Mechanics and Materials Flashcards
Scalar vs Vector
- A scalar is a quantity which only has a magnitude (size)
- A vector is a quantity which has both a magnitude and a direction
Is distance/displacement vector or scalar and explain why
- Distance is a scalar quantity because it describes how far an object has travelled overall, but not the direction it has travelled in
- Displacement is a vector quantity because it describes how far an object is from where it started and in what direction
How can vectors be represented and how does this work
by an arrow:
The arrowhead indicates the direction of the vector
The length of the arrow represents the magnitude
What are the two methods used to add vectors
- Calculation – if the vectors are perpendicular
- Scale drawing – if the vectors are not perpendicular
Describe how vectors can be found using the triangle vs parallelogram method
- To combine vectors using the triangle method:
Step 1: link the vectors head-to-tail
Step 2: the resultant vector is formed by connecting the tail of the first vector to the head of the second vector - To combine vectors using the parallelogram method:
Step 1: link the vectors tail-to-tail
Step 2: complete the resulting parallelogram
Step 3: the resultant vector is the diagonal of the parallelogram
Describe the forces acting on an inclined plane
When are forces in equilibrium
- At rest
- Moving at constant velocity
What are coplanar forces
Forces that act in the same plane
What is a moment
the turning effect of a force
When do moments occur
when forces cause objects to rotate about some pivot
What is the equation stating the moment of a force
Moment (N m) = Force (N) × perpendicular distance from the pivot (m)
What is the unit of a moment
N m
What is the principle of moments
For a system to be in equilibrium, the sum of clockwise moments about a point must be equal to the sum of the anticlockwise moments (about the same point)
What is a couple
a pair of equal and opposite coplanar forces that act to produce rotation only
What kind of forces does a couple contain
Forces that are:
- Equal in magnitude
- Opposite in direction
- Perpendicular to the distance between them
Does an object with a couple accelerate
No- Couples produce a resultant force of zero, so, due to Newton’s Second law (F = ma), the object does not accelerate
What kind of moment system does not require a pivot
a couple
What is the moment of a couple equal to
Force × Perpendicular distance between the lines of action of the forces
Centre of mass def
the point at which the weight of the object may be considered to act
Where is the position of the centre of mass for a uniform regular solid
at its centre
Where is the position of the centre of mass for symmetrical objects with uniform density
at the point of symmetry
When is an object stable
when its centre of mass lies above its base
How is the base width, centre of mass and stability linked?
- The wider base an object has, the lower its centre of mass and it is more stable
- The narrower base an object has, the higher its centre of mass and the object is more likely to topple over if pushed
What is instantaneous speed (or velocity)
the speed (or velocity) of an object at any given point in time