Topic 2 Mechanics Flashcards
Define: displacement.
The distance in a given direction from a fixed origin. It is a vector quantity.
What is the standard index unit for displacement?
m, metres
What is the symbol for displacement?
s
Define: velocity.
Velocity is the rate of change of displacement. It is a vector quantity.
What is the formula for calculating velocity?
v = s / t
- v is velocity in m s-1
- s is change in displacement in m
- t is time in s
What is the standard index unit for velocity?
m s^-1
What is the symbol for velocity?
u = initial velocity v = final velocity
Define: speed.
Speed is the rate of change of distance. It is a scalar quantity.
What is the formula for calculating speed?
v = d/t Where: v is speed in m s^-1 d is distance in m t is time in s
What is the standard index unit for speed?
m s^-1
What is the symbol for speed?
u = initial speed v = final speed
How are speed and velocity different?
Velocity has direction and is a vector quantity whereas speed is a scalar quantity.
Define: acceleration.
The rate of change with time of the velocity vector. It is a vector quantity.
What is the formula for calculating acceleration?
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
What is the standard unit for acceleration?
m s^-2
What is the symbol for acceleration?
a
What is an instantaneous value of speed?
Speed at a particular moment in time
What is an instantaneous value of velocity?
Velocity at a particular moment in time
What is an instantaneous value of acceleration?
Acceleration at a particular moment in time
What is an average value of speed?
Speed over a period of time.
What is an average value of velocity?
Velocity over a period of time
What is an average value of acceleration?
Acceleration over a period of time
Under which conditions can the equations for uniformly accelerated motion be applied?
Under conditions where the acceleration is constant.
What is the equation of uniformly accelerated motion that involves initial speed, final speed, acceleration and time?
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
What is the equation of uniformly accelerated motion that involves displacement, initial speed, final speed, and time?
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
What is the equation of uniformly accelerated motion that involves displacement, initial speed, final speed and acceleration?
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
What is the equation of uniformly accelerated motion that involves displacement, initial speed, acceleration and time?
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
When is an object in free fall?
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.
Why is free fall an example of uniformly accelerated motion?
As the only force acting on the object is that of gravity.
What is terminal velocity?
The point by which the velocity of a falling object remains constant and acceleration is zero.
What effect does terminal velocity have on an object?
- At the start, the object accelerates downwards because of its weight. There is no air resistance. There is a resultant force acting downwards
- 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.
- 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.
What does the gradient of a displacement-time graph give?
The velocity.
What does the gradient of a velocity-time graph give?
The acceleration.
What does the area under a velocity-time graph give?
The displacement.
What does the gradient of an acceleration-time graph give?
The rate of change of acceleration.
What does the area under an acceleration-time graph give?
The change in velocity.
Define: force.
The cause of a deformation or a velocity change. A force is a vector quantity.
What is the standard unit for force?
N, Newtons
Define: weight.
Gravitational force. The force between objects as a result of their masses.
What is the formula for weight on Earth?
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
What is the symbol for tension?
T
Define: drag
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.
What effect does a higher speed have on drag force?
Higher speed equals higher drag force.
When will an object experience upthrust?
When it is in a fluid medium.
When will an object float?
When the upthrust force is equal to the weight.
Define: frictional forces.
Forces that oppose the motion of a body.
What is the symbol for a frictional force?
f
What does Hooke’s law state?
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.
What is the standard unit for the spring constant?
N m-1
What are the equations for Hooke’s law? (2)
- F∞x
- F=kx
Define: resultant force.
The overall force acting on an object when all the individual forces acting on that object have been added together.
What will happen if two objects are dropped at the same time in a vacuum?
They will fall at the same rate due to the lack of air resistance.
State Newton’s First Law of Motion.
An object continues in uniform motion in a straight line or at rest unless a resultant external force acts.
State the condition for translational equilibrium.
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.
State Newton’s Second Law of Motion.
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.
What are the two equations for Newton’s Second Law of Motion?
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
Define: linear momentum.
A vector quantity whose direction is the same as that of the velocity of the body.
What is the symbol for momentum?
p
What is the standard unit for momentum?
kg m s^1 OR N s
Define: impulse.
The area under the curve of a force-time graph and equals the total momentum change of the mass.
What is the formula for momentum?
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
What is the formula for impulse?
∆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
State the law of conservation of linear momentum.
When no external forces act on a system, the total momentum of the system stays the same.
State Newton’s Third Law of Motion.
If Body A exerts a force F on Body B, then Body B exerts an equal but opposite force on Body A.
FAB = -FBA
Define: work
Work done is the energy transferred. It is a vector quantity.
What is the standard unit for work?
Joules, J
What is the formula for work?
W = F s
- W is the work done in J
- F is the force applied in N
- s is the displacement covered in m
What does the area under a force-displacement graph show?
The work done by a non-constant force.
Define: kinetic energy.
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
How are work done and kinetic energy related?
The work done by the net force on a body is equal to the change in the kinetic energy of the body.
What is the equation for the change in gravitational potential energy.
∆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
State the principle of conservation of energy.
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
What are the nine different forms of energy?
- Chemical
- Kinetic
- Elastic potential
- Electrical
- Thermal
- Sound
- Gravitational potential
- Nuclear
- Light
Define: inelastic collision.
An inelastic collision is where kinetic energy is lost.
Define: power.
Power is the rate at which work is done.
What is the equation for power?
P = E / t
- P is power in W
- E is energy transferred in J
- t is time in s
What is the standard unit for power?
Watt, W or J s-1
What is the formula that relates power, force and velocity?
P = F v
- P is power in W
- F is force in N
- v is velocity in m s-1
What is the formula that relates power, work and time?
P=(∆W)/(∆t)
Define: efficiency.
The ratio of useful energy to the total energy transferred.
What is the formula for efficiency?
efficiency
= useful out / total in
= Wout / Win
= Pout / Pin
When is an object in static equillibrium?
When it is at rest.
When is an object in dynamic equilibrium?
When it is moving at a constant velocity.
How is energy lost in collisions?
Almost always in reality collisions are inelastic as energy is lost as sound and friction.
Define: elastic collision
An elastic collision is when the total kinetic energy of the objects is the same before and after the collision.
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?
The magnitude of the component of weight of the block parallel to the plane.
How would a displacement-time graph of an object in free fall be drawn?
How would a velocity-time graph of an object in free fall be drawn?
How would an acceleration-time graph of an object in free fall be drawn?
Determine relative velocity in one and in two dimensions.
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.
Identify 9 forces.
- Gravitational force/weight
- Electrostatic force
- Magnetic force
- Normal reaction
- Friction
6.
- Compression
- Upthrust
- Lift
Define: gravitational force/weight
The force between objects as a result of their masses.
Define: electrostatic force
The force between objects as a result of their electric charges.
Define: magnetic force
The force between magnets and/or electric currents.
Define: normal reaction
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.
Define: friction
The force that opposes the relative motion of two surfaces and acts along the surfaces.
Define: tension
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.
Define: compression.
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.
Define: upthrust
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.
Define: lift
Can be exerted on an object when a fluid flows over it in an asymmetrical way.
How can work done be calculated when displacement is not in the same direction as the force?
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
How can work done be calculated when lifting something vertically?
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
How can work done be calculated when compressing or extending a spring?
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
Define: totally inelastic collision
A collision where a large amount of mechanical energy is lost but momentum is conserved.
