Week 10 (Mar. 17 - 21)
Read: Mass, Momentum and Force (Chap. 19); and Absolute and Relative Motion (ASGv2 Chap. 20).
Key topics: Mass, momentum, inertia, force, centripetal force, absolute and relative motion.
PHY 201 Lecture: Bernoulli's law, Torricelli's law, and the barometric equation
Key topics: Mass, momentum, inertia, force, centripetal force, absolute and relative motion.
PHY 201 Lecture: Bernoulli's law, Torricelli's law, and the barometric equation
Quiz: No quiz on Monday since spring break was last week.
Homework:
Lab: In lab this week, we will learn how to construct and analyze force (or “free body”) diagrams using a camera and Logger Pro software. The lab consists of two parts.
Part 1: Force table analysis: Attach 3 spring scales to a ring and to the different points on the perimeter of the force table. Place a ruler on the force table for scale calibration. Photograph the force table and insert the picture into an open Logger Pro session. Here is a sample force table picture. Note: Logger Pro can be persnickety about usable image formats; you may need to use jpeg. Also: be sure to save your original photograph, since Logger pro references your original image; it does not actually import the image. Make the image as large as possible in logger pro without it being too blurry. You should set the scale of the image using the ruler in the image. Also set the origin at an appropriate place in the image (probably the exact center point of the ring to which the three scales are attached. Here is a sample Logger Pro analysis screenshot. Find the x and y components of each force using trigonometry. In order to do this, you will need to determine the magnitude and direction of each force. To find the magnitude of a particular force, you can just read the spring scale. To find the angle, you will need to find two (x,y) coordinates for each force. The origin can be one and the distant end of the scale could be another. From these points, you can find the angle of the force. If the ring in the middle is in equilibrium, then the sum of the x and y components of the forces must be zero. Is it? If not, then why not? Are the spring scales calibrated correctly? To check this, you might hang known weights from each spring scale.
Part 2: Friction ramp analysis: Determine the mass of a felt-padded wooden block using a balance or scale. Then place the block on a slightly inclined ramp so that it does not slide down. (maybe 8 degrees) . Hold a ruler aligned perpendicular to the surface of the ramp. Also, suspend a string with a plumb line beneath the block. Then photograph the ramp, plumb line, ruler, and block from the side. These objects will act as guides when aligning your coordinate system. Now insert your photograph into an open Logger Pro session. Construct a free body diagram in your lab book. You should align the x-axis with the surface of the ramp. Using logger pro, identify the magnitude and direction of the three forces acting on the block. In particular, you should identify the forces due to (i) the weight of the block, (ii) the normal force exerted by the ramp on the block, and (iii) the friction force exerted by the ramp on the block. Once you are comfortable with this procedure, incline the ramp a bit further until you find the maximum angle that the ramp can be tilted before the block begins to slip. At this particular angle, take another photograph and analyze all the forces. The ratio of the friction force to the normal force when the block is just about to slip is called the coefficient of static friction. What is its value? Look up a few values to see if your result is sensible.
Chapter 19: Let's start with some biographical comments on Isaac Newton.
To understand the American revolution of 1776, one must understand what they were rebelling against: the British monarchy. Similarly, to understand the scientific revolution, one must understand what they were rebelling against: the scientific philosophy of Aristotle and his medieval followers. In the next four lecture videos, I provide an overview of the traditional Aristotelian/Medieval philosophy of science. This will help you understand the context in which Newton was doing his work.
Newton's Principia begins with some definitions. The next few videos discuss Newton's definitions of "mass", "inertia", "momentum", and "force".
Chapter 20: In his "Scholium" at the end of his definition, Newton steps back and considers what one means by terms such as "space" and "time" and "motion". In particular, he considers whether all measurements of these quantities are relative, or whether there is a such thing as absolute space, absolute time, and absolute motion? This may seem a bit abstract, but it is extremely important, since Einstein's 20th century book Relativity was largely a reaction to (and rejection of) Newton's views on space, time and motion.
Homework:
- Inertia and Force (Ex. 19.1),
- Centripetal Force (Ex. 19.2);
- Relative linear motion (Ex. 20.1)
- PHY 201: Absolute rotational motion (Ex. 20.2)
Lab: In lab this week, we will learn how to construct and analyze force (or “free body”) diagrams using a camera and Logger Pro software. The lab consists of two parts.
Part 1: Force table analysis: Attach 3 spring scales to a ring and to the different points on the perimeter of the force table. Place a ruler on the force table for scale calibration. Photograph the force table and insert the picture into an open Logger Pro session. Here is a sample force table picture. Note: Logger Pro can be persnickety about usable image formats; you may need to use jpeg. Also: be sure to save your original photograph, since Logger pro references your original image; it does not actually import the image. Make the image as large as possible in logger pro without it being too blurry. You should set the scale of the image using the ruler in the image. Also set the origin at an appropriate place in the image (probably the exact center point of the ring to which the three scales are attached. Here is a sample Logger Pro analysis screenshot. Find the x and y components of each force using trigonometry. In order to do this, you will need to determine the magnitude and direction of each force. To find the magnitude of a particular force, you can just read the spring scale. To find the angle, you will need to find two (x,y) coordinates for each force. The origin can be one and the distant end of the scale could be another. From these points, you can find the angle of the force. If the ring in the middle is in equilibrium, then the sum of the x and y components of the forces must be zero. Is it? If not, then why not? Are the spring scales calibrated correctly? To check this, you might hang known weights from each spring scale.
Part 2: Friction ramp analysis: Determine the mass of a felt-padded wooden block using a balance or scale. Then place the block on a slightly inclined ramp so that it does not slide down. (maybe 8 degrees) . Hold a ruler aligned perpendicular to the surface of the ramp. Also, suspend a string with a plumb line beneath the block. Then photograph the ramp, plumb line, ruler, and block from the side. These objects will act as guides when aligning your coordinate system. Now insert your photograph into an open Logger Pro session. Construct a free body diagram in your lab book. You should align the x-axis with the surface of the ramp. Using logger pro, identify the magnitude and direction of the three forces acting on the block. In particular, you should identify the forces due to (i) the weight of the block, (ii) the normal force exerted by the ramp on the block, and (iii) the friction force exerted by the ramp on the block. Once you are comfortable with this procedure, incline the ramp a bit further until you find the maximum angle that the ramp can be tilted before the block begins to slip. At this particular angle, take another photograph and analyze all the forces. The ratio of the friction force to the normal force when the block is just about to slip is called the coefficient of static friction. What is its value? Look up a few values to see if your result is sensible.
Chapter 19: Let's start with some biographical comments on Isaac Newton.
To understand the American revolution of 1776, one must understand what they were rebelling against: the British monarchy. Similarly, to understand the scientific revolution, one must understand what they were rebelling against: the scientific philosophy of Aristotle and his medieval followers. In the next four lecture videos, I provide an overview of the traditional Aristotelian/Medieval philosophy of science. This will help you understand the context in which Newton was doing his work.
Newton's Principia begins with some definitions. The next few videos discuss Newton's definitions of "mass", "inertia", "momentum", and "force".
Chapter 20: In his "Scholium" at the end of his definition, Newton steps back and considers what one means by terms such as "space" and "time" and "motion". In particular, he considers whether all measurements of these quantities are relative, or whether there is a such thing as absolute space, absolute time, and absolute motion? This may seem a bit abstract, but it is extremely important, since Einstein's 20th century book Relativity was largely a reaction to (and rejection of) Newton's views on space, time and motion.