Struggling with Moments?

Balancing turning forces – the principle of moments

When an object is balanced on a pivot the turning effect of the forces on one side of the pivot must balance the turning effect of the forces on the other side of the pivot - if they didn’t it would not balance.

In the picture two girls are sitting on a see saw. They have moved until it is balanced. They are the same weight and so to balance the see saw they must sit the same distance from the pivot.

In the picture one of the girls gets off and a man sits on instead. They move until the see saw is balanced. The girl is much lighter than the man and so she has to sit further away from the pivot then he does so that she can balance his extra weight.
You can investigate this in the lab by using sets of weights hanging on a wooden ruler:
The principle of moments

You should remember that the turning effect of a force is called the moment of the force and is found by multiplying the force by its distance from the pivot. When the see saw is balanced we say that the anticlockwise moments (those trying to turn the object anticlockwise) equal the clockwise moments (those trying to turn the object clockwise). In our example the man’s weight tries to turn the see saw clockwise and the girl’s weight tries to turn it anticlockwise.

The rule for something to be balanced is called the principle of moments and is written as follows:

 When an object is balanced (in equilibrium) the sum of the clockwise moments is equal to the sum of the anticlockwise moments.

Force 1 x distance 1 from pivot  = Force 2 x distance 2 from pivot

F₁ d₁ = F₂ d₂

Struggling with circular motion?

Circular motion

Objects move in a straight tine at a constant speed unless a force acts on them. This is Newton’s First Law. However, many things move in curved paths, especially circles, and so there must be a force acting on them to pull them out of their straight line paths and make them turn corners.

The tighter the curve that the object is made to move in, the bigger the change of direction and so the bigger the force.

Examples of objects moving in curves are:

• The hammer swung by a hammer thrower

• Clothes being dried in a spin drier

• Chemicals being separated in a centrifuge

• Cornering in a car or on a bike

• A stone being whirled round on a string

• A plane looping the loop

• A DVD, CD or record spinning on its turntable

• Satellites moving in orbits around the Earth

• Many fairground rides

We call the force that makes objects move in a circle the CENTRIPETAL FORCE

(the name comes from Latin and means centre-seeking)

The centripetal force always acts towards the centre of the circle to pull the object out of its straight-line path. Although an object may travel round the circle at a constant speed its direction of motion is always changing and so its velocity must be changing. Since a change of velocity is an acceleration there must be a force acting on the object - the centripetal force.

What produces the centripetal force?

The actual way the force is produced depends on the particular example:

In a spin drier it is the wall of the drum pressing on the clothes. When a car, motorbike or bicycle corners it is the friction between the wheels and the road. (You know how difficult it is to corner on ice where there is hardly any friction.)

When the Earth orbits the Sun it is the pull of gravity.

When a railway train corners it is the force of the rails on the flanged wheels.

When a stone is whirled round on a string it is the tension in the string.

Medical Applications of Physics Prezi

A link to the Prezi from last lesson.  Remember sections of Ultrasound, X-rays and Total Internal Reflection were not covered in the lesson.

http://prezi.com/ivzvuu7rtck3/p3-revision-medical-applications-of-physics/

Test Yourself Mark Scheme - Pendulums

(a)   (i) and (ii)

       A suspended object will always stop so that its centre of mass is directly below the point of suspension.

The pendulum bob is a symmetrical object and so the centre of mass must be on an axis of symmetry. For a circle it will always be at the centre of the circle. The position of the stationary pendulum bob is clearly marked and supported with a well-explained reason.

(b)   The frequency would halve. 

Inversely proportional means more than simply ‘as one quantity increases the other quantity decreases’. If two quantities are inversely proportional, when one doubles the other will halve.

(c)   (i)  Hertz 

This could also have been given in symbol form (Hz). However, if you use symbols make sure they are correct. Hz gets a mark but hz would not.

       (ii)   time period, T = 22 ÷ 10 = 2.2 s 

               = 0.45 Hz 

The other values for frequency have been rounded to one decimal place so it would be okay to round this answer to 0.5.

       (iii)  No it does not support the hypothesis. If the hypothesis were correct then doubling the length from 0.5 m to 1.0 m should make the frequency go from 0.7 Hz to 0.35 Hz and it does not.

Marks are not awarded for simply saying yes or no. In this case 1 mark is given for a relevant calculation supporting the ‘no’. The answer could equally have used the example of doubling the length from 0.25 m to 0.50 m.

Test Yourself - Pendulums

	(a)   The diagram shows a simple pendulum at one point in an oscillation (swing).

       (i)    Draw a cross (´) on the diagram so that the centre of the cross marks the position of the centre of mass of the pendulum bob.                                                                             (1 mark)

       (ii)   Draw a circle on the diagram to show the position of the pendulum bob once the pendulum stops swinging.

              Give a reason for your choice of position.                                     (2 marks)

(b)   A student has written the following hypothesis.

              ‘The frequency of a simple pendulum is inversely proportional to the length of the pendulum.’

       If this hypothesis is correct, what would happen to the frequency of a pendulum each time the length is doubled?                                                                                                   (1 mark)

(c)   The student investigated the hypothesis by timing 10 swings of a pendulum. The student repeated this for several different lengths. The student’s experimental data and calculated data are recorded in the table.

Length of pendulum in metres	Time for 10 swings in seconds	Frequency in _____
0.25	10	1.0
0.50	14	0.7
0.75	17	0.6
1.00	20	0.5
1.25	22

       (i)    What is the unit of frequency?                                                         (1 mark)

       (ii)   Calculate the frequency of the pendulum when the length equals 1.25 m.

              Write down the equation you need to use and show how you work out your answer.      (3 marks)

       (iii)  Do the data in the table support the student’s hypothesis?

              Support your answer with a calculation.                                         (1 mark)

Test Yourself Mark Scheme - Moments & Hydraulics

(a)   1 Liquids are virtually incompressible. 

       2 Pressure is transmitted equally in all directions throughout a liquid. 

 Both of the properties have been expressed clearly and concisely. In the first answer if the word ‘virtually’ had been omitted the mark would still have been given. If you forget the word ‘incompressible’ you could say ‘cannot be squashed’.

(b)    2 ´ 10⁵ N 3

 ome of the data have been given in standard form. You can leave them like this and give an answer in standard form or rewrite 8 ´ 10⁶ as 8 000 000 and give the answer as 200 000 N. However, for some questions, mainly those involving very big or very small numbers, you should understand and be able to use standard form.

(c)   If the maximum weight were exceeded the moments would no longer balance. The resultant moment would cause the crane to topple. 

Although it is not clear if it is the whole crane or just the jib that would topple, the marks have been given for the idea that a resultant moment will cause something to rotate.

Test yourself - Moments & Hydraulics

The diagram shows a mobile crane. The tower is raised and lowered hydraulically.

(a)   What two properties of a liquid are used by a hydraulic machine?      (2 marks)

(b)   The clockwise moment about point P, caused by the weight W, is 8 ´ 10⁶ Nm.

       Calculate, in newtons, the size of the weight W.

       Write down the equation you need to use and show how you work out your answer.  (2 marks)

(c)   The maximum weight that the crane can be used to lift is 5 ´ 10⁵ newtons.

       Explain why this maximum weight must not be exceeded.                    (2 marks)

P3.2 Using physics to make things work - Summary Sheet

I have now uploaded the summary sheets for Using physics and Keeping things moving.  

Summary Sheets