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
Q
How do you split up a resultant force?
A
- 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
Q
What is Newton’s second law of motion in terms of resultant force?
A
- 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
Q
What is Newton’s second law of motion in terms of momentum?
A
- 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
Q
What is Newton’s third law of motion?
A
- 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
Q
What are the requirements for a third law pair?
A
- The same type of force
- The same magnititude
- Opposite in direction
- Acting on different objects
30
Q
What is linear momentum?
A
- 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
Q
What is the principle of conservation of momentum?
A
- 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
Q
What is the difference between external and internal forces?
A
- 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
Q
What is impulse and how do you calculate it?
A
- 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
Q
How do you calculate impulse from a force-time graph?
A
- Impulse = area under graph on a force-time graph
35
Q
How is impulse used in everyday life?
A
- 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
Q
When is momentum and kinetic energy conserved in collisions?
A
- Momentum is conserved in both elastic and inelastic collisions
- Kinetic energy is conserved in elastic collisions but not inelastic collisions
37
Q
Safety features in a car
A
- Crumple zones = increases contact time
- Seat belts = stretch slightly to increase contact time
- Air bags = cushion the person and also increases contact time
38
Q
What is the work done on an object?
A
- 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
Q
What is mechanical work and how do you calculate it?
A
- 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
Q
How to calculate mechanical work done if the force applied is not parallel?
A
- If the force applied is at an angle θ to the object’s displacement:
- Work done = force x displacement x cos θ
41
Q
What is power and how do you calculate it?
A
- Power is the rate of doing work or the rate of energy transfer
- Power = work done / time
- Power = energy transferred / time
42
Q
How to calculate power using velocity?
A
- If an object is moving at constant velocity with a constant force:
- Power = force x velocity
43
Q
What is the area under a force-displacement graph?
A
- Area under graph is work done
- Work done = force x displacement
44
Q
What is a variable force?
A
- 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
Q
What is efficiency of a system?
A
- The ratio of the useful power output of a system to its total power input
46
Q
What is 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 amount of energy in a closed system always remains constant
47
Q
What is density and how do you calculate it?
A
- Density is the mass per unit volume of an object
- Density = mass / volume
48
Q
When does a material obey Hooke’s law?
A
- The extension of the material is dierctly proportional to the applied force (load) up to its limit of proportionality
49
Q
What is the equation for Hooke’s law?
A
- Force = spring constant x extension
50
Q
What is the spring constant?
A
- 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
Q
What is the force-extension graph for a material that obeys Hooke’s law?
A
- 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
Q
What is tensile stress and strain and how do you calculate it?
A
- 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
Q
What is the ultimate tensile stress?
A
- The maximum force per unit cross sectional area a wire is able to support until it breaks
54
Q
What points are shown on a stress-strain graph?
A
- 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
Q
What is the elastic strain energy and how to calculate it?
A
- 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
Q
What is the breaking stress?
A
- The maximum stress a material can stand before it fractures
- Extension after plastic deformation (elastic limit)
57
Q
Elastic vs plastic deformation
A
- 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
Q
Work done when loading and unloading a metal wire
A
- 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
Q
What is the Young Modulus?
A
- 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
Q
How do you calculate the Young Modulus of a material?
A
- Young moduls = tensile stress / tensile strain
- Young modulus = (Force x original length) / (cross sectional area x extension)
- Unit is pascals (Pa)
61
Q
How to find Young Modulus from a stress-strain graph?
A
- The Young Modulus is the gradient of the graph when the line is linear (elastic region)
