Forces in Equilibrium

Question 1

What is vector quantity?

Answer 1

Any physical quantity that has a direction as well as a magnitude

Question 2

What is a scalar quantity?

Answer 2

Any physical quantity that has a magnitude only (not directional).

Question 3

Examples of scalar quantities?

Answer 3

Mass
Density
Energy
Speed
Distance
Temperature
Time
Pressure
Length, Area + Volume

Question 4

Examples of vector quantities?

Answer 4

Displacement
Velocity
Acceleration
Momentum
Force

Question 5

How is distance, the scalar quantity, different to displacement, the vector quantity?

Answer 5

Distance depends on the route you take - there is no single direction. However, displacement id the distance in a single given dirction. The direct distance from the start point to the end point.

Question 6

How can vectors be represented?

Answer 6

As an arrow
Length of arrow represents the magnitude of vector quantity
Direction of arrow represents the direction of vector quantity

*If asked to draw a scale diagram, remember to include a scale (use a ruler + protractor)

Question 7

How to add two vectors together?

Answer 7

Scale diagrams

Trigonometry and Pythagorus

Question 8

How to use scale diagrams to add two vectors?

Answer 8

Choose a scale (e.g. 1cm=1N) and indicate it on the paper.
Draw a triangle using the scale, where two of its sides are the vectors.
Join the two vectors together to form the third side of the triangle which is the resultant vector.
Next, using the scale determine the magnitude of the the resultant vector, measuring it with a ruler.
Next, using a protractor find the angle of the force (stating e.g. 46degrees clockwise from 16N force)

Question 9

A scale diagram cam be used whenever there are two vectors. When can we use trigonometry and pythagorus to add vectors?

Answer 9

When adding two perpendicular vectors i.e. at right angles to each other.

Question 10

How to add two perpendicular vectors together?

Answer 10

Pythagorus to find the magnitude of resultant vector and Trigonometry so SOHCAHTOA, for direction of resultant vector.

Question 11

If forces act in the same direction….

Answer 11

…add them together to find the resultant force.

Question 12

If forces act in the opposite direction…

Answer 12

…subtract them from each other to find the resutlant force.

Question 13

How to resolve forces into to perpendicular componenets?

Answer 13

Using figure 11 on pg98
To find the horzontal component: F x cosθ
To find the vertical component: F x sinθ

Question 14

How to draw free body diagrams?

Answer 14

Objects represented as dot or square.
Show forces that act on the body but not the forces the body exerts on the rest of the world.
Forces are vectors so the arrow should show magnitude and direction (and label the force)

Question 15

If a body is in equilibrium, what will the free body diagram look like.

Answer 15

The forces acting on it will be opposite in direction but equal in magnitude so resultant force is 0

Question 16

Examples of when a body is in equilibrium?

Answer 16

Stationary or moving with a constant velocity

Question 17

When 2 forces act on a point object, the object is in equilibrium if?

Answer 17

If the two forces acting on it are opposite in direction but equal in magnitude, the resultant force is 0.

Question 18

When 3 forces act on a point object, the object is in equilibrium if?

Answer 18

If any of the two forces acting on it are opposite in direction (when resolved) but equal in magnitude to the third force, the resultant force is 0.

Question 19

How to check if the 3 forces acting on a point object is in equilibrium?

Answer 19

Resolve each force along the same parallel or perpendicular line, before balancing. Use pythagorus if possible.

Question 20

When 3 forces act on a point object…

Answer 20

… you can form a closed loop triangle.

Question 21

What is the moment of a force?

Answer 21

The moment of a force about any point is defined as the force x perpendicular distance from the line of action of the force to the point.

Question 22

What is the equation to calculate the moment of a force?

Answer 22

M = Fd
Moment = Force x perpendicular distance from the line of action of the force

M = Moment (Nm)
F = Force (N)
d = Perpendicular distance from the line of action of the force (m)

Question 23

What is the principle of moments?

Answer 23

For an object in equilibrium, the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about that same point.

Question 24

Define centre of mass

Answer 24

The centre of mass of a body is the point through which a single force on the body has no turning effect/where the weight of the body acts.

Question 25

If the mass of an object is uniform…

Answer 25

Its centre of mass is at its centre.

Question 26

How can the priniciple of moments be written as an equation?

Answer 26

F₁d₁ = F₂d₂

Question 27

How to solve single-support problems?

Answer 27

Use the formula F₁d₁ = F₂d₂ to calcualte whatever is being asked where F₁d₁ is the sum of all the clockwise moments acting about a point and F₂d₂ is the sum of anticlockwise moments acting about the same point.

*Choosing a point where more than one or more forces acts means less calculations as such forces have zero moment about this point (as distance is 0)

Question 28

How to solve two-support problems?

Answer 28

If the centre of mass of e.g. a beam is midway between two supports, the weight of the beam is shared equally.
If the centre of mass of the beam is not midway between the two supports, we need to take moments about each support so doing F₁d₁ = F₂d₂ for both supports to calculate whatever is beign asked.

*IMPORTANT: When you’re taking moments about point X, the first pillar, you’re calculating the support force acting on the other pillar, point Y. When you’re taking moments about point Y, the second pillar, you’re calculating the support force acting on the first pillar, X.

Question 29

What is a couple?

Answer 29

A couple is a pair of equal and opposite forces acting on a body, parallel to each other, but not in the same direction (not same line of action).

Question 30

What type of force does a couple not produce?

Answer 30

A couple does not cause any resultant linear force, but does produce a turning effect (a moment).

Question 31

Equation calcualte moment of a couple?

Answer 31

Moment of a couple (Nm) = size of one of the forces (N) x perpendicular distance between the line of action of the forces(m)

A variation of M = Fd.

Question 32

What does the stability of an object depend on?

Answer 32

Its centre of mass

Base area

Question 33

The more stable an object is…

Answer 33

The lower its centre of mass and/or the wider its base area.

Question 34

What is stable equilbrium?

Answer 34

This is when an object, displaced by a force, from equilibrium returns to equilibrium as its centre of mass remains inside the pivot point.

Question 35

What is unstable equilbrium?

Answer 35

Unstable equilibrium is when an object, displaced by a force, from equilbrium does not return to equilbrium, as its centre of mass has been moved outside of the pivot point.

Question 36

For tiliting of an object to occur, what equation must be true:

Answer 36

Fd > W x b/2

Question 37

If tilting does not occur, what equation must not be true?

Answer 37

Fd < W x b/2

Question 38

What does unstable equilibrium means?

Answer 38

Unstable equilibrium means that there is a resultant moment, which provides a turning force (clockwise or anticlockwise depending on which way it tipes).

Question 39

For an object to topple, what must be true?

Answer 39

First it must tilt, so this equation, Fd > W x b/2, is true. But for it to also topple, the line of action of the weight (of the object) must pass the pivot point.

Question 40

In the equation Fd = Wb/2, which is the anticlockwise and clockwise moments?

Answer 40

Using figure 3 pg108,
The clockwise moment of force F about pivot P is = Fd, where d is the perpendicular distance from the force.
The anticlockwise moment of force W about pivot P is W x b/2, where b is the width of the base.

Question 41

For objects on a slope, how can we calculate the maximum angle before an object topples?

Answer 41

Resolve forces parallel to the slope, by doing F = W x sinθ. F is friction in this case
Resolve forces perpedicular to the slope, by doing S = W x cosθ. S is the support force.
Next divide the first equation by the second equation so, F/S = W x sinθ/W x cosθ = tanθ

e. g. is F = 5 and S = 2, we would do tan⁻¹(5/2) = 68ᵒ
* If there are two support forces, ie acting up at each wheel, S = Sₓ + Sᵥ.