Mechanics Flashcards
1
Q
What is a moment and how to calculate it?
A
- A moment if the turning effect of a force about a pivot
- Moments occur when forces cause objects to rotate about some pivot
- M = f x d
- Moment = force x distance
2
Q
What must you remember when caculating a moment?
A
- Always measure perpendicular distance from pivot. Use trigonometry to calculate the perpenndicular distance
3
Q
What is the principle of moments?
A
- For a system to be in equilibrium, the sum of clockwise moments about a point must be the same as the sum of anticlockwise moments about the same point
4
Q
What is a couple?
A
- A pair of equal and opposite coplanar forces that acts to produce rotation only
- They are equal in magnititude, opposite in direction and perpendicular to the distance between them
5
Q
What are the characteristics of a couple and how to calculate it?
A
- They produce a resultant force of 0, so according to F=ma, they do not accelerate
- They do not depend on a pivot
- Moment of a couple = force x perpendicular distance between the lines of action of the forces
6
Q
What is the importance of the centre of mass of an object?
A
- The centre of mass of an object is the point at which the weight of the object may be considered to act
7
Q
Where is the centre of mass?
A
- For uniform regular solids , it is at the centre of the object
- For symetrical objects, it is at the point of symmetry
8
Q
How does centre of mass differ between different objects and how does it effect the object?
A
- For wider objects, the centre of mass is lower and hence more stable
- For narrower objects, the centre of mass is higher and hence easier to topple over
9
Q
How does centre of mass and centre of gravity differ?
A
- In a uniform gravitational field, the centre of mass is the same as the centre of gravity
- When an object is in space, the centre of gravity will be more towards the object with a greater gravitational field
10
Q
What is instantaneous velocity?
A
- The velocity of an object at any given point in time
- This could be for an object moving at constant velocity or accelerating
11
Q
What does a displacement time graph show?
A
- The gradient equals velocity (sloped gradient = accelerating)
- Y intercept shows initial displacement
- Area under graph shows total distance travelled
12
Q
What does a velocity time graph show?
A
- Gradient equals acceleration
- Y intercept shows the initial velocity
- Straight line shows uniform acceleration
- Area under graph is displacement
13
Q
What does an acceleration time graph show?
A
- Y intercept shows initial acceleration
- Gradient shows rate of acceleration
- Area under graph is velocity
14
Q
SUVAT equations variable representations
A
- S = displacement
- U = initial velocity
- V = final velocity
- A = acceleration
- T = time
15
Q
What is a projectile?
A
- A particle moving freely, under gravity, in a two-dimensional plane
16
Q
How to calculate projectile motion?
A
- The trajectory of an object going through projectile motion can be broken into a vertical component and horizontal component
- These components are completely independent of eachother
17
Q
Horizontal and vertical components of a projectile
A
- Displacement horizontal: maximum at the end when the total time has passed
- Dislacement vertical: maximum at the top of the motion when half of the time has passed
- Velocity horizontal: always constant
- Velocity vertical zaro at maximum height
- Acceleration horizontal: 0 (velocity is constant)
- Acceleration vertical: acceleration of free fall, 9.81 m/s2
18
Q
How does air resistance effect projectile motion?
A
- Any object moving through air experiences air resitance which causes drag
- The drag acts in the opposite direction to the direction of motion of the object
- Horizontal component: reduces velocity and range
- Vertical component: reduces maximum height
19
Q
Factors effecting projectile motion
A
- Larger surface area = greater air resitance
- Greater mass = larger force of weight
20
Q
What is a drag force?
A
- Forces that oppose the motion of an object through a fluid
- E.G: friction and air resistance
21
Q
What do drag forces do?
A
- Always in the opposite direction to the motion of the object
- Never speed up an object or start them moving
- Either slow down an object or keep it at constant velocity
- Convert kinetic energy into heat or sound
22
Q
What is lift?
A
- Lift is an upwards force on an object moving through a fluid. It acts in the perpendicular direction to the fluid flow (air / water flow)
23
Q
What is terminal velocity and how is it reached?
A
- For a body in free fall, the only force acting is its weight and its acceleration is only g, due to gravity
- The drag force increases as the body accelerates
- Due to Newton’s second law, this decreas in resultant force also decreases the acceleration
- When the drag force is equal to the objects acceleration due to gravity, the resultant force will be 0 and the object will no longer accelerate
- This is the maximum velocity the object will reach, also known as terminal velocity
24
Q
What is Newton’s first law of motion?
A
- An object will remain at rest or constant velocity until acted on by a resultant force
25
How do you split up a resultant force?
- As force is a vector, you can split a force into its horizontal and vertical components
- If the resultant force is 0, the total force acting to the left = total force to the right AND total force acting up = total force acting down
26
What is Newton's second law of motion in terms of resultant force?
- The resultant force acting on an object with constant mass is directly proportional to its acceleration
- F = ma
- Acceleration is always in the same direction as the resultant force
27
What is Newton's second law of motion in terms of momentum?
- The resultant force of an object is equal to its rate of change of momentum
- The change in momentum is in the same direction as the resultant force
28
What is Newton's third law of motion?
- If object A exerts a force on object B, then object B will exert a force on object A which is equal in magnititude but opposite in direction
29
What are the requirements for a third law pair?
- The same type of force
- The same magnititude
- Opposite in direction
- Acting on different objects
30
What is linear momentum?
- When an object with mass is in motion and therefore has velocity, it also has momentum
- Linear momentum is the momentum of an object that is moving in one dimension only
- The linear momentum of an object stays constant unless it is acted upon by an external resultant force
- Momentum = mass x velocity
31
What is the principle of conservation of momentum?
- The total momentum before a collision is equal to the total momentum after a collision, provided no external forces act (in a closed system)
32
What is the difference between external and internal forces?
- External forces are forces that act on the system from the outside, e.g: friction and weight
- Internal forces are forces exchanged by the particles in the system, e.g: tension in a string
- Systems with no external forces are describes as a closed system
33
What is impulse and how do you calculate it?
- The change of momentum of an object, when the object is acted upon by a force for an interval of time
- Impulse = resultant external force x change in time
- Change in momentum = resultant external force x change in time
- Therefore: Impulse = change in momentum
34
How do you calculate impulse from a force-time graph?
- Impulse = area under graph on a force-time graph
35
How is impulse used in everyday life?
- As change in momentum = force x change in time, if we increase the change in time, and momentum is kept constant, then the force exerted will be reduced
- Impact forces are reduced by increasing contact time, e.g: using bubble wrap in packaging
36
When is momentum and kinetic energy conserved in collisions?
- Momentum is conserved in both elastic and inelastic collisions
- Kinetic energy is conserved in elastic collisions but not inelastic collisions
37
Safety features in a car
- Crumple zones = increases contact time
- Seat belts = stretch slightly to increase contact time
- Air bags = cushion the person and also increases contact time
38
What is the work done on an object?
- Work done by a force is equal to a transfer of energy
- The work done by a resultant force on a system is equal to the change in energy in that system
39
What is mechanical work and how do you calculate it?
- The amount of energy transferred when an external force causes an object to move over a certain distance
- If constant force is applied parallel to the direction of the object's displacement, then work done = force x displacement
40
How to calculate mechanical work done if the force applied is not parallel?
- If the force applied is at an angle θ to the object's displacement:
- Work done = force x displacement x cos θ
41
What is power and how do you calculate it?
- Power is the rate of doing work or the rate of energy transfer
- Power = work done / time
- Power = energy transferred / time
42
How to calculate power using velocity?
- If an object is moving at constant velocity with a constant force:
- Power = force x velocity
43
What is the area under a force-displacement graph?
- Area under graph is work done
- Work done = force x displacement
44
What is a variable force?
- If the force applied on an object is not constant, then it is variable
- If this is the case, the following equations cannot be used
- W = Fs and P = Fv
45
What is efficiency of a system?
- The ratio of the useful power output of a system to its total power input
46
What is the principle of conservation of energy?
- Energy cannot be created or destroyed, it can only be transferred from one form to another
- The total amount of energy in a closed system always remains constant
47
What is density and how do you calculate it?
- Density is the mass per unit volume of an object
- Density = mass / volume
48
When does a material obey Hooke's law?
- The extension of the material is dierctly proportional to the applied force (load) up to its limit of proportionality
49
What is the equation for Hooke's law?
- Force = spring constant x extension
50
What is the spring constant?
- It is the property of a material being stretched and measures the stiffness of the material
- The greater the spring constant, the stiffer the material
51
What is the force-extension graph for a material that obeys Hooke's law?
- Force and extension is directly proportional up to a certain point
- This point is known as the limit of proportionality. Beyond this point, the material no longer obeys Hooke's law
- The point after the limit of proportionality is known as the elastic limit. Beyond this point, the material will no longer return to its original shape after being stretched
- The gradient of the graph is the reciprocal of the spring constant
52
What is tensile stress and strain and how do you calculate it?
- If the forces applied stretch the object, they are tensile forces
- Tensile stress is defined as the force applied per unit cross-sectional area of the material
- Tensile stress (σ) = force applied / cross sectional area
- Tensile strain is defined as the extension per unit length of the material
- Tensile strain = extension / original length
- Tensile strain has no units
53
What is the ultimate tensile stress?
- The maximum force per unit cross sectional area a wire is able to support until it breaks
54
What points are shown on a stress-strain graph?
- Hooke's law region: gradient is constant, Hooke's law is obeyed
- Area under the graph shows the energy stored / work done per unit volume
- Limit of proportionality: wire stops obeying Hooke's law
- Elastic limit: wire will not longer return to its original length
- Yield stress: the force per unit area at which the material extends plastically with no increase in stress
- Breaking point: the maximum stress a material can stand before it fractures
- Elastic region: the region up to the elastic limit
- Plastic region: the region after the elastic lim
55
What is the elastic strain energy and how to calculate it?
- Area under a force-extension / stress-strain graph
- Shows the work done / energy stored per unit volume of the material
- If the material obeys Hooke's law:
- Elastic strain energy = 1/2 x average force x extension
56
What is the breaking stress?
- The maximum stress a material can stand before it fractures
- Extension after plastic deformation (elastic limit)
57
Elastic vs plastic deformation
- Elastic deformation: when the load is removed, the material will return to its original length. This is the elastic region in a force-extension graph (region up to the elastic limit)
- Plastic deformation: the material is permenantly deformed. When the load is removed, it will no longer return to its original shape. This is beyond the elastic limit
58
Work done when loading and unloading a metal wire
- If a metal wire is stretched beyond its limit of proportionality, it will undergo plastic deformation
- When the force is removed, the wire is unloaded, this causes the extension to decrease
- The unloading line is parallel to the loading line however, it does not go through the origin (the y-intercept is now lower)
- The area between the loading and unloading lines shows the work done to permenantly deform the metal wire
59
What is the Young Modulus?
- The Young Modulus is the measure of the ability of a material to withstand changes in length with an added load
- This gives information about the stiffness of the material
60
How do you calculate the Young Modulus of a material?
- Young moduls = tensile stress / tensile strain
- Young modulus = (Force x original length) / (cross sectional area x extension)
- Unit is pascals (Pa)
61
How to find Young Modulus from a stress-strain graph?
- The Young Modulus is the gradient of the graph when the line is linear (elastic region)
