1. Gravity 3/31/2009 Version

2. Consent for Participation in Research Construct Centered Design Approach to Developing Undergraduate Curriculum in Nanoscience Education Why am I being asked? You are being asked to participate in a research study focused on improving methods to teach students about 3- dimensional force interactions by allowing us to evaluate your in class responses to lecture questions. Your instructor is collecting your responses electronically. We will anonymously evaluate your responses to evaluate the effectiveness of the lecture material. This study is being conducted by Carmen Lilley and Robert Klie at the University of Illinois at Chicago.

3. Consent for Participation in Research Why is this research being done? The concept of 3-dimensional force interactions are relevant to understanding how object move at many length scales. In the case of the macroscale, concepts of gravity and electromagnetic forces are foundational knowledge to students in introductory physics. At the nanoscale, 3- dimensional electrostatic force interactions will result in what is called self-assembly, where environments are designed such that elements in those environments organize themselves into useful patterns. These concepts are difficult to teach with conventional white-board/black- board lectures. Using modern interactive, 3D computer graphics it may be possible to improve the learning of these concepts.

4. YES - I give my consent to allow my responses to be anonymously evaluated for research purposes and also certify that I am 18 years or older in age. Please press ‘A’ or NO - I decline to allow my responses to be anonymously evaluated and understand that by doing so, there is no impact to my course grade or relationship with the University of Illinois at Chicago. Please press ‘B’ Consent for Participation in Research

5. Question 1 Which of the following statements is correct: A - There is a gravitational field between the Earth and the person B - There is a gravitational field between the person and the dog C - Both A and B D - Neither of the above

6. Question 2 What is the direction of the gravitational force on the Earth’s surface? A - Gravity does not have direction B - Towards the Earth’s center of mass C - Away from the Earth’s center of mass D - Tangent to the Earth’s surface

7. Question 3 Given the following two objects, which of the following will increase the force on object B: A – Increasing the radius of object A B – Increasing the mass of object B C – Increasing the distance between objects A and B D – None of these will affect the force on object B

8. Question 4 Which of the following images correctly represents the gravitational field for the Earth and Moon? A B C D

9. Body Forces Body forces are forces that act on an object (for example a mass such as solid sphere or a charged spherical particle.) These forces permeate through the body of the object and thus the body force acts on the material throughout its volume. Imagine a mass, a body force acts on all points that describe that mass. Thus, the units of force for a body force are Force/Volume.

10. Gravity We are most commonly aware of gravity. We typically imagine gravity as being one dimensional when we consider gravity acting on an object on the Earth’s surface. For example here we see a person and a dog on the Earth’s surface.

11. Gravity We typically think of gravity on earth as being one dimensional where gravity acts “downward” towards the Earth’s center of mass. This is because we typically model the Earth as a sphere with a uniform density and therefore, it’s center of mass is located at the center of the sphere. The arrows shown in the figure are called field lines. These field lines indicate the direction in which the force is acting.

12. Gravity However, gravitational force is a force that acts between masses. This force is an attractive force. Thus, in addition to a gravitational force existing between the person and Earth or the dog and the Earth which is attractive, there is also an attractive gravitational force acting between the person and the dog. The gravitational force between the person and the dog is much smaller than the gravitational force between the person and Earth or the dog and Earth.

13. Gravity The magnitude of the gravitational force between two objects can be calculated with Newton’s Law of Gravity and is expressed in this equation: where : –G is called the universal gravitation constant and is equal to 6.67 x 10 -11 Nm 2 /kg –m 1 is the mass of object one –m 2 is the mass of object two –r is the distance between the two objects

14. Gravity If we consider m 1 to be the mass of the Earth (m 1 = 6 x 10 24 kg) and r to be the radius of the earth (r = 6.4 x 10 6 m), then the magnitude of force between an object on the Earth’s surface and the Earth is given by : Where –g is gravity on the Earth’s surface and is equal to 9.8 m/s 2 –m 2 is the mass of the –g is the gravitational acceleration that acts on an object when the object is located on the Earth’s surface and it will face “downwards” towards the center of mass of the Earth.

15. Gravity If we compare the force interaction between the person and the dog we can see that the force is much smaller, even though the distance between them is much smaller. This is because the mass of the person and the dog are much smaller that the mass of the Earth. A typical man weighs 70 kilograms. A typical dog weighs 15 kilograms. If we assume they are standing 1 meter apart then the force exerted on the man by the dog (and vice- versa) is: 7 x 10 -8 N. The force exerted on the man from the Earth is: 686 N or 10,000,000,000 times larger than the force on the man by the dog. On the Earth’s surface, the force that dominates is gravity because of the mass of the Earth. We call this the dominant force for this special case.

16. Gravitation Acceleration Field around the Earth Lets look at the gravitational acceleration field that exists around the Earth by zooming out our view so that we can see the entire planet. To draw the field lines we can imagine a “test” object that has some mass m. Let’s call this object particle P. If we move this particle around the Earth and sketch arrows that show the direction of the force, these arrows will face the Earth because the force between particle P and the Earth is an attractive force.

17. Gravitation Acceleration Field around the Earth If we imagine that the arrows’ color changes with magnitude of the force, then we can see that these arrows become brighter as we move towards the Earth and darker as we move away. This is because the magnitude of the force decreases at a rate of 1/r 2 with increasing distance away from Earth. There is a single force vector tangent to the gravitational field at all points in the gravitational field. If field lines were to intersect, this implies that there would be multiple directions for that force vector which is inaccurate.

18. Gravitation Acceleration Field around the Earth We should also note that the field is continuous, meaning it occupies all space around the Earth and exists at an infinite distance.

19. Gravitation Acceleration Field around the Earth If we draw a line that connects the arrows, then we get continuous lines which again are called field lines. These field lines are used to represent the gravitational acceleration and direction exerted on an object at a distance r. Assuming Earth is a perfect sphere then the field lines are radial lines normal to the Earth’s surface.

20. Gravitation Acceleration Field around the Earth We can also illustrate the shape of the gravitational field that exists around the Earth by using a cloud to represent the field shape. The edge of the cloud shows a constant value or magnitude of the gravitational field - these lines are called isolines. If we sketch the isolines around the Earth, then we see that we have a series of concentric circles.

21. Gravitation Acceleration Field around the Earth Remember that the field lines indicate the direction and shape of the gravitational acceleration as it varies throughout space. An isoline shows the shape of the region where the gravitational acceleration field is constant.

22. Gravitation Acceleration Field around the Earth We have been drawing these diagrams in two dimensions, but the forces exist in three dimensions as shown in these animations below.

23. Gravitation Acceleration Field around the Moon Now let’s look at the Moon in isolation. We can carry out the same procedure of moving particle P around the Moon to determine its gravitational acceleration field. We can see that the shape of the field is similar to that of the Earth because we model both the Earth and the Moon as spheres.

24. Gravitation Acceleration Field around the Moon Notice also that the magnitudes of the fields are different because the Moon has much less mass than the Earth. The mass of the Moon is 7.4x10 22 kg and the mass of the Earth is 600x10 22 kg so the mass of the Moon is approximately 81 times smaller than the mass of the Earth.

25. Gravitation Acceleration Field around the Earth and Moon To study the gravitational field that exists when we consider the Moon and the Earth together, we use what is called linear superposition where we directly add the gravitational acceleration fields that we have previously seen. Note then that the gravitational fields lines are no longer spherical, but vary with position around the Earth and Moon.

26. Gravitation Acceleration Field around the Earth and Moon We have been drawing these diagrams in two dimensions, but the forces exist in three dimensions as shown in these animations below.

27. Gravitation Acceleration Field around the Earth and Moon Imagine then the other planets, stars, meteors, objects with a mass that exist in space. We can draw gravitational field lines around all these objects and these gravitational fields lines would all overlap since they exist at infinite distances. However, since the magnitude of the gravitational field decreases with distance at a rate of 1/r 2, their influence decreases as we move further away from them. Thus, the gravitational force acting on any object, even on the Earth’s surface, is a sum of all objects that exist in space, but the dominant force or forces acting on the object will depend on distance between objects and the mass of the interacting objects.

28. Question 5 Which of the following statements is correct: A - There is a gravitational between the Earth and the person B - There is a gravitational field between the person and the dog C - Both A and B D - Neither of the above

29. Question 6 What is the direction of the gravitational force on the Earth’s surface? A - Gravity does not have direction B - Towards the Earth’s center of mass C - Away from the Earth’s center of mass D - Tangent to the Earth’s surface

30. Question 7 Why do Gravitational Field Lines never cross? A - The are radial to the center of mass of an object B - They are parallel C - Gravitational field lines are vectors, so at a point the field vectors add to a single vector. D - Field lines are concentric circles

31. Question 8 Given the following two objects, which of the following will increase the force on object B: A – Increasing the radius of object A B – Increasing the mass of object B C – Increasing the distance between objects A and B D – None of these will affect the force on object B

32. Question 9 There are three equal masses placed at each corner of an equilateral triangle with sides length d. Point A is located at the midpoint of one side of the triangle. Point B is located at the center of the triangle Which statement below best describes the magnitude of the gravitational field at point B: A - It is greater than at point A B - It is the same as at point A and both are greater than zero C - It is less than at point A D - The magnitude at A and B are both zero

33. Question 10 Which of the following images correctly represents the gravitational field for the Earth and Moon? A B C D

34. Question 11 Which of the following images correctly represents the gravitational field for three identical masses? A B C D