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