Mechanics and Materials (1): Forces in Equilibrium

Question 1

What is the definition of a vector?

Answer 1

A physical quantity that has direction as well as magnitude

Question 2

What is the definition of a scalar?

Answer 2

A physical quantity that is not directional

Question 3

What is the definition of displacement?

Answer 3

The distance in a given direction

Question 4

What is the definition of velocity?

Answer 4

The speed in a given direction

Question 5

What is the equation for the total displacement of a multistep journey?

Answer 5

Total displacement vector = the sum of the individual displacement vectors

Question 6

What has to be true to add any two vectors?

Answer 6

They have to be of the same type

Question 7

When answering a displacement question what two values do you need to include?

Answer 7

The magnitude and angle of displacement

Question 8

What is the general equation that shows the magnitude of the resultant forces between two forces, F1 and F2, and the angle between the resultant and F1?

Answer 8

1. The magnitude of the resultant force, F = (F1^2 + F2^2)^1/2
2. The angle is given by tan(theta) = F2/F1

Question 9

What is true when an object is equilibrium?

Answer 9

If the two forces acting on the object are equal but opposite/ the resultant is 0N/ the two forces are balanced

Question 10

In what two instances can equilibrium occur?

Answer 10

• stationary object
• object moving at a constant velocity

Question 11

For an object laying flat on a surface what is the reaction force equal to?

Answer 11

The weight of the object acting downwards

Question 12

In what scenario is the resultant zero when three forces are applied to an object?

Answer 12

• If the resultant of any two of the forces is equal and opposite to the third force

To check this:
- Resolve each force along the same parallel and perpendicular lines
- Balance the components a long each line

Question 13

If you have a suspended weight that is attached to ropes of different tensions what are the first steps you need to do?

Answer 13

You need to resolve vertically and horizontally and set ma = 0

Question 14

What is a positive and negative of using a a longer spanner when loosening a nut on a bicycle?

Answer 14

Positive - less force is required to loosen the nut
Negative - If the spanner is too long then it could snap if too much force is applied to it

Question 15

What is the definition of the moment of a force at any point?

Answer 15

The force x the perpendicular distance from the line of action of the force to the pivot

Question 16

What is the equation for the moment of a force?

Answer 16

p = F x d

Question 17

What are the units for a moment of a force?

Answer 17

Nm

Question 18

What is an object that is not a point object referred to as?

Answer 18

a body

Question 19

When will a body not turn if a force is applied to it?

Answer 19

If the force acts through its centre of mass

Question 20

State the principle of moments?

Answer 20

Sum of the clockwise moments = sum of the anticlockwise moments

Question 21

What is the definition of the centre of mass (in regards to moments)

Answer 21

The point through which a single force on the body has no turning effect

Question 22

At a pivot which is held up by a knifes edge with a metre rule balanced on top, what is the reaction force upwards?

Answer 22

The sum of the weights placed along the rule and the weight of the rule itself

Question 23

If you have a beam with a mass that is rested on top of two pillars, how will the weight of the beam be shared between them?

Answer 23

The weight will be shared depending on how far away the centre of mass of the beam is relative to each pillar

• You take moments about each pillar using the reaction force and distance from the other pillar + the distance from the centre of mass of the beam and its weight

Question 24

What is the definition of a couple?

Answer 24

A pair of coplanar forces that are equal in magnitude but opposite in direction

Question 25

How do you calculate the moment of a couple?

Answer 25

Moment of a couple = force x perpendicular distance between the lines of action of the forces

Question 26

Will the moment for a couple always be the same no matter where you take the moments from?

Answer 26

Yes

Question 27

What is the definition of stable equilibrium?

Answer 27

If a body is in stable equilibrium it means that it will return to its equilibrium position if displaced and released

Question 28

What is the definition of unstable equilibrium?

Answer 28

If a body is in unstable equilibrium then if it is displaced slightly from equilibrium and then released the body will not return back to the equilibrium position

Question 29

When does tilting occur?

Answer 29

When an object at rest on a surface is acted upon by a force that raises it up from one side

Question 30

For tilting to occur what must be true?

Answer 30

The moment due to the force being applied must be greater than the moment due to the weight from the pivot

Question 31

When will toppling occur?

Answer 31

Toppling will occur if a body is tilted too far. This is when an object has been tilted so far that the line of action of weight passes beyond the pivot and, therefore, when the body is released it falls over

Question 32

What is the furthest that a body can be tilted without it toppling?

Answer 32

To the position where the line of weight passes through the pivot

Question 33

When will a tall object on a slope topple over?

Answer 33

If the line of action of weight acts beyond the pivot/ beyond the wheelbase for vehicles

Question 34

How does centre of mass link to stability?

Answer 34

The lower the centre of mass the more stable a body will be

Question 35

What is the name of a diagram that shows all the forces acting on an object?

Answer 35

Free body force diagram

Question 36

The vector sum of three forces on a body in equilibrium is?

Answer 36

F1 + F2 + F3 = 0

F1 + F2 = -F3