Mechanics and Materials (1): Forces in Equilibrium Flashcards
What is the definition of a vector?
A physical quantity that has direction as well as magnitude
What is the definition of a scalar?
A physical quantity that is not directional
What is the definition of displacement?
The distance in a given direction
What is the definition of velocity?
The speed in a given direction
What is the equation for the total displacement of a multistep journey?
Total displacement vector = the sum of the individual displacement vectors
What has to be true to add any two vectors?
They have to be of the same type
When answering a displacement question what two values do you need to include?
The magnitude and angle of displacement
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?
- The magnitude of the resultant force, F = (F1^2 + F2^2)^1/2
- The angle is given by tan(theta) = F2/F1
What is true when an object is equilibrium?
If the two forces acting on the object are equal but opposite/ the resultant is 0N/ the two forces are balanced
In what two instances can equilibrium occur?
- stationary object
- object moving at a constant velocity
For an object laying flat on a surface what is the reaction force equal to?
The weight of the object acting downwards
In what scenario is the resultant zero when three forces are applied to an object?
- 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
If you have a suspended weight that is attached to ropes of different tensions what are the first steps you need to do?
You need to resolve vertically and horizontally and set ma = 0
What is a positive and negative of using a a longer spanner when loosening a nut on a bicycle?
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
What is the definition of the moment of a force at any point?
The force x the perpendicular distance from the line of action of the force to the pivot
What is the equation for the moment of a force?
p = F x d
What are the units for a moment of a force?
Nm
What is an object that is not a point object referred to as?
a body
When will a body not turn if a force is applied to it?
If the force acts through its centre of mass
State the principle of moments?
Sum of the clockwise moments = sum of the anticlockwise moments
What is the definition of the centre of mass (in regards to moments)
The point through which a single force on the body has no turning effect
At a pivot which is held up by a knifes edge with a metre rule balanced on top, what is the reaction force upwards?
The sum of the weights placed along the rule and the weight of the rule itself
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?
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
What is the definition of a couple?
A pair of coplanar forces that are equal in magnitude but opposite in direction
How do you calculate the moment of a couple?
Moment of a couple = force x perpendicular distance between the lines of action of the forces
Will the moment for a couple always be the same no matter where you take the moments from?
Yes
What is the definition of stable equilibrium?
If a body is in stable equilibrium it means that it will return to its equilibrium position if displaced and released
What is the definition of unstable equilibrium?
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
When does tilting occur?
When an object at rest on a surface is acted upon by a force that raises it up from one side
For tilting to occur what must be true?
The moment due to the force being applied must be greater than the moment due to the weight from the pivot
When will toppling occur?
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
What is the furthest that a body can be tilted without it toppling?
To the position where the line of weight passes through the pivot
When will a tall object on a slope topple over?
If the line of action of weight acts beyond the pivot/ beyond the wheelbase for vehicles
How does centre of mass link to stability?
The lower the centre of mass the more stable a body will be
What is the name of a diagram that shows all the forces acting on an object?
Free body force diagram
The vector sum of three forces on a body in equilibrium is?
F1 + F2 + F3 = 0
F1 + F2 = -F3
