Statistics and Mechanics Chapter 8 - Modelling in Mechanics

Question 1

Particle meaning

Answer 1

Dimensions of the objects are negligble.

Question 2

Particle modelling assumptions

Answer 2

Mass of the object is concentrated at a single point.
Rational forces and air resistance can be ignored.

Question 3

Rod meaning

Answer 3

All dimensions but one are negligible, like a pole or a beam.

Question 4

Rod modelling assumptions

Answer 4

Mass is concentrated along a line.
No thickness.
Rigid (does not bend or buckle)>

Question 5

Lamina meaning

Answer 5

Object with area but negligible thickness, like a sheet of paper.

Question 6

Lamina modelling assumptions

Answer 6

Mass is distributed across a flat surface.

Question 7

Uniform body meaning

Answer 7

Mass is distributed evenly

Question 8

Uniform body modelling assumptions

Answer 8

Mass of the object is concentrated at a single point at the geometrical centre of the body - the centre of mass.

Question 9

Light object meaning

Answer 9

Mass of the object is small compared to other masses, like a string or a pulley.

Question 10

Light object modelling assumptions.

Answer 10

Treat object as having zero mass.
Tension the same at both ends of a light strings.

Question 11

Inextensible string meaning

Answer 11

A string that does not stretch under load.

Question 12

Inextensible string modelling assumptions

Answer 12

Acceleration is the same in objects connected by a taut inextensible string.

Question 13

Smooth surface modelling assumptions

Answer 13

Assume that there is not friction between the surface and any objects on it.

Question 14

Rough surface meaning

Answer 14

If a surface is not smooth, it is rough.

Question 15

Rough surface modelling assumptions

Answer 15

Objects in contact with the surface experience a frictional force if they are moving or are acted on by a force

Question 16

Wire meaning

Answer 16

Rigid thin length of metal

Question 17

Wire modelling assumptions

Answer 17

Treated as one-dimensional

Question 18

Smooth and light pulley (all pulleys)

Answer 18

Pulley has no mass.
Tension is the same on either side of the pulley.

Question 19

Bead meaning

Answer 19

Particle with a hole in it for threading on a wire or string

Question 20

Bead modelling assumptions

Answer 20

Moves freely along a wire or string.
Tension is the same on either side of the bead.

Question 21

Peg meaning

Answer 21

A support from which a body can be suspended or rested

Question 22

Peg modelling assumptions

Answer 22

Dimensionless and fixed.
Can be rough or smooth as specified in question.

Question 23

Gravity meaning

Answer 23

Force of attraction between all objects. Acceleration due to gravity is denoted by g. In maths, g = 9.8. In physics, g = 9.81.

Question 24

Gravity modelling assumptions

Answer 24

Assume that all objects with mass are attracted towards the Earth.
Earth’s gravity is uniform and acts vertically downwards.
g is constant and is taken as 9.8 ms^-2, unless otherwise stated in the question

Question 25

Name the 7 forces that you are most likely to find in force diagrams.

Answer 25

1 - weight (mass x acceleration due to gravity)
2 - normal reaction (perpendicular and opposite to the force an object exerts on another object)
3 - friction (opposite to direction of motion)
4 - tension (if an object is being pulled along by a string, the force acting on the object is called the tension in the string)
5 - thrust (if an object is being pushed)
6 - buoyancy (the force that allows an object to float on water)
7 - air resistance

Question 26

How would you convert km h^-1 to m s^-1?

Answer 26

Set it up as a fraction (distance value over time value). Convert from km to m (multiply by 1000). Convert from h to s (multiply by 60x60). Divide through.

Question 27

How would you convert 1cm^2 to m^2?

Answer 27

cm to m is divide by 100. cm^2 to m^2 is divide by 100^2.

Question 28

4 examples of scalar quantities (magnitude and direction)

Answer 28

1 - displacement
2 - velocity
3 - acceleration
4 - force/weight

Question 29

4 examples of scalar quantities (magnitude only)

Answer 29

1 - distance
2 - speed
3 - time
4 - mass

Question 30

If right is positive, what does it mean if a particle has negative velocity and negative acceleration?

Answer 30

The particle is moving to the left and its speed is increasing.
(When the direction of the acceleration opposes the direction of motion, the particle is slowing down. This is also called deceleration.)

Question 31

What does speed = |velocity| mean?

Answer 31

The value for the speed is the absolute value for the velocity.
If the velocity is -9.5ms^1, the speed is 9.5ms^-1.

Question 32

Which direction is the vector j?

Answer 32

1 unit up.

Question 33

Which direction is the vector i?

Answer 33

One unit to the right.