Mechanics Goodnotes Recap Flashcards
Scalar Quantity?
A scalar quantity only has magnitude
Vector Quantity?
A vector quantity has a magnitude and a direction
Scalar Quantity Examples?
Examples of scalar quantities are speed, distance, time
Vector Quantity Examples?
Displacement, Velocity, Momentum
Scaled Diagrams?
Drawn from tip to tail and have length measured and the angle of the resultant vector found. Scaled diagrams are useful in finding the resultant vector of two vectors
Perpendicular Vectors?
If two vectors are perpendicular to each other it means trigonometry can be used to work out the angle between the vectors and the resultant vector
Resolving Vectors?
Knowing the resultant vector, a starting point is split into two components at right angles to each other. The two components, horizontal and vertical, are perpendicular to each other so form a right angled triangle which can have the known quantities re-arranged to find the unknown vector
Slope and Vectors?
If an object is on a slope, the angle of the slope is adjacent to the object, leading to weight of the object being perpendicular to the slope and meeting the weight of the slope at the same angle as the slopes incline
Perpendicular Vectors Relationship?
The relationship between 2 perpendicular vectors is the two vectors have no effect on each other. This means two directions can be dealt with separately and a force that affects 1 vector can be worked out without needing to consider the other vector
Forces and Vector quantities?
Forces are examples of vector quantities. This means the arrows of force in a free body diagram need to show direction and magnitude of forces acting on an object
Free-Body Diagrams?
Force diagram showing a single body that should include all forces acting on a body but not all the forces it exerts on the surroundings
Equilibrium?
While forces in an object are balanced with each other and cancel each other out
Force and equilibrium?
There are no resultant forces acting on an object in equilibrium. When there are forces acting on an object in equilibrium they need to have equal magnitude and opposite directions so they cancel each other out
Equilibrium and Velocity?
An object in equilibrium can be at rest or moving with a constant velocity
Equilibrium Problems?
Equilibrium problems can be solved by force vectors in a closed loop or by resolving forces in 2 perpendicular distances
Closed Loop in equilibrium?
Forces acting on an object in equilibrium form a closed loop when drawn tip to tail
Tip to tail equilibrium diagrams?
When 3 forces are tip to tail and create a closed loop it is referred to as a vector triangle. If a vector triangle involves more than 3 forces it is called a vector polygon
Resolving forces in equilibrium?
Resolving forces for objects in equilibrium is no different than forces in perpendicular components. If an object is in equilibrium the sum of the components in each direction equals zero. The components of each force in each direction is found with trigonometry
Force Boards?
A method of investigating equilibrium. They can be used to apply forces to an object and vary forces and the directions they act in find different conditions for equilibrium
Mass?
The amount of matter an object is composed of
Mass Relationships?
The greater an object’s mass the greater the resistance to change its velocity. The mass of an object doesn’t change if the strength of the gravitational field changes
Weight?
Weight is a force typically measured in Newtons (N) and is a force experienced by a mass due to a gravitational field. Weight can change depending on the size of the gravitational field
Weight Formula?
Weight = Mass x Gravitational Field Strength
W = Mg
Moment?
A turning effect of a force around a turning point
Moment factor?
The moment of a force depends on the size of the force and far the force is applied from the turning point
Moment Equation?
Moment of a Force = Size of a force x perpendicular distance between force and turning point
Principle of moments?
The principle of moments states 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
Moments Factor?
If moments aren’t balanced the object will turn
Lever’s Purpose?
Levers are most useful where a large turning effect is required
Levers examples?
Spanner, wheelbarrows, scissors
Levers?
Levers increase the distance from the pivot and the applied force so less force is needed to generate the same moment
Effort Force in Levers?
An effort force otherwise input force acts against a load force otherwise output force by the means of a rigid object rotating around a pivot
Moments and Couples?
A couple doesn’t cause any resultant linear force but produces a turning effect called a moment. The size of the moment is dependant on the size of forces and the distances between them
Couple?
A couple is a pair of forces of equal size which acts parallel to each other in opposite directions
Moment Couple Equations?
Moment in Couple = Size of Force x perpendicular distance between line of action of forces
M = f x d
Centre of mass?
The single point that the whole weight of the objects acts through whatever the orientation of the object
Centre of mass trends?
An object always balances around the centre of mass. The centre of mass can fall outside the object. For a uniform regular solid the centre of mass is at the centre of the object
Finding centre of mass?
If an object is hung freely from a point draw a vertical line downwards from the point of suspension from the plum line. Hang the same object from another point and draw a line downwards from the plum line. The intersection of these two points are the centre of mass
Object toppling?
An object will topple over if its line of action falls outside its base area. This is because a resultant moment is produced providing a tuning force
Stability and area?
The higher the centre of mass the smaller the base area and the less stable the object will be. Objects are very stable if they have a low centre of mass and a wide base are
Forces on suppourts?
An object held by supports won’t have the same force acting through each support the same. The closer the centre of mass to a support the stronger the force on the support. The force on supports is affected by the principle of moments as the centre of mass experiences a larger force
Speed?
How fast something is moving regardless of direction
Displacement?
How far an object has travelled from its starting point in a given direction
Velocity?
Rate of change of an objects displacement
Acceleration?
Rate of change of an objects velocity
Uniform Acceleration?
Constant acceleration of an object
SUVAT meaning?
“S” stands for displacement in (m). “U” stands for initial velocity in (ms-1). “V” stands for final velocity in (ms-1). “A” stands for acceleration in (ms-2). “T” stands for time in (s)
SUVAT key equations?
v= u + at
s = ut + (1/2 a t^2)
s = ((u + v) / 2 ) x (t)
v^2 = u^2 + 2as
Displacement-Time Graphs?
Plotted to show information about moving objects. SUVAT equations can be used to work out the data values of what is drawn on the displacement time graph
Displacement-Time Graph Gradient?
The gradient of displacement-time graphs is velocity
Acceleration on Displacement-Time Graphs?
Acceleration is the rate of change of velocity so on a displacement-time graph the acceleration is the rate of change of the gradient
Acceleration and Deceleration?
Acceleration is shown by a graph with an increasing gradient. Deceleration is shown with a graph with a decreasing gradient
Gradient trends on a displacement-time graph?
A displacement-time graph always produces a curve. If an object is accelerating at a uniform rate then the rate of change of the gradient will be constant. Changing the acceleration changes the gradient on a displacement-time graph
Velocity on a displacement-time graph?
Velocity is the gradient on a displacement-time graph. When velocity is constant the displacement-time graph produces a straight line relationship
Velocity Equation?
Velocity = Change in displacement / Time
v = Δs / Δt
Instantaneous Velocity?
An objects velocity at a particular point
Tangent on displacement-time graphs?
A tangent to the curve finds gradient on a displacement-time graph but as well the instantaneous velocity at the point its drawn
Gradient not constant on displacement-time graph?
If the gradient isn’t constant the gradient doesn’t show a straight line relationship. This also means the object is accelerating and the velocity is constantly changing
Average Velocity?
The total change in displacement of the object divided by the total time taken
Velocity-Time Graph gradient?
The gradient of a velocity-time graph is the acceleration
Acceleration Formula?
a = ΔV / ΔT
acceleration = change in velocity / time taken
Acceleration trends on a velocity-time graph?
Uniform acceleration always produces a gradient that shows a straight line relationship. The steeper the gradient the greater the acceleration of the object
Velocity-Time graphs compared to Speed-Time graphs?
A speed-time graph has a similar trend to a velocity-time graph but a key difference is velocity-time graphs can have negative regions
Velocity-TIme graph negative regions?
Show an object travelling in the opposite direction
Area under a velocity-time graph?
The area under a velocity-time graph is displacement
Area under speed-time graph?
Displacement = Average Velocity x time
Distance = average speed x time
s = ((u + v)/2) x t
Non-Uniform Acceleration?
If acceleration is changing the gradient is a curve instead of a straight line
Non-Uniform Acceleration trends?
Increasing acceleration produces a steeper curve whereas decreasing acceleration produces a gradient with a less severe gradient
Drawing Graphs using ICT?
Using technology and in particular an ultrasound position detector can be used to collect data for distance and time. It is a type of data logger which automatically records distance from a sensor several times per second. Software is then used to produce a real time displacement-time graph
Advantages of data loggers?
Data plotted is more accurate as it doesn’t have human error. Automatic systems have a much higher sampling rate. Data can be displayed in real time
Acceleration on an acceleration-time graph?
Acceleration is given by the position on the y-axis the object is
Positive and Negative acceleration on acceleration-time graph?
Positive acceleration means the object is speeding up. Negative acceleration means the object is slowing down which is also called de-accelerating.
“0” significance on an acceleration-time graph?
If acceleration has a value of 0 on an acceleration-time graph it means the object is moving at constant velocity but is at rest if there is no acceleration that is negative on the acceleration-time graph
Area under an acceleration-time graph?
The area under an acceleration time graph is equal to the total change in velocity
Total Change in Velocity equation?
Δv = a x t
Change in Velocity = Acceleration x Time
Finding overall change in velocity on a graph with acceleration and deacceleration?
Treat the area under the time graph with its respective positive and negative values
Newtons 1st Law?
Velocity of an object will not change unless a resultant force acts upon it
Result of Newtons 1st Law?
A body will stay stationary or move in a straight line at constant speed unless a resultant force acts upon it
Acceleration significance to Newtons 1st Law?
If forces acting on a body aren’t balanced the overall force will make the body accelerate. Acceleration is caused by the resultant force causing the object to change speed and or direction
Newton’s Second Law of motion?
Acceleration of an object is proportional to the resultant force acting on it
Equation of Newton’s Second Law?
F = ma
Force = Mass x Acceleration
Result of Newton’s Second Law?
The more force acting on a certain mass the more acceleration the object has
Rules of Newton’s Second Law equation?
Resultant force is the vector sum of all forces acting on an object. Resultant force is always measured in metres (m), mass is always measured in kilograms (kg), acceleration is measured in same direction as resultant force and has units metres per second squared (ms-2)
Newton’s Third Law of motion?
Object A exerts a force on Object B and as a result Object B exerts an equal and opposite force on Object A
Newton’s Third Law and Force interaction?
The forces acting on the two objects interact rather than equal and opposite on the same object. This law considers the two forces representing the same interaction but from different perspectives
Newton’s Third Law and Force?
Newton’s 3rd law applies in all situations and to all types of force. Forces must be equal to the same type not one of each type
Freefall result?
When gravity is the only force acting upon an object
Freefall?
The motion of an object undergoing an acceleration of “g”
Free fall factors?
Acceleration is a vector quantity, “g” acts vertically downwards, “g” magnitude is normally 9.81 ms-2, “g” can vary at certain points on Earth’s surface, weight is only force acting on object in freefall, objects can have initial velocity in any direction and still undergo freefall as long as force providing initial velocity is no longer acting on the objects
Galileo’s Freefall experiments?
Galileo Galilee is an Italian physicist who investigated objects in freefall. All objects in freefall accelerate to ground at the same rate. This claim changed 1000 year claim of heavier objects falling to ground faster. Galileo used systematic experiments that could get repeat results and be compared to mathematical description
Galileo investigation resolution?
The issue trying to prove his theory was the impact of air resistance causing objects to fall too quickly. An inclined smooth plane slowed the ball down and reduced the effect of air resistance. Rolling ball along different fractions of slope found distance proportional to time taken while ball accelerating at a constant rate
Newton and Galileo?
Newtons and Galileo’s results prove free-falling objects have the same acceleration. Newton mathematically showed objects are attracted towards Earth due to gravity. Newton’s second law explains why all objects fall at the second rate
