Foundation Mechanics Forces and Friction H10FM1 & H10FM2
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UNIVERSITY OF NOTTINGHAM
FOUNDATION MECHANICS
LABORATORY 1
FORCES AND FRICTION
Aims:
1. To use vector addition to prove equilibrium of a series of forces 2. To investigate the Laws of Friction
Introduction
This laboratory is split into two sections, each one should take you about one hour to
complete. They are based on the self contained Leeds Mechanics Kit.
NOTE:
Before you come to the laboratory session, you should complete the attached worksheet
to help you understand some of the concepts.
The report should be written according to the material available on WebCT in the Study
Skills lecture on writing laboratory reports. You are STRONGLY advised to use the
report writing template and adapt it.
You should include a copy of the sheet obtained during part (1). You only need to add
any method if you did something different to the method in this laboratory sheet.
Remember that you have ONE WEEK to complete the report.
You need to submit the report electronically via the Turnitin option on the WebCT site
for Foundation Mechanics.
Foundation Mechanics Forces and Friction H10FM1 & H10FM2
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Part 1 Vector addition of forces
Equipment
Leeds Mechanics Kit
A selection of masses
Length of inelastic string
Pulleys
Mass hangers
Sheets of paper
Blutak or other self-adhesive fixing agent
Ruler
Protractor
Method
1. Lift the lid of the box into the upright position and fix it in position using the support inside the box.
2. Place each of the two pulleys into two of the holes along the edge of the lid (see figure 1)
Figure 1 Leeds Mechanics Kit as a Force Board
3. Attach a piece of paper to the lid (as shown in figure 1) using the Blutak.
4. The inelastic string is hung over the pulleys and the mass holders are attached to each of the three ends.
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5. Select three masses to attach to each of the mass holders that will enable the system to attain equilibrium.
6. Mark the position of the string onto the paper. Note the TOTAL mass on the end of each of the mass holders.
7. Now repeat the set up for another four sets of different masses, so that each of you has at least one original set of results to include into your report (note, you will
also need the results of the other members of your laboratory group.
Analysis of results
Once you have obtained the direction of the string on your piece of paper, draw the
SPACE DIAGRAM showing the position of the string during the experiment.
Measure the angles s shown in figure 2.
Knowing the masses applied to the end of the string, mark on the Space Diagram the
tension in each of the strings.
From this space Diagram construct the VECTOR DIAGRAM or use the ideas of
resolving forces to analyse the results (i.e. resolve each of the tensions into its vertical
and horizontal component and use these components to mathematically establish
equilibrium), and if the calculations suggest that equilibrium hasnt been established, look at the experimental set up and ask is there a net force on it?
What you should obtain, for each test is something like this:-
F2 F3
2 3
F1
Figure 2 Angles to be measured
The loads F1, F2 and F3 are assumed to be the same as the weights attached to the string
(if there is no friction over the pulleys is this a valid assumption?)
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The angles 2 and 3 can be measured from the vertical extension of the line of action of load F1.
If we now resolve horizontally
F3 sin 3 = F2 sin 2
Resolving vertically should give
F1 = F2 cos 2 + F3 cos 3
What you need to do is calculate the percentage differences from the two equations for
EACH test.
For example, if we had the following results
F1 = 16 N, F2 = 12 N, F3 = 16 N, 2 = 40o and 3 = 45
o, then
Horizontally 16 sin (45o) 12 sin (40o)
There is an error here as the left hand side does not equal the right hand side. You can
find the error by taking away the two results and dividing it by one of them.
Thus
Error = 16 sin (45o) - 12 sin (40
o) x 100 = 18.7 %
16 sin (45o)
Vertically Calculated F1 = 16 cos (45o) + 12 cos (40
o) = 20.5 N
Now calculate (F1 Calculated F1) x 100 = (16 20.5) x 100 = -28.2% F1 16
This will give you a percentage error. The question is that you must address is is this significant? Now discuss this in the discussion!
Points for discussion
1. Why is each string assumed to be light and each pulley smooth? 2. Why is the string assumed to be inelastic? 3. Within reasonable experimental error, has equilibrium been established? 4. How can two forces be combined to produce a resultant?
Foundation Mechanics Forces and Friction H10FM1 & H10FM2
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Part 2 Friction
Equipment
Leeds Mechanics Kit
Friction plane
Wooden block
Masses of various sizes
Mass holder
Method
1. Find the mass of the wooden block by weighing it.
2. Set up the apparatus as shown in the figure below (figure 3)
Figure 3 Friction experiment
3. Start off with the plane horizontal.
4. Place the wooden block on the friction plane. Add masses to the mass holder until the wooden block is JUST on the point of sliding (you may find that light tapping
on the wooden block helps determine this point).
5. Record the mass (M1) of the wooden block and the mass applied to the mass holder to just start the block moving (m).
6. Increase the mass of the wooden block by adding masses to it. Find the new mass that has to be applied to the mass holder to JUST start the wooden block moving
(m).
7. Repeat the procedure (5) and (6) for 5 more different masses (M1), recording the applied mass to the mass holder (m) to JUST start it moving.
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8. Plot a graph of applied mass (m) against the mass of the wooden block (including any additional masses you have applied!).
9. Now remove all the applied masses from the wooden block and place it on the inclined plane. Increase the inclination of the plane to a point when the wooden
block just starts to slip (figure 4). Measure the angle of the plane from the
horizontal.
Figure 4 Inclined plane with friction
10. Now add 100g to the mass of the wooden block. Repeat the method of part (9), increasing the angle of the plane until the block just starts to move.
11. Repeat for an additional 100 g.
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Theory
Horizontal plane
A schematic diagram of the experiment
Wooden block Pulley
Plane
Mass hanger with additional mass
Assuming the block can be modeled as a particle, a free body diagram of the experiment
is
Normal reaction, N
Friction, F Tension is string, T
Mass of wooden block AND applied masses, Mg
If the string is light and inextensible, the pulley is frictionless and the block is in
equilibrium and JUST on the point of moving, we can resolve the forces horizontally and
vertically.
Horizontal F = T (1)
Vertical N = Mg (2)
For limiting friction F = N (3)
Or T = Mg
Draw a graph of the tension in the string against the mass of the wooden block and the
applied masses (i.e. T against Mg); this should give a straight line with a gradient equal
to the coefficient of friction.
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Find the coefficient of friction from this graph.
(Question: how does the tension in the string relate to the weight of the mass hanger and
the additional masses?)
Inclined plane
Assuming
1. The block is a particle 2. Limiting friction is applicable 3. The block is just on the point of slipping
4. The inclination of the plane to the horizontal is
Normal reaction, N
Friction (opposing motion) F
Mass of wooden block and any applied masses
Mg
Resolving parallel to the plane
F = Mg sin (4)
Resolve perpendicular to the plane
N = Mg cos (5)
Limiting friction
F = N (6)
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Combining equations (4), (5) and (6) gives
Mg sin = Mg cos or = tan
Analysis of results
You should draw neat tables in EXCEL and use EXCEL to draw the graphs and extract
the relevant information.
Think about what the TOTAL applied weight is on one side of the pulley and what the
tension in the string is. Also think carefully about the TOTAL mass of the wooden block!
Compare the coefficient of friction obtained from the horizontal plane to that obtained by
the inclined plane. Are there any differences? Should there be?
Points for discussion
1. How do you know when the block is just on the point of sliding? How did you ensure consistency between different experiments?
2. How close are the two values of the coefficient of friction from both parts of the experiment? Are they the same? Should they be?
3. Why is it important that the block be on the point of sliding and not actually sliding?
4. How does M relate to M1? What is missing from the assumption? 5. Should the block be placed in the same position every time? Why? 6. Why does the tangent of the angle of inclination give the coefficient of
friction?
7. Does the angle of inclination vary when the mass of the block is changed? Would you expect this?
8. Can the coefficient of friction exceed unity? 9. Where is friction useful and when is it a nuisance? 10. How could you reduce the friction?
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Worksheet for part 1
1. A swing of weight W is supported by two vertical ropes as shown below.
T1 T2
W
a) What can you say about the three forces? b) How large would T1 and T2 be?
2. A weight W is supported by two strings as shown below.
T1 T2
W
b) What can you say about the three forces? c) What is the combined effect of the three forces? d) If the two strings were removed, what single force would be required
to keep the weight in equilibrium?
e) What is the combined effect of T1 and T2?
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3. How can three forces of 50N, 40 N and 30N be placed so that they are in equilibrium? What are the angles between the forces?
4. What does it mean that a pulley is frictionless? Why are strings considered to be
light and inextensible?
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Worksheet for part 2
Take hold of a long stick (a metre rule is ideal for this) and hold is with just your fingers.
Finger 1 Finger 2
Figure A Supporting a ruler asymmetrically
Support the stick asymmetrically (as shown in fig A) with the index fingers of both
hands.
Now try to move your fingers gently towards each other and observe what happens.
Why finger moves first? Why?
Now replace one of your fingers with a pencil and repeat the procedure of moving the
pencil and the other finger towards each other.
Which moves first now? Why?
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Try again, but use an eraser rather than a pencil.
Which moves first now? Why
If a mass is at rest on an incline plane, determine the values of for which the mass remains at rest.
Block of mass M kg
Can the friction force ever be zero?
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Writing your report
Include in your report:-
1. Aims (from this lab sheet) 2. A BRIEF introduction 3. The results in a table, showing all the key points, such as the horizontally
and vertically resolved forces
4. A TYPICAL calculation (dont repeat all the calculations) 5. A discussion based on the questions posed on this lab sheet. 6. Give your results and compare them to what you would have expected. If
they are not as the theory predicts, try and explain why there are
differences (and dont just say experimental error, try to be more subjective)
7. A list of WHAT YOU FOUND OUT in the conclusions, which answer the AIMS