Mechanics Flashcards
Four equations of motion
v=u+at
s=ut+1/2at^2
v^2=u^2+2as
S=1/2(u+v)t
what does the gradient on a velocity time graph mean
straight = Constant
acceleration
Curved = Changing acceleration
Newtons First law
an object will remain at rest or move with a constant velocity unless acted on by a resultant force. If the net force is zero, then the object will not change its state of motion. This is also known as the law of inertia, because it implies that objects resist changes in their motion.
Newtons second law
Force (N) = mass(kg) x acceleration (ms^-2)
- use when an object experiences a resultant force (accelerating or deaccelerating)
Newtons third law
For every action there is an equal and opposite reaction
- “if object A exerts a force on object B then object B exerts an equal and opposite force on object A”
Third law rules
- equal in magnitude
- opposite in direction
- the same type of force
- acting on different objects
mass of earth
6 x 10^24
size of an atom
10^-10 - 10^-15
why does the earth move towords a person using newtons third law
When a person stands on the Earth, the Earth exerts a gravitational force on the person, pulling them down. This is the person’s weight. According to Newton’s third law, the person also exerts a gravitational force on the Earth, pulling it up. This force is equal in magnitude but opposite in direction to the Earth’s force on the person2
However, the person does not notice this force because it is very small compared to the Earth’s mass. The Earth’s mass is about 6 x 10^24 kg, while the average human mass is about 70 kg. This means that the Earth’s acceleration due to the person’s force is about 10^-23 m/s^2, which is negligible. The person’s acceleration due to the Earth’s force is about 9.8 m/s^2, which is noticeable3
Therefore, the Earth does move towards the person, but by a very tiny amount that is impossible to measure.
what is statics?
statics is the section of mechanics that studies objects that are in static equilibrium. in other words - objects that are moving at a constant velocity or are stationary. the key concept to apply is: the sum of the forces = 0
EF = 0
force is a vector
what are dynamics?
Dynamics is the section of mechanics that studies the motion of bodies under the action of forces
in other words- objects that are accelerating due to a net resultant force.
The key concept to apply is: The sum of the forces = m x a
or EF=ma
Force is a vector
how to resolve a vector
1.Draw a sketch of the vector and its components, using a right-angled triangle.
2. Label the magnitude and direction of the vector, and the angle it makes with the horizontal or vertical axis.
3.Choose a suitable coordinate system, such as x and y, for the components.
4.Use trigonometry, such as sine and cosine, to find the magnitude of the horizontal and vertical components.
5. Remember that the horizontal component is adjacent to the angle, and the vertical component is opposite to the angle.
pythagoras formula
a^2+b^2=c^2
only usable on right angle traingles
Soh
sin(x)=Opposite/Hypotenuse
cah
cos(x)= adjacent/hypotenuse
toa
tan(x)=opposite/adjacent
Cosline rule
Cos(A)=b^2+c^2-a^2/2bc
a^2=b^2+c^2-2bcCos(A)
sin rule
when working out side=
a/Sin(A)=b/Sin(B)=c/Sin(C)
when working out angle=
Sin(A)/a=Sin(B)/b=Sin(C)/c
Displacement- time graph?
This graph shows how the displacement (position) of an object changes over time
gradient of displacement - time graph?
The gradient of the graph is the velocity of the object. The steeper the graph, the faster the object is moving. A horizontal line means the object is at rest. A curved line means the object is accelerating or decelerating.
how to find instantaneous velocity?
To find the instantaneous velocity of an object, you need to draw a tangent to the curve and calculate its gradient2
Velocity - time graph?
This graph shows how the velocity (speed and direction) of an object changes over time
gradient of velocity - time graph?
The gradient of the graph is the acceleration of the object. A positive gradient means the object is speeding up. A negative gradient means the object is slowing down. A horizontal line means the object is moving at a constant speed.
area under a velocity - time graph?
The area under the graph is the displacement of the object. To find the displacement of an object, you need to calculate the area under the graph using the trapezium rule or other methods
Acceleration - time graph?
This graph shows how the acceleration (rate of change of velocity) of an object changes over time.
gradient of acceleration - time graph?
The gradient of the graph is the rate of change of acceleration, also known as the jerk. A positive gradient means the object is increasing its acceleration. A negative gradient means the object is decreasing its acceleration. A horizontal line means the object has a constant acceleration.
area under an acceleration-time graph?
The area under the graph is the change in velocity of the object. To find the change in velocity of an object, you need to calculate the area under the graph using the trapezium rule or other methods4
definition of speed
the rate of change of distance
definition of velocity
the rate of change of displacement
equation for speed and velocity
v= change in displacement / change in time
s= change in distance/change in time
both measured in ms^-1
definition of acceleration
the rate of change of velocity
acceleration equation
a= final velocity(v) - initial velocity(u) / change in time (t)
measured in ms^-2
decelerating is slowing down and is indicated using a minus sign (-)
what must always be true when using suvat
the acceleration must be uniform
what is a scalar quantity
is one that has a magnitude not a direction
what is a vector quantity
a vector quantity is one that has a magnitude and a fixed direction
Give five examples of scalar quantities
distance, speed, mass, energy , temperature
give 5 examples of vector quantities
displacement, velocity, acceleration, momentum, force
how is a vector quantity represented
- as an arrow
- the direction of the arrow represents the direction of the quantity
- the length of the arrow represents the magnitude of the quantity
what does resolving the vector involve
splitting the vector into two perpendicular components
describe the relationship between perpindicular components
they are independent of eachother
how should the components of a projectile be handled when carrying out calculations
- the horizontal and verticle components are independent of each other and so should be treated seperately
- suvat should be used separately for each component
what is a moment
is the turning effect of a force
state the equation used to calculate the moment of a force
moment of force = force x distance from pivot
what distance must we use
the perpindicular distance between the line of action of the force and the axis of rotation
what is the unit of moment
NM
what is the priniciple of moments
for an object to be in equillibrium the sum of the clockwise moments about a point must be equal to the sum of the anticlockwise moments
what is an objects centre of gravity?
the single point through which the objects entire weight can be said to act
what will happen if the line of action an objects centre of gravity lies outside its base
the objects weight will produce a resultant moment and so if unsupported may fall
work done equation
w = f x Change in S
what force is used when calculating the work done by a force over a distance
the component of the force this is in the direction of the objects motion
conservation of energy
the law of conservation of energy states that energy can not be created or destroyed - it can only br transferred between different forms
