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Assignment 6 Collisions, circular motion and oscillations
Introduction
Aims
This assignment will test your ability to: ?? answer multiple-choice questions ?? describe practical situations and interpret measurements.
You do not need to have studied the physics that underlies these experiments in order to be able to complete the tasks.
The assessment objectives for the A level that are relevant to this assignment are to: ?? apply knowledge and understanding of scientific ideas,
processes, techniques and procedures:
?? 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.
National Extension College
Your tutor will assess the following aspects of your work: ?? your application of appropriate physical principles ?? your use of appropriate equations ?? the accuracy of your calculations ?? your use of graphs and drawings where directed ?? your use of appropriate units.
Are you ready to do this assignment?
Before you tackle this assignment, ensure that you have studied Section 6 of the course, and Chapters 1, 2 and 15 of the textbook. While you are encouraged to do the experiments, this is not essential, since sample data will be given to you. However, if you have your own data, please substitute it.
In addition to the usual writing materials (or computer) you will need a sharp pencil, ruler and protractor, 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.
You will need to refer to the equation sheets for A-level Physics, which are to be found in the downloadable documents in this Section (6).
1 A spectator throws a snowball from the sidelines and it hits and sticks to a skater on the ice. In this collision we can say the following:
Table 1 Data for Question 1
Choice Type of collision Kinetic energy Momentum
(a) Elastic Conserved Conserved
(b) Inelastic Not conserved Conserved
(c) Elastic Conserved Not conserved
(d) Inelastic Not conserved Not conserved
Choose the correct description from choices (a) to (d) In Table 1
(1 mark)
2 A ball on a string is being swung round in the clockwise direction. When it reaches the position shown in Figure 1, the string is cut. Which of the arrows in (a) to (d) indicates the direction in which the ball will continue to move?
(1 mark)
Figure 1 Illustration for Question 2
3 Figure 2 shows the displacement plotted as a function of time (horizontal axis) for an oscillation.
Figure 2 Illustration for Question 3
From the graphs (a) to (d) in Figure 3, choose the graph that could represent:
(a) velocity versus time for this oscillation
(1 mark) (b) acceleration versus time for this oscillation.
(1 mark)
Figure 3 Possible responses for questions 3(a) and 3(b)
4 The graph in Figure 4 shows the force on a tennis ball as a function of time. The tennis ball has a mass of 0.06 kg. Estimate the initial speed of the ball as it leaves the racquet. (4 marks)
Figure 4 Force–time graph for the tennis ball
5 There is a bend in a level road (i.e. there is no camber) which has a radius of 25 m. The tyres on a vehicle are in good condition and the road is dry. In these circumstances the maximum frictional force is equal in magnitude to the gravitational force on the vehicle.
(a) What is the maximum speed at which the vehicle can go
around the bend without skidding?
(2 marks)
There is black ice on the bend one morning, reducing the magnitude of the friction to 0.10 times the gravitational force on the vehicle.
(b) What is the maximum speed at which the vehicle can go around the bend on black ice without skidding?
6 Figures 5 and 6 show the data from the use of the Tracker software in Core Practical 10.
(a) Mass A. The upper plot shows the displacement versus time in the x direction and the lower plot gives the corresponding data for the y direction.
The grid lines on the horizontal axis are 0.2 seconds apart.
The grid lines on the vertical axis are 5 units apart.
Figure 5 Data from the collision of two pucks; Mass A
(b) Mass B. The upper plot shows the displacement versus time in the x direction and the lower plot gives the corresponding data for the y direction.
The grid lines on the horizontal axis are 0.2 seconds apart.
The grid lines on the vertical axis are 5 cm apart.
Figure 6 Data from the collision of two pucks; Mass B
Use this data, or your own, to demonstrate that momentum is conserved.
(16 marks)
7 Astronauts living in space for considerable periods of time have to adapt to weightlessness. One method of creating artificial gravity is to build a space station in the form of a ring, and spin it so that the centripetal force on the humans mimics the feel of a gravitational force.
A space station is planned to have a radius of 500 m (Figure 7). It will be spun so that the centripetal acceleration is 9.80 m s–2.
Figure 7 Space station (not to scale)
(a) What will be the angular velocity of the feet of the astronauts?
(3 marks) (b) At how many revolutions per minute will the space station need to spin?
(3 marks)
8
(a) Calculate the length of a pendulum which will have a period of one second, correct to three significant figures.
(3 marks)
(b) If this pendulum is transported to the moon, where the acceleration due to gravity is 1.62 m s–2, what will be its period on the moon?
(3 marks)
9 Use the data in Tables 2 and 3, from Core Practical 16, to find the unknown masses, by drawing a suitable graph.
Table 2 Measurements of the oscillation of a spring
Mass added/g Mean time for 10 oscillations/s
5 15.0
10 15.6
15 16.4
20 17.2
25 17.8
Table 3 Measurements of the oscillations of the unknown masses
Times for 10 oscillations/s
Mass 1 17.33 17.19 17.22 17.13 17.21
Mass 2 16.53 16.44 16.50 16.22 16.46
(4 marks for a suitable graph, 4 for finding the unknown masses)
10 A boat is lying alongside a jetty. The boat is bobbing up and down with simple harmonic motion which has a period of 5 s. The amplitude of the rise and fall is 0.6 m. At its highest point the boat is just level with the jetty. In order to comfortably step off the boat onto the jetty the difference in height needs to be
no more than 0.3 m. For how long, in each cycle, is the boat within that range?
(6 marks)
11 The terminal velocity, v, of a body falling in air was measured as a function of the projected area, A, that it presented. The following results were obtained:
Table 4 Data for Question 11
Projected area A/m2 Terminal velocity v/m s–1
0.5 51.1
1.0 36.2
2.0 25.6
3.0 20.9
4.0 18.1
5.0 16.2
6.0 14.7
10.0 11.4
It is thought that the two quantities are related to one another by the equation:
v = C An
where n and C are both constants. Using your calculator to do any necessary processing, plot a suitable graph to find the value of n.
(6 marks) (Total for assignment 60 marks)