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Assignment 4: Materials & vibrations
Introduction
Aims
In this assignment you will answer questions based on the contents of Section 4 of the course. You will:
? describe practical situations and interpret measurements
? solve problems in materials and vibrations, using the methods taught in the Section, using the equations on the data sheet.
These are question types that are used in the 'A' level examination papers.
The assessment objectives for the A level are to:
? demonstrate knowledge and understanding of scientific ideas, processes, techniques and procedures
? apply knowledge and understanding of scientific ideas, processes, techniques and procedures:
• in a theoretical context
• in a practical context
• when handling qualitative data
• when handling quantitative data
? analyse, interpret and evaluate scientific information, ideas and evidence, including in relation to issues, to:
• make judgements and reach conclusions
• develop and refine practical design and procedures.
The Open School Trust
? your application of appropriate physical principles
? your use of appropriate equations
? the accuracy of your calculations ? your use of appropriate units.
An error in calculation in one step of a question will not normally lead to a loss of marks in subsequent calculations, provided the principles are applied correctly and your answers are consistent with the figures you have used.
Are you ready to do this assignment?
Before you tackle this assignment, ensure that you have done the quizzes and most of the practice exam questions in each of Chapters 12 to 14 inclusive. This assignment also contains material from Core Practicals 4, 5 and 7, with sample data for those who were not able to do the experiments.
In addition to the usual writing materials (or computer) you will need a sharp pencil, ruler, graph paper and a calculator.
The Assignment
In calculations, use g = 9.81 m s-2 for the acceleration of free-fall unless told otherwise.
1 It is proposed that the following parameters affect the resistive force on a ball bearing falling through a viscous liquid
a) The diameter of the ball
b) The mass of the ball
c) The viscosity of the liquid
d) The velocity of the ball
Table 1 Key for question 1
Choice for your answer Factors from the list that affect the resistive force
A All of them
B Just a), c) and d)
C Just b), c) and d)
D Just c) and d)
2 The graph in Figure 1 shows the variation of velocity with time for a sphere falling through a liquid.
Velocity Upthrust on Viscous
sphere, U drag, F
Weight of
Time sphere, W
Figure 1 The forces on a falling sphere and the graph of velocity vs time
Which of the following statements is true?
A At point 1, W U + F
B At point 2, W U + F
C At point 1, W U + F
D At point 2, W U + F
(1 mark)
3 Figure 2 is used in questions 3, 4 and 5.
Figure 2 Graphs of stress versus strain for 4 materials, A to D
Which of the lines A-D represents the stiffest material? (1 mark)
4 In the drawing for question 3, Figure 2, which material is brittle? (1 mark)
5 In the drawing for question 3, Figure 2which material could be a polymer? (1 mark)
6 Figure 3 shows two waves. What is the phase difference in radians between these waves?
Figure 3 Illustration of two waves for Question 6
A Zero
B ?
C ?/2
D 3?/2
(1 mark)
7 My microwave oven states that the frequency is 2.45 GHz. The speed of electromagnetic radiation in air is 3 x 108 m s-1. The wavelength of the microwaves in my oven is:
A 0.12 m
B 0.12 cm
C 8.3 m
D 8.3 cm
(1 mark)
8 This question concerns Core Practical 4; the measurement of viscosity of a liquid using the falling ball method. If you were not able to do this experiment, base your answer on the school experiment and use the sample data given.
a) Write a report of the falling ball method of measuring viscosity. Ensure you describe the importance of the shape of the falling object, laminar flow and the attainment of terminal velocity.
(5 marks)
b) Using a graduated syringe I found that 20 droplets was 0.89 ml (don’t forget that one ml is equivalent to 1 cm3). Calculate the radius of one drop, expressing your answer in m. (3 marks)
c) I found that 50 ml of the oil I used had a mass of 46.34 g.
Calculate the density of the oil in kg m-3. (2 marks) At the temperature of the room where the experiment was done, the density of water is 998.2 kg m-3.
The timings for the droplets of water falling through the oil were:
Table 2 Data from a falling ball experiment
Distance fallen/ cm Timings/s
10 13.40 13.47 13.51 13.21 13.40
d) Using these data (or your own), calculate the viscosity of the oil
(4 marks)
9 This question concerns Core Practical 7, investigating the relationship between the length and the frequency of vibration of a string.
a) Describe a school experiment to investigate the relationship between the length of a string and the fundamental frequency at
which it vibrates. (3 marks)
The data obtained for the kite string that I used in my experiment is in the table below:
Table 3 Data of length of string and frequency of vibration
Frequency/Hz Length of string/cm
300 18.7
400 14.0
500 11.3
600 9.5
b) State the equation that links frequency to the length of string,
when mass per unit length and tension are kept constant. Define
all the quantities in the equation. (2 marks)
c) Plot a suitable graph from the data above (or your data) to demonstrate that this equation is valid. (4 marks)
d) How would you modify the experiment to demonstrate the relationship between frequency and tension in the string?
(3 marks)
10 This question concerns Core Practical 5; the measurement of the Young modulus. Please base your answer on your own experiment and your own data, if you were able to do it. If you were not, please base it on the school experiment described in the text book, and use the sample data below.
a) Write a report of your experiment to measure the Young modulus of a material, or the school experiment. Ensure that you list all the measurements that need to be made. (4 marks)
These were my results, which were obtained on nylon fishing line:
Table 4 Data for the Young modulus experiment
marker/ cm Position of bottom marker /cm
0 6.9 108.4
50 7 110.1
100 7.2 112.2
150 7.4 113.8
200 7.6 115.7
250 7.7 116.9
b) Use these results, or your own, to find the extension as a function of load, and plot a graph of load versus extension.
(4 marks)
c) Does this graph indicate that the material obeys Hooke’s law?
(1 mark)
d) The nylon line has a diameter of 0.13 mm. Calculate the Young modulus of this material. (4 marks)
11 A school child is designing a catapult for shooting dried peas, which have a mass of 4g each.
He wants to estimate the initial velocity of the peas and measures the force-extension characteristics of the rubber band that he has.
The measurements are in the table:
Table 5 Data for Question 11
Mass hanging from rubber catapult/ g Extension / cm
250 0.7
500 2.0
750 3.5
a) Plot a graph of force versus extension and use it to estimate the energy stored in the rubber, in Joules, when the load is 750 g
(be careful with the units) (5 marks)
b) If all this energy is transferred to the pea, estimate the initial maximum velocity of the pea when the catapult is drawn back to a 3.5 cm extension and released. (3 marks)
12 This question concerns longitudinal and transverse waves.
a) Distinguish between longitudinal and transverse waves, and give an example of each (4 marks)
b) What are two key differences between electromagnetic waves and mechanical waves (4 marks)
Total for assignment 62 marks