Forces in equilibrium (topic 6)

Question 1

Vector (definition)

Answer 1

Physical quantity that has both direction and magnitude

Question 2

Scalar (definition)

Answer 2

Physical quantity that has magnitude and is not directional

Question 3

How is displacement represented on a scale diagram?

Answer 3

An arrow from the first point to the second point; where the length of the arrow is in proportion to the shortest distance between the points

Question 4

How is velocity represented on a diagram?

Answer 4

Arrow in the direction of motion; where the length is proportional to the speed of the object

Question 5

How are force and acceleration represented on a diagram?

Answer 5

Arrow in the appropriate direction and in proportion to the magnitude of the object. Acceleration is a double-headed arrow.

Question 6

Rule for adding two vectors (example)

Answer 6

OB = OA + OB

Question 7

How to find the result of two perpendicular vectors

Answer 7

The resultant vector forms the hypotenuse of a right-angle triangle, so answer can be found with Pythagoras and tan theta = o/a

Question 8

How to find the result of two vectors acting along the same line

Answer 8

• The sum if both act in the same direction
• The difference if they act in opposite directions

Question 9

Equilibrium (definition)

Answer 9

An object is not accelerating in any direction as all forces acting on it are balanced

Question 10

How to see if an object is in equilibrium if its forces are acting at different angles

Answer 10

Resolve to get all forces on horizontal/vertical planes

Question 11

Method for testing the how equilibrium occurs with three forces acting on an object

Answer 11

A string is hung between two pulleys on clamp stands, with weightds either side to create tension. A second string with a weight attached is tied in the middle of the hanging string. Where the two strings meet now shows the angles between the three tensions acting at that point.

Question 12

What is parallelogram rule?

Answer 12

For an object in equilibrium with three forces acting in different directions, the third has magnitude equal to the diagonal length of a parallelogram formed from the other two forces.

Question 13

Moment equation

Answer 13

moment = Fd
where d is PERPENDICULAR distance from line of action to pivot

Question 14

Unit of moments

Answer 14

Newtonmetres

Question 15

Principle of moments

Answer 15

If a body is in equilibrium, then clockwise moments = anticlockwise moments

Question 16

Body (definition)

Answer 16

Object not modelled as a particle

Question 17

Centre of mass (definition)

Answer 17

The point in a body through which a single force on the body has no turning effect

Question 18

Test to find centre of mass (3)

Answer 18

Hang object from different points behind a mass on a plumb line. Draw in pencil along the string. Where lines cross is centre of mass

Question 19

Calculating weight of a metre rule using balance (3)

Answer 19

With a weight tied to one side balance object on a sharp edge. Measure distance from pivot to centre and distance from pivot to weight on the other side. Use principle of moments with the known moment of the weight to find force of ruler’s weight.

Question 20

Rule for an object with one support

Answer 20

Total downwards force = support force

Question 21

Will taking moments from a different point give different answers?

Answer 21

No. Moments can be taken from any point.

Question 22

Equation for support force in two-support problems

Answer 22

S = Wd / D

Wd= moment of weight on support
D = distance between supports

Question 23

If the centre of mass of a beam is equal distances from supports at either end, then…

Answer 23

Weight of the beam is shared equally so support force = W/2

Question 24

How to eliminate an unknown turning effect in a moments question

Answer 24

Take all moments from the point at which the unknown moment acts, so d = 0; Fd = 0.

Question 25

Couple (definition)

Answer 25

Pair of equal and opposite forces acting on a body, but not along the same line

Question 26

Stable equilibrium (definition)

Answer 26

A body that will returns to its equilibrium position if displaced (e.g. hanging basket)

Question 27

When does stable equilibrium occur?

Answer 27

Centre of mass of the object is directly below the point of support when the object is at rest

Question 28

Why does stable equilibrium occur?

Answer 28

The support force is above the centre of mass When the object is moved so centre of mass is not in line with support, greater vertical component returns object to equilibrium.

Question 29

Unstable equilibrium ( definition)

Answer 29

A body that will not return to equilibrium if displaced and released.

Question 30

Why does unstable equilibrium occur?

Answer 30

The centre of mass is above the support force, so if the body is displaced, the vertical component increase will make the body move further away from the equilibrium position.

Question 31

Tilting (definition)

Answer 31

An object at rest on a surface is acted on by a force that raises it on one side only. (e.g. bookshelf tilting along one edge)

Question 32

What must be true for tilting to occur?

Answer 32

Fd > Wb/2

The clockwise moment from the force F causing tilting must be greater than the anticlockwise moment of weight W (b/2 is the horizontal distance from W to pivot)

Question 33

Toppling (definition)

Answer 33

An object is tilted so that its centre of mass is is beyond the pivot, so it falls over.

Question 34

How to make an object more stable?

Answer 34

• increase width of base
• change distribution of mass so that centre of mass is lower

Question 35

Why is it easier for an object to topple when on a slope?

Answer 35

The horizontal base of the object has decreased (as it is diagonal). Hence it is easier for the centre of mass to go beyond the pivot.

Question 36

How to work with forces in different directions with a body on a slope?

Answer 36

Resolve weight and use adjusted vertical and horizontal components

Question 37

What does a free body diagram show?

Answer 37

Only the forces acting on an object (not the forces it exerts on other objects)

Question 38

Triangle rule

Answer 38

If three forces are in equilibrium, then vectors of F1, F2 and F3 should have sum of 0, as any two of the forces have a resultant equal and opposite to the third force.

Question 39

What must be true for three forces to be in equilibrium, and why?

Answer 39

Their lines of action must all intersect at the same point otherwise they will produce a turning force.

Question 40

Two requirements for a body to be in equilibrium

Answer 40

1) resultant force must be 0
2) moments of forces about the same point must balance (principle of moments)