?

A

N, Newtons

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39
Q

Define: weight.

A

Gravitational force. The force between objects as a result of their masses.

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40
Q

What is the formula for weight on Earth?

A

W = m g

  • W is weight in N
  • m is the mass of the body in kg
  • g is the gravitational field strength of Earth in m s-2 OR N kg-1
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41
Q

What is the symbol for tension?

A

T

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42
Q

Define: drag

A

Forces that oppose the motion of a body through a fluid. They are directed opposite to the velocity of the body and generally depend on the speed of that body.

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43
Q

What effect does a higher speed have on drag force?

A

Higher speed equals higher drag force.

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44
Q

When will an object experience upthrust?

A

When it is in a fluid medium.

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45
Q

When will an object float?

A

When the upthrust force is equal to the weight.

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46
Q

Define: frictional forces.

A

Forces that oppose the motion of a body.

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47
Q

What is the symbol for a frictional force?

A

f

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48
Q

What does Hooke’s law state?

A

Up to the elastic limit, the extension, x of a spring is proportional to the tension force, F. The constant of proportionality k is called the spring constant.

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49
Q

What is the standard unit for the spring constant?

A

N m-1

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50
Q

What are the equations for Hooke’s law? (2)

A
  1. F∞x
  2. F=kx
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51
Q

Define: resultant force.

A

The overall force acting on an object when all the individual forces acting on that object have been added together.

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52
Q

What will happen if two objects are dropped at the same time in a vacuum?

A

They will fall at the same rate due to the lack of air resistance.

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53
Q

State Newton’s First Law of Motion.

A

An object continues in uniform motion in a straight line or at rest unless a resultant external force acts.

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54
Q

State the condition for translational equilibrium.

A

If the resultant force of an object is zero; an object that is constantly at rest and an object that is moving with uniform velocity in a straight line must be in equilibrium.

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55
Q

State Newton’s Second Law of Motion.

A

The net force on a body is proportional to that body’s acceleration and is in the same direction as the acceleration. The rate of change of momentum of a body is equal to the net external force acting on the body.

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56
Q

What are the two equations for Newton’s Second Law of Motion?

A

F = m a

  • F is force in N
  • m is mass in kg
  • a is acceleration in m s-2

F=(∆p)/(∆t)

  • F is force in N
  • p is momentum in N s-1
  • t is time in s
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57
Q

Define: linear momentum.

A

A vector quantity whose direction is the same as that of the velocity of the body.

58
Q

What is the symbol for momentum?

A

p

59
Q

What is the standard unit for momentum?

A

kg m s^1 OR N s

60
Q

Define: impulse.

A

The area under the curve of a force-time graph and equals the total momentum change of the mass.

61
Q

What is the formula for momentum?

A

p = m v

  • p is linear momentum in kg m s^-1 OR N s
  • m is mass in kg
  • v is velocity in m s^-1
62
Q

What is the formula for impulse?

A

∆p = F ∆t = m ∆V

  • p is linear momentum in kg m s-1 OR N s
  • F is force in N
  • t is time in s
63
Q

State the law of conservation of linear momentum.

A

When no external forces act on a system, the total momentum of the system stays the same.

64
Q

State Newton’s Third Law of Motion.

A

If Body A exerts a force F on Body B, then Body B exerts an equal but opposite force on Body A.

FAB = -FBA

65
Q

Define: work

A

Work done is the energy transferred. It is a vector quantity.

66
Q

What is the standard unit for work?

A

Joules, J

67
Q

What is the formula for work?

A

W = F s

  • W is the work done in J
  • F is the force applied in N
  • s is the displacement covered in m
68
Q

What does the area under a force-displacement graph show?

A

The work done by a non-constant force.

69
Q

How are work done and kinetic energy related?

A

The work done by the net force on a body is equal to the change in the kinetic energy of the body.

70
Q

Define: kinetic energy.

A

The energy of a body or a system with respect to the motion of the body or of the particles in the system.

E = 1/2 m v^2

Where:

E is kinetic energy in J

m is mass in kg

v is velocity in m s^-1

71
Q

What is the equation for the change in gravitational potential energy.

A

∆E = m g ∆h

  • E is gravitational potential energy in J
  • m is mass in kg
  • g is gravitational field strength in (on Earth = 9.81) N kg^-1
72
Q

State the principle of conservation of energy.

A

Energy cannot be created or destroyed. It can only be transferred from one form to another:

  • the total energy of any closed system must be constant
  • energy is neither created or destroyed, it only changes form
  • there is no change in the total energy of the Universe
73
Q

What are the nine different forms of energy?

A
  1. Chemical
  2. Kinetic
  3. Elastic potential
  4. Electrical
  5. Thermal
  6. Sound
  7. Gravitational potential
  8. Nuclear
  9. Light
74
Q

Define: inelastic collision.

A

An inelastic collision is where kinetic energy is lost.

75
Q

Define: power.

A

Power is the rate at which work is done.

76
Q

What is the equation for power?

A

P = E / t

  • P is power in W
  • E is energy transferred in J
  • t is time in s
77
Q

What is the standard unit for power?

A

Watt, W or J s-1

78
Q

What is the formula that relates power, force and velocity?

A

P = F v

  • P is power in W
  • F is force in N
  • v is velocity in m s-1
79
Q

What is the formula that relates power, work and time?

A

P=(∆W)/(∆t)

80
Q

Define: efficiency.

A

The ratio of useful energy to the total energy transferred.

81
Q

What is the formula for efficiency?

A

efficiency

= useful out / total in

= Wout / Win

= Pout / Pin

82
Q

When is an object in static equillibrium?

A

When it is at rest.

83
Q

When is an object in dynamic equilibrium?

A

When it is moving at a constant velocity.

84
Q

How is energy lost in collisions?

A

Almost always in reality collisions are inelastic as energy is lost as sound and friction.

85
Q

Define: elastic collision

A

An elastic collision is when the total kinetic energy of the objects is the same before and after the collision.

86
Q

A wooden block is sliding down an inclined plane at a constant speed. What is the magnitude of the frictional force between the block and the plane equal to?

A

The magnitude of the component of weight of the block parallel to the plane.

87
Q

How would a displacement-time graph of an object in free fall be drawn?

A
88
Q

How would a velocity-time graph of an object in free fall be drawn?

A
89
Q

How would an acceleration-time graph of an object in free fall be drawn?

A
90
Q

Determine relative velocity in one and in two dimensions.

A

If two objects are moving in the same straight line but are travelling at different speeds, then we can work out their relative velocities by addition or subtraction.

91
Q

Identify 9 forces.

A
  1. Gravitational force/weight
  2. Electrostatic force
  3. Magnetic force
  4. Normal reaction
  5. Friction
  6. Tension
  7. Compression
  8. Upthrust
  9. Lift
92
Q

Define: gravitational force/weight

A

The force between objects as a result of their masses.

93
Q

Define: magnetic force

A

The force between magnets and/or electric currents.

94
Q

Define: normal reaction

A

The force exerted when a body touches another body. This force is perpendicular to the body exerting the force. If two surfaces are smooth then this is the only force that acts between them.

95
Q

Define: friction

A

The force that opposes the relative motion of two surfaces and acts along the surfaces.

96
Q

Define: tension

A

The force that arises in any body when it is stretched. When a string (or a spring) is stretched, it has equal and opposite forces on its ends pulling outwards. The tension force is the force that the end of the string applies to another object.

97
Q

Define: electrostatic force

A

The force between objects as a result of their electric charges.

98
Q

Define: compression.

A

When a rod is compressed it has equal and opposite forces on its ends pushing inwards. The compression force is the force that the ends of the rod applies to another object. This is the opposite of tension.

99
Q

Define: upthrust

A

The upward force that acts on an object when it is submerged in a fluid. It is the force that causes some objects to float in water.

100
Q

Define: lift

A

Can be exerted on an object when a fluid flows over it in an asymmetrical way.

101
Q

How can work done be calculated when displacement is not in the same direction as the force?

A

W = F s cos(θ)

Where:

W is work done in N m OR J

F is the force in N

s is the distance in m

102
Q

How can work done be calculated when lifting something vertically?

A

W = m g h

Where:

W is work done in N m OR J

m is mass in kg

g is Earth’s gravitational field strength = 10 N kg-1

h is height change in m

103
Q

How can work done be calculated when compressing or extending a spring?

A

W = (k x^2) / 2

Where:

W is work done in N m OR J

k is the spring constant in N m-1

x is the extension in m

104
Q

Define: totally inelastic collision

A

A collision where a large amount of mechanical energy is lost but momentum is conserved.

105
Q

When an object is thrown directly up, what is its velocity at maximum height and what would this look like in an equation?

A

velocity is zero, therefore:

0 = u - gt

which comes from:

v = u + at

106
Q

When an object is thrown directly up, what is its maximum height and what would this look like in an equation?

A

Maximum height:

hmax = ut - 1/2(gt2)

which comes from:

s = ut + 1/2(at2)

107
Q

When an object is thrown directly up, what is its velocity2 at maximum height and what would this look like in an equation?

A

velocity = 0 so velocity2 = 0, therefore:

0 = u2 - 2gh

which comes from:

v2 = u2 + 2as

108
Q

A situation in which an object travels up and back down, what is the time period?

A

As the object travels up and down, the whole motion takes a time of 2t

109
Q

An object is projected upwards at an angle of θ to the ground. What is its initial velocity (in the vertical direction)?

A

u sin θ

110
Q

An object is projected upwards at an angle of θ to the ground. What is its initial velocity (in the horizontal direction)?

A

u cos θ

111
Q

An object is projected upwards at an angle of θ to the ground. What is the total horizontal range when it hits the floor?

A

2t (u cos θ)

112
Q

What is the procedure for drawing free-body diagrams?

A
  • Begin by sketching the general situation with all the bodies that interact (e.g. ball and earth)
  • Select the body of interest (e.g. ball)
  • Draw, to scale, and label all the forces that act on this body due to the other bodies and forces.
  • Add force vectors together (either by drawing or calculation) to give the net force acting on the body. The sum can later be used to draw other conclusions about the motion of the object.
113
Q

Define: translational equilibrium

A

When an object is either at rest or moving at a constant velocity (not just constant speed)

114
Q

What forces are acting on an object at translational equilibrium (at rest or constant velocity)?

A

From Newton’s I and II laws, as there is no change in velocity, there must be no resultant force acting on the object, i.e. all forces are in balance.

115
Q

Define: static friction

A

Friction when there is no relative movement between the surfaces

116
Q

Define: dynamic friciton

A

Friction when there is relative movement between the objects

117
Q

What does the amount of friction depend on?

A

The two surfaces, not just one.

118
Q

What is the static friction force equation?

A

Ff ≤ μsR

where:

  • Ff is the frictional force exerted by the surface on the object
  • μs is the coefficient of static friction
  • R is the normal reaction of the surface on the object, this is the weight (mg) if flat
119
Q

What does the static friction equation show?

A

The “less than or equal to” symbol shows us that the static friction can vary from zero up the maximum value of the pull on the object, at which point the object is just about to move.

Once the pull force exceeds the frictional force, there is no more static friction as the object is dynamic.

120
Q

What is the dynamic friction force equation?

A

Ff = μdR

where:

  • Ff is the frictional force exerted by the surface on the object
  • μd is the coefficient of dynamic friction
  • R is the normal reaction of the surface on the object, this is the weight (mg) if flat
121
Q

What does the dynamic friction equation show?

A

The frictional force is constant and, according to simple theory, is not thought to be dependant on the relative speed between the two surfaces.

122
Q

What is resistance in a fluid (gas or liquid) called?

A

Drag (force)

123
Q

What is terminal velocity?

A

When the velocity is maximised i.e. no more acceleration - forces are balanced and the object is at translational/dynamic equilibrium.

124
Q

Define: elastic potential energy

A

After a force has acted on an object to change its shape, some materials are able to revert back to their original shape by storing the required energy after the force is removed.

125
Q

At what point does an object reach terminal velocity?

A

When the drag force is equal to weight (mg)

126
Q

When speed doubles what typically happens to the drag force?

A

It increases by at least a factor of four.

NB: this is only a generalisation and not entirely accurate

127
Q

What is one joule in terms of force?

A

One joule is one newton metre

or

One joule is one newton of force through a distance of 1 metre

128
Q

As work done is in the direction of the force, what must you do if the force acts at an angle to the movement?

A

Multiply the work done by cos θ where θ is the angle between the force direction and the direction of movement.

129
Q

What is the area underneath a force-displacement graph?

A

The work is done, as W = Fs

130
Q

Derive the kinetic energy equation

A

acceleration is a = F/m (Newton’s II law)

therefore v = 0 + (F/m)T (SUVAT)

so, after rearranging, F = (mv)/T

the distance travelled, s = (v+0)T/2 (SUVAT)

Work done, W = Fs, is the kinetic energy so:

EK = mv/T x vT/2

EK = mv2/2 = 1/2(mv2)

131
Q

What type of force is the gravitational force?

A

Conservative, as they conserve energy

132
Q

ANSWER:

A snowboarder is moving down a curved slope starting from rest (u = 0). The vertical change in height of the slope is Δh = 50m.

What is the speed of the snowboarder at the bottom of the slope?

Air resistance and friction are negligible.

A

As air resistance and friction are negligible, the decrease in GPE is equal to the increase in KE.

mgΔh = 1/2(mv2)

(50)(9.81) = 1/2v2

v2 = 2 x 50 x 9.81

v = √(2x50x9.81)

v = 31 ms-1

133
Q

How is GPE related to work done?

A

GPE is the work done when an object is raised at a constant speed through a change in height of Δh.

Work done = force x distance

GPE = mg x Δh

134
Q

How should you approach this type of question:

“A snowboarder is moving down a curved slope starting from rest (u = 0). The vertical change in height of the slope is Δh = 50m.

What is the speed of the snowboarder at the bottom of the slope?”

A

Use GPE and KE equations.

Do NOT use SUVAT equations, despite they may give the same answer for this question. The examiner WILL discount your answer as the physics is incorrect.

135
Q

What is the area below a force-extension graph?

A

Work done extending the spring.

136
Q

What is the thermal energy produced when loading and unloading a spring?

A

Thermal energy produced = work done (loading) - work done (unloading)

or the area under loading graph - area under unloading graph.

137
Q

Where is the elastic limit of a spring shown on a diagram?

A

As force-extension graphs follow a linear line, once the line curves/flatten/inverses, the elastic limit has been reached.

138
Q

How is momentum transferred?

A

Through collisions

139
Q

In an elastic collision of two objects with identical mass, what happens to the relative velocity of both objects?

A

As the first object approaches the second, stationary object, it has a velocity of u.

As no energy is lost (elastic collision), all the kinetic energy is transferred to the second object.

As the second object has the same mass, it will travel as a velocity v, which is identical to u.

Momentum is conserved.

140
Q

What is conserved in elastic collisions:

  • momentum?
  • total energy?
  • kinetic energy?
A
  • momentum is conserved
  • total energy is conserved
  • kinetic energy is not conserved (some lost to heat)

IB Physics HL (13 decks)

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