SMU PHYSICS 1303: Introduction To Mechanics

SMU PHYSICS 1303: Introduction to Mechanics Stephen Sekula1 1 Southern Methodist University Dallas, TX, USA SPRING, 2019 S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 1

Outline Investigating Extended Bodies and Momentum Problem Solving in Conservation of Momentum S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 2

Check-In For Class I Check-in using the web app. The link is available from Canvas. n.html I If you have any trouble checking in with the web app, try it a few times. If that still doesn’t work, come see an instructor so we can mark you as present. I Make sure you have the PollEverywhere app or website ready to go to participate in classwork I Download these slides to follow along during class and, later, to skip ahead through the in-class problems. Find them on the class materials website, linked from Canvas: html S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 3

Investigating Extended Bodies and Momentum Investigating Extended Bodies and Momentum S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 4

Investigating Extended Bodies and Momentum Announcements I Due Today I You should have read HRW Chapter 9.1–9.4 and watched all of the video on "Extended Material Bodies" the video on "Momentum" from 00:00 to 39:37. I Assigned I HRW Chapter 9.5–9.9; finish watching the video, "Momentum". I Homework 7 due this Thursday I Other Items I Participate in the survey to identify possible topics for the last lecture of the semester (last day of our class) I You suggest topics, and we rank-vote them later as a class I Survey closes April 12 at 11:59pm. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 5

Investigating Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 6

Investigating Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum Instructor Problem: The Center of Mass of the Sun-Earth System The Sun is a miasma of incandescent plasma with a mass of Msun 1.99 1030 kg and a radius of 6.6 108 m. You can approximate the Sun as a symmetric and homogenous ball of gas whose own center-of-mass is located dead-center in the middle of the star. The Earth can similarly be treated as a body whose own center-of-mass is located dead-center in the middle of the planet, and Earth’s mass is mearth 5.97 1024 kg. The center-to-center distance of the Earth and Sun is 1.5 1011 m. I Find the center-of-mass of the Earth-Sun system, relative to the center of the sun. Is the COM inside or outside the Sun? I What is the approximate momentum of the Earth as it goes about the Sun? (the speed of the earth can be determined assuming the earth moves in uniform circular motion about the sun and that this takes 1 year) S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 7

Investigating Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum Student Problem: Hammer and its Center-of-Mass x 0 Red Dot Marks COM of handle alone w L Green Dot Marks COM of hammer head alone S. Sekula (SMU) Determine the center of mass of a sledgehammer. The head of the hammer can be treated as a mass of 3.3kg of horizontal width w 5.5 cm, whose own center-of-mass is located exactly in the middle of the head. The handle can be treated as a 0.84m-long line whose total mass is 0.35kg whose own center-of-mass of located in the exact middle of the handle. Neglect the fact that the handle is inserted into the hammer head; instead, treat the handle as joined flush with the hammer head. SMU — PHYS 1303 SPRING, 2019 8

Investigating Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum Student Problem: Bed of Nails and the Mass per Nail A “bed of nails” is precisely what it sounds like: a bed made from nails all pointing in the same direction. The bed of nails depicted here has 2 nails per square inch. The human body has a cross-sectional area of about 0.68 m2 . If a certain human has a mass of 93 kg and lays on the nails, what is the mass supported by each? Is this harmful? For comparison, the threshold for pain from contact with a sharp object like a nail is about 1kg of mass pressing down (pulled by gravity) on each nail. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 9

Investigating Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum Student Problem: Hammer Fall The sledgehammer is held so that its COM (mass M 3.6kg) is vertically at rest 2.0m above the floor. It is then allowed to swing in a circular arc, falling under only the influence of gravity (the hands on the hammer provide tension in the handle, but tension acts perpendicular to the circular motion so it does no work). I What will be the kinetic energy of the hammer at waist height (about 1.0m from the floor)? I What will be the speed of the hammer when it reaches waist height? I What will be the momentum of the hammer at that same height? S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 10

Investigating Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum Student Problem: Hammer Strike The sledgehammer now strikes a cinder block that rests atop a small inverted bed of nails, that rests atop a human chest. The human is resting, in turn, on a much larger bed of nails. The sledgehammer encounters the cinder block first. To strike the small bed of nails, it must pass all the way through the cinder block. The cinder block will break under the impact of the hammer, slowing the hammer (ideally, to a stop!) as it passes through the material. Breaking such a block requires about 1300N of force. If this force is achieved by striking with the hammer, over what time will the force act? S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 11

Investigating Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum Student Problem: Chest Compression A cinder block is made from concrete and has a mass of about 14kg. If dropped from a height of about 1.0in above the bed of nails on my chest, it will free fall until striking the board. If all of its kinetic energy goes into compressing my chest upon impact (my chest has a spring constant of about k 30kN/m, if modeled as a spring), how much will my chest compress upon impact? Does the number you find seem reasonable? S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 12

Investigating Extended Bodies and Momentum Problem Solving in Extended Bodies and Momentum Reminders I Assigned I HRW Chapter 9.5–9.9; finish watching the video, "Momentum". I Homework 7 due this Thursday I Other Items I Participate in the survey to identify possible topics for the last lecture of the semester (last day of our class) I You suggest topics, and we rank-vote them later as a class I Survey closes April 12 at 11:59pm. S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 13

SMU PHYSICS 1303: Introduction to Mechanics Stephen Sekula1 1Southern Methodist University Dallas, TX, USA SPRING, 2019 S. Sekula (SMU) SMU — PHYS 1303 SPRING, 2019 1