Mechanics (Unit 2) Flashcards Preview

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Flashcards in Mechanics (Unit 2) Deck (38):
1

Difference between a scalar and a vector

vector has magnitude (size) and direction, whereas scalar only has magnitude (size).

2

Examples of scalars

speed, mass, time, energy, power

3

Examples of vectors

displacement, velocity, acceleration, force, weight

4

Adding perpendicular vectors by calculation

• draw vectors as a right angled triangle
• use pythagoras’ theorem to find magnitude of resultant vector
• use trigonometry to calculate the angle of resultant vector (sin=o/h; cos=a/h; tan=o/a)

5

Adding vectors
by scale drawing

• write down scale eg 1cm=2N
• draw vectors to correct length and angle to each other “tip to tail”
• add the resultant vector line (from original tail to free tip)
• measure length and angle of resultant vector
• convert length into appropriate quantity (using scale) to find magnitude of resultant vector

6

Conditions for equilibrium of two or three coplanar forces acting at a point

total resultant force equals zero
or
if the vectors representing the forces are added together they will form a closed triangle.

7

Two conditions for a body to remain in equilibrium

1. resultant force acting on body is zero
2. resultant moment about any point is zero
object could be stationary OR travelling at constant velocity

8

Definition of a moment

force multiplied by the perpendicular distance between the line of action of the force and the pivot.

9

Units of moment

Nm

10

Principle of Moments

in equilibrium, the sum of the clockwise moments about a point equals the sum of the anticlockwise moments.

11

Definition of moment of a couple

(one) force multiplied by the perpendicular distance between the lines of actions of the two forces.

12

Definition of centre of mass

point in a body through which weight appears to act
or
point in a body where the resultant moment is zero

13

Stable equilibrium

When a body is displaced then released, it will return to its equilibrium position

14

Unstable equilibrium

When a body is displaced then released, it will not return to its equilibrium position.

15

Displacement

distance in a given direction

16

Velocity

rate of change of displacement
or
change in displacement divided by the time taken

17

Acceleration

rate of change of velocity
or
change in velocity divided by the time taken

18

Gradient of displacement and velocity time graphs

Gradient of a displacement time graph = velocity
Gradient of a velocity time graph = acceleration

19

Area under velocity and acceleration time graphs

Area under a velocity time graph = displacement
Area under an acceleration time graph = velocity

20

Average velocity

total displacement divided by total time

21

Instantaneous velocity at a point

rate of change of displacement at that point
gradient at a point on a displacement time graph (need to draw a tangent to calculate gradient)

22

Conditions for an object falling at terminal velocity

• resultant force on object is zero (weight and drag forces are balanced)
• acceleration is zero (F=ma)
• object travels at a constant velocity

23

Factors affecting drag force on an object

• the shape of the object
• its speed
• the viscosity of the fluid/gas (measure of how easily fluid/gas flows past a surface)

24

Explain why an object reaches terminal velocity falling through air

• initially only force acting is weight, so object accelerates at g.
• drag force increases with increasing speed.
• therefore resultant force decreases.
• eventually drag force = weight, forces are balanced.
• so resultant force is zero.
• as F=ma, acceleration is zero so object falls at constant speed.

25

Horizontal and Vertical motion of a projectile

In absence of resistive forces
Horizontal motion: no force horizontally, no acceleration so constant velocity.
Vertical motion: constant force due to weight, constant acceleration (equal to g).

26

Newton’s Laws of motion

1st Law
An object will continue at rest or uniform velocity unless acted on by a resultant force
2nd Law
The acceleration of an object is proportional to resultant force acting on it, ie F=ma (providing mass is constant)
3rd Law
If object A exerts a force on a second object B, then object B will exert an equal and opposite force on object A.

27

Principle of conservation of energy

Energy is neither created or destroyed, only converted from one form to another

28

Energy conversions of an object falling in presence of resistive forces

loss in gpe = gain in ke + work done against resistance
work done typically appears as heat

29

Definition of work done

force multiplied by distance moved in the direction of the force

30

Units of work done

J

31

Power

rate at which energy transferred
or
energy transferred (work done) divided by time taken

32

Units of Power

W (Watts) or Js^-1

33

Resolving vectors into two perpendicular components

See sheet

34

Resolving components along, and perpendicular to, an inclined slope

See sheet

35

Displacement and Velocity time graphs for uniform acceleration

See sheet

36

Displacement and velocity time graphs for non-uniform acceleration

See sheet

37

Sketch time graphs for an object falling under gravity then reaching terminal velocity

See sheet

38

Sketch time graphs for a bouncing ball

See sheet