Mechanics

Question 1

what is a vector quantity? + examples

Answer 1

any physical quantity that has direction as well as magnitude
eg. velocity, acceleration, force

Question 2

what is a scalar quantity? + examples

Answer 2

any physical quantity that is not directional
eg. distance, mass, speed, density, volume, energy

Question 3

how can you represent a vector?

Answer 3

• any vector can be represented as an arrow
• length of arrow = magnitude of the vector
• direction of arrow = direction of vector

Question 4

how can you find the overall resultant force of 2 or more forces?

Answer 4

use a scale diagram - the resultant force is the line connecting the start and end after drawing tip to tail

Question 5

how can you calculate forces and distances that are perpendicular to each other (and the angles they act to each other) mathematically?

Answer 5

using pythagoras’s theorem to find magnitude of the force/distance and trigonometry to find the angle

Question 6

what is the resultant magnitude of vectors acting on the same line?

Answer 6

• the sum of the vectors if they are acting in the same direction
• the difference if they are acting in the opposite direction

Question 7

how do you resolve a vector into its components?

Answer 7

draw a diagram to show the force with an arrow to make it a vector
then split it into 2 perpendicular components kind of like a right angled triangle with the original vector as the hypotenuse

Question 8

for a force F resolved into 2 perpendicular components…

Answer 8

• Fcosθ parallel to a line at angle θ to the line of action of the force
• Fsinθ perpendicular to the line

Question 9

when can you say that an object is in equilibrium?

Answer 9

if the 2 forces acting on it are equal and opposite to each other or the sum of all forces acting on the object are equal to 0
The object will be at rest or travelling at a constant velocity

Question 10

how do you check if the resultant force of 3 forces = 0?

Answer 10

• resolve each force along the same parallel and perpendicular lines
• balance the components along each line

Question 11

what is a moment?

Answer 11

• it is the turning effect of a force
• the moment of a force around any point is defined as force × the perpendicular distance from the line of action of the force to the point
• the longer the perpendicular distance the larger the moment

Question 12

what is the unit of a moment?

Answer 12

Nm - the newton metre

Question 13

what is the moments equation?

Answer 13

Moment = Fd (moment = force × distance)

Question 14

what is the principle of moments?

Answer 14

for an object to be in equilibrium:
the sum of clockwise moments = the sum of anticlockwise moments

Question 15

what is the moment of an object if force is applied at the centre of mass?

Answer 15

zero - this is because there is no perpendicular distance between CoM and the point where force is applied

Question 16

what is the centre of mass?

Answer 16

the point through which a single force on the body has no turning effect
its the point where you consider the weight to act when studying the effect of forces on a body

Question 17

what is the reaction/normal contact force if an object is in equilibrium?

Answer 17

it is equal and opposite to the total downwards forces acting on the object

Question 18

where can moments be taken from?

Answer 18

they can be taken from any point - so it makes sense to take moments from a point with one or more forces acting on it (F = 0)

Question 19

for a beam with 2 supports…

Answer 19

• if the CoM is halfway between the supports, the support/reaction force of each support is half the weight
• if the CoM closer to one support than the other, the support/reaction force will be greater on the support closer to the CoM

Question 20

what is a couple?

Answer 20

a pair of equal and opposite forces acting on a body, but not along the same line

Question 21

what is the equation for the moment of a couple?

Answer 21

moment of a couple = force × perpendicular distance between the lines of actions of the forces

Question 22

what is stable equilibrium?

Answer 22

it is a state of balance in which a body will tend to return to its original equilibrium point if it is displaced from that point

Question 23

why do objects in stable equilibrium not topple?

Answer 23

when these objects are displaced, the centre of mass does not pass over the pivot. This means that the moment of the weight of the object brings it back to equilibrium

Question 24

what is unstable equilibrium?

Answer 24

it is a state of balance where if the body is displaced from the point of equilibrium, it tends to move away from that point

Question 25

why do objects in unstable equilibrium topple?

Answer 25

The centre of mass is no longer above the support, which causes the moment of the weight to act to turn the object further from the original point of equilibrium, causing it to topple

Question 26

what makes an object more stable?

Answer 26

having a low CoM and a wide base

Question 27

what is tilting?

Answer 27

this is when an object at rest on a surface is acted on a force that raises it up on one side

Question 28

when does toppling occur?

Answer 28

when an object is tilted too far

Question 29

what is the furthest an object can be tilted before it topples on release?

Answer 29

the position where the line of action of weight passes beyond the pivot

Question 30

when will a lorry topple on a slope?

Answer 30

- when the angle of the slope is too great - when the line of action of weight lies outside of the wheelbase (one of the wheels is acting as a pivot)

Question 31

what is a free body force diagram?

Answer 31

a diagram which only shows the forces acting on an object

Question 32

what is the vector sum rule and when is it used?

Answer 32

F1 + F2 + F3 = 0 this is used to check whether an object is in equilibrium when 3 forces are acting on it

Question 33

how do you find a missing force using the vector sum rule using a scale diagram?

Answer 33

draw the scale diagram out using the correct angles draw a line to close the triangle (since resultant force = 0) - the magnitude and direction of this line is the missing force

Question 34

how do you find a missing force using the vector sum rule mathematically?

Answer 34

draw out the diagram roughly use the sine rule to work out the missing length, provided you know 2 angles and a corresponding length

Question 35

what are the conditions required for an object to be in equilibrium?

Answer 35

- resultant force must = 0 - ie. they must form a closed shape when a scale diagram is drawn - principle of moments must apply - sum of clockwise moments = sum of anticlockwise moments