Academic Physics Mechanics. Chapter 10 Center of Gravity

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1 1 Academic Physics Mechanics Chapter 10 Center of Gravity

2 10.1: Center of Gravity 2 The center of gravity of an object is the point located at the objects average position of weight. For a symmetrical object, like a ball, this point is at the geometric center of the object. For an irregular object, like a wrench, this point is toward the heavier end. Objects not made of the same substance throughout may have the center of gravity quite far from the geometric center. Sliding wrench animation Notice that the center of mass, marked by the white dot, follows a straight line path, while other parts of the wrench rotate about this point.

10.1: Projectiles A juggling ball follows a smooth parabolic path when thrown into the air because its center of gravity is at its geometric center.

3 10.1: Projectiles A juggling ball follows a smooth parabolic path when thrown into the air because its center of gravity is at its geometric center. 3 A juggling club seems to wobble all over the place, but it really rotates around a special point that stays on a parabolic path. How to Juggle a Juggling Club

called the center of gravity of the bat, and A movement

4 10.1: Projectiles The motion of the juggling club is the sum of two motions: 4 A spin around that special point, called the center of gravity of the bat, and A movement through the air as if all the weight were at the center of gravity.

10.1: Fireworks 5 NetLogo Models - Fireworks For an exploding projectile, like fireworks, the center of gravity continues to follow a parabolic path after the explosion.

5 10.1: Fireworks 5 NetLogo Models - Fireworks For an exploding projectile, like fireworks, the center of gravity continues to follow a parabolic path after the explosion. The internal forces during the explosion do not change the projectile's center of gravity. If air resistance is negligible, the center of gravity of the dispersed fragments at any time will be where the center of gravity would have been if the explosion never occurred.

6 10.1: Fireworks NetLogo Models - Fireworks A fireworks bomb follows a parabolic path until it explodes. A fireworks rocket has an engine, so it does not follow a parabolic path; there is a force acting on it other than gravity while in the air. When the canister explodes (in either case), each of the fragments follows a parabolic path. Also, the center of mass of all of the fragments follows a parabolic path. 6

7 10.1: 2012 Winter X Games 7 At the 2012 Winter X Games in Aspen, Colorado, Heath Frisby landed the first ever front flip on a snowmobile in competition. Video Commentary DO NOT TRY THIS AT HOME!

8 10.2: Center of Mass vs. Center of Gravity The center of mass of an object is the point located at the object's average position of mass. The center of gravity of an object is the point located at the objects average position of weight. When the acceleration due to gravity is the same at all points on the object, these two points will be at the same location. 8

9 10.2: Center of Mass vs. Center of Gravity The center of gravity of the One World Trade Center (formerly known as the Freedom Tower, replacing the destroyed World Trade Center Twin Towers) in New York City will be about 1 mm lower than its center of mass. 9

10 10.2: Center of Mass vs. Center of Gravity The wobble in a star as it and its planets orbit around their common center of gravity is looked for by scientists searching for extrasolar planets. 10

11 10.2: Center of Mass vs. Center of Gravity Bumble Ball baby toys (also fun with some dogs apparently) work by having a motor swing a heavy mass around inside the ball, altering its center of mass. 11

12 10.3: Locating the Center of Gravity The center of gravity of an object is its balance point. The center of gravity of a uniform object, such as a meter stick, is at the midpoint, its geometric center. 12 Finding the center of gravity for irregularly shaped objects or objects with varying densities, is a bit trickier.

10.3: Locating the Center of Gravity Some objects can be supported by two fingers. Sliding your fingers to the center while balancing the object will end up with your fingers at the balance point.

13 10.3: Locating the Center of Gravity Some objects can be supported by two fingers. Sliding your fingers to the center while balancing the object will end up with your fingers at the balance point. Other objects can be suspended. The center of gravity will be directly below the suspension point. By suspending the object from at least one other point, you can determine where the center of gravity is. The center of gravity may be located where no actual material exists. 13

14 10.4: Toppling Pin a plumb line to the center of gravity of a heavy object and tilt it until it topples over as shown. You can see that the object will begin to topple when the plumb line extends beyond the supporting base of the object. 14 If the center of gravity of an object is above the area of support, the object will remain upright. If the center of gravity of an object is outside the area of support, the object will topple. Concepts-at-a-Glance

15 10.4: The Leaning Tower of Pisa After 800 years in which the Leaning Tower of Pisa tilted steadily to the south, engineers have finally moved it back 45 centimeters (17 inches) and got it stable. Ten years ago, the tower's movement, of roughly 1 mm per year, had brought it to the brink of collapse and made it unsafe for tourists. NOVA Fall of the Leaning Tower Italy Guides Wikipedia 15

16 10.5: Stability Try balancing the pole end of a broom or mop on the palm of your hand. The support base is very small and relatively far beneath the center of gravity, so it is difficult. 16 Equilibristics

17 10.5: Stability 17 Stable equilibrium - the center of gravity must be raised in order to make the object topple. Neutral equilibrium - the center of gravity remains at the same height when the object is displaced. Unstable equilibrium - the center of gravity is above the support base but will be lowered when the object is displaced.

18 10.5: Examples of Equilibrium 18 What type of equilibrium does each object have? A book laying flat on the desk A book standing up on the desk A pen standing on its end A stool on its four feet A stool on its side Some well known toys use center of gravity and stability

defy gravity. Some magic tricks make use of the same principles.

19 10.5: Tricks with Stability 19 Some center of gravity tricks make use of a neutral equilibrium or unstable equilibrium situation to appear to defy gravity. Some magic tricks make use of the same principles. Chair suspension trick performed by Tim Mannix Chair suspension trick explained

20 10.5: Engineering for Stability The center of gravity of a building is lowered if much of the structure is below ground. This is important for tall, narrow structures like the Space Needle in Seattle. 20

side as the car goes around a corner and causes body lean.

21 10.5: Engineering for Stability This is also important when engineering cars. The center of gravity height, relative to the road, determines load transfer from side to side as the car goes around a corner and causes body lean. Height of the center of gravity relative to the wheelbase determines load transfer between front and rear when the car accelerates or decelerates. 21

22 10.6: Human Center of Gravity Tricks Stand against a wall with your right side facing the wall, then put your right foot and cheek against the wall. Try to lift your left foot off the floor. Place an object on the floor about 20 inches from a wall. Stand with your back against the wall, feet together, and heels against the wall. Try to pick up the object on the floor without moving your feet or bending your knees. While standing up, bend over and hold your toes with your hands, keeping your knees slightly bent. Try to jump forward in this position without removing your hands from your toes while you are jumping. 22

23 10.6: Human Center of Gravity Tricks Sit in a straight-back armless chair, keeping your back against the back of the chair and your feet flat on the floor. Fold your arms across your chest. Keeping your feet flat and your back straight, try to stand up. Place a chair or stool against the wall. Stand three feet away from the wall, facing the stool. Bend over so that your back is horizontal and put your head against the wall. Lift the stool, then try to stand up. If your center of gravity extends beyond your support base, you will topple! 23

24 10.6: Center of Gravity of People 24 When you stand erect with your arms hanging at your sides, your center of gravity is within your body. For males, the center of gravity is typically 2 to 3 cm below their navel, midway between their front and back. For females, the center of gravity is typically slightly lower because women tend to be proportionally larger in the pelvis and smaller in the shoulders. In children, the center of gravity is higher because of their proportionally larger heads and shorter legs.

25 10.6: Center of Gravity of People 25

26 Center of Gravity Review AP B Video 11: Center of Mass Khan Video Academy Center of Mass MIT Lecture 15: Center of Mass PhysicsLAB Tutorial Center of Mass Hyperphysics Tutorial 26

Chapter 8 Rotational Motion and Equilibrium. 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction

Chapter 8 Rotational Motion and Equilibrium Name 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction 1. The distance between a turning axis and the