Mechanics (Unit 2)

Question 1

Difference between a scalar and a vector

Answer 1

vector has magnitude (size) and direction, whereas scalar only has magnitude (size).

Question 2

Examples of scalars

Answer 2

speed, mass, time, energy, power

Question 3

Examples of vectors

Answer 3

displacement, velocity, acceleration, force, weight

Question 4

Adding perpendicular vectors by calculation

Answer 4

• draw vectors as a right angled triangle
• use pythagoras’ theorem to find magnitude of resultant vector
• use trigonometry to calculate the angle of resultant vector (sin=o/h; cos=a/h; tan=o/a)

Question 5

Adding vectors

by scale drawing

Answer 5

• write down scale eg 1cm=2N
• draw vectors to correct length and angle to each other “tip to tail”
• add the resultant vector line (from original tail to free tip)
• measure length and angle of resultant vector
• convert length into appropriate quantity (using scale) to find magnitude of resultant vector

Question 6

Conditions for equilibrium of two or three coplanar forces acting at a point

Answer 6

total resultant force equals zero
or
if the vectors representing the forces are added together they will form a closed triangle.

Question 7

Two conditions for a body to remain in equilibrium

Answer 7

1. resultant force acting on body is zero
2. resultant moment about any point is zero
   object could be stationary OR travelling at constant velocity

Question 8

Definition of a moment

Answer 8

force multiplied by the perpendicular distance between the line of action of the force and the pivot.

Question 9

Units of moment

Answer 9

Nm

Question 10

Principle of Moments

Answer 10

in equilibrium, the sum of the clockwise moments about a point equals the sum of the anticlockwise moments.

Question 11

Definition of moment of a couple

Answer 11

(one) force multiplied by the perpendicular distance between the lines of actions of the two forces.

Question 12

Definition of centre of mass

Answer 12

point in a body through which weight appears to act
or
point in a body where the resultant moment is zero

Question 13

Stable equilibrium

Answer 13

When a body is displaced then released, it will return to its equilibrium position

Question 14

Unstable equilibrium

Answer 14

When a body is displaced then released, it will not return to its equilibrium position.

Question 15

Displacement

Answer 15

distance in a given direction

Question 16

Velocity

Answer 16

rate of change of displacement
or
change in displacement divided by the time taken

Question 17

Acceleration

Answer 17

rate of change of velocity
or
change in velocity divided by the time taken

Question 18

Gradient of displacement and velocity time graphs

Answer 18

Gradient of a displacement time graph = velocity

Gradient of a velocity time graph = acceleration

Question 19

Area under velocity and acceleration time graphs

Answer 19

Area under a velocity time graph = displacement

Area under an acceleration time graph = velocity

Question 20

Average velocity

Answer 20

total displacement divided by total time

Question 21

Instantaneous velocity at a point

Answer 21

rate of change of displacement at that point

gradient at a point on a displacement time graph (need to draw a tangent to calculate gradient)

Question 22

Conditions for an object falling at terminal velocity

Answer 22

• resultant force on object is zero (weight and drag forces are balanced)
• acceleration is zero (F=ma)
• object travels at a constant velocity

Question 23

Factors affecting drag force on an object

Answer 23

• the shape of the object
• its speed
• the viscosity of the fluid/gas (measure of how easily fluid/gas flows past a surface)

Question 24

Explain why an object reaches terminal velocity falling through air

Answer 24

• initially only force acting is weight, so object accelerates at g.
• drag force increases with increasing speed.
• therefore resultant force decreases.
• eventually drag force = weight, forces are balanced.
• so resultant force is zero.
• as F=ma, acceleration is zero so object falls at constant speed.

Question 25

Horizontal and Vertical motion of a projectile

Answer 25

In absence of resistive forces
Horizontal motion: no force horizontally, no acceleration so constant velocity.
Vertical motion: constant force due to weight, constant acceleration (equal to g).

Question 26

Newton’s Laws of motion

Answer 26

1st Law
An object will continue at rest or uniform velocity unless acted on by a resultant force
2nd Law
The acceleration of an object is proportional to resultant force acting on it, ie F=ma (providing mass is constant)
3rd Law
If object A exerts a force on a second object B, then object B will exert an equal and opposite force on object A.

Question 27

Principle of conservation of energy

Answer 27

Energy is neither created or destroyed, only converted from one form to another

Question 28

Energy conversions of an object falling in presence of resistive forces

Answer 28

loss in gpe = gain in ke + work done against resistance

work done typically appears as heat

Question 29

Definition of work done

Answer 29

force multiplied by distance moved in the direction of the force

Question 30

Units of work done

Answer 30

J

Question 31

Power

Answer 31

rate at which energy transferred
or
energy transferred (work done) divided by time taken

Question 32

Units of Power

Answer 32

W (Watts) or Js^-1

Question 33

Resolving vectors into two perpendicular components

Answer 33

See sheet

Question 34

Resolving components along, and perpendicular to, an inclined slope

Answer 34

See sheet

Question 35

Displacement and Velocity time graphs for uniform acceleration

Answer 35

See sheet

Question 36

Displacement and velocity time graphs for non-uniform acceleration

Answer 36

See sheet

Question 37

Sketch time graphs for an object falling under gravity then reaching terminal velocity

Answer 37

See sheet

Question 38

Sketch time graphs for a bouncing ball

Answer 38

See sheet