Center of Mass Basic Concept Calculating Demos Center

Center of Mass Basic Concept Calculating Demos

Center of Mass: Point at which mass seems to be concentrated Balance Point Rotation about

Finding the COM: Regular solids: COM is the center. Show to find X Balances on COM: Trial and error meter stick irregular solid Sliding fingers meter stick with mass broom pointer on spinner broom on spinner Murray’s Theorem Rectangular solid Hangs with COM below point of suspension: Chalk line/Solids COM isn’t in object!/High jumpers

Finding the COM: Teeter Totter equation (derive) L m 1 m 2 X

Finding the COM: Teeter Totter equation in general: (weighted average!) m 1 X 2 X 3 m 2 m 3

Example: Find the distance the COM is from the left side of the beam. The 45. 0 kg uniform beam is 14. 0 m long, has a 12. 0 kg box 4. 0 m from the left side, and a 30. 0 kg box centered 13. 0 m from the left side. 30. 0 kg 12. 0 kg 45. 0 kg 4. 0 m 13. 0 m 7. 0 m 8. 66 m from the left side

Whiteboards: Center of mass 1|2|3|4|5

The center of the 5. 00 kg is 34. 0 cm from the center of the 2. 00 kg. How far from the 5. 00 kg center is the COM? (hint: X 5 kg = 0) 5 kg 34. 0 cm solution 9. 71 cm 2 kg

How far is the COM of the earth moon system from the center of the earth? Earth’s mass: 5. 97 x 1024 kg Moon’s Mass: 7. 36 x 1022 kg Earth-Moon Distance: 3. 84 x 108 m (The earth’s radius is 6. 38 x 106 m. Is this COM closer to the center or the surface of the earth? ) solution 4. 68 x 106 m

A uniform meter stick has a mass of 85. 0 grams, and I place a 15. 0 gram clamp at the 24. 0 cm mark, and the 55. 0 cm mark. At what mark would it balance? (Assume the meter stick to have a COM at 50. 0 cm) solution 47. 3 cm

A uniform meter stick has a mass of 116 grams, and has a 24. 0 g mass at the 40. 0 cm mark. Where do you clamp a 32. 0 g mass to make it balance at the 42. 0 cm mark? solution 14. 5 cm

A uniform meter stick has a mass of 95. 0 grams, and has a 12. 0 g mass at the 13. 0 cm mark. What mass do you put at the 85. 0 cm mark to make it balance at the 56. 0 cm mark? solution 37. 4 g

A 75. 0 kg window cleaner is 1. 5 m from the right side of a scaffold that is a 62. 0 kg uniform beam, 10. 0 m long. There is an 18. 0 kg toolbox 3. 00 m from the left side. Where is the center of mass of the whole thing? 18. 0 kg 62. 0 kg 6. 46 m from the left side, 3. 54 m from the right

COM Demos!!!!!!! Irregular solids Air Table/spin Stability Tip O’ Meter Miata Vs. 4 Runner “g” force Tower of pisa Paradox roller Hammer and Ruler Fork, Spoon, match Meter sticks: (4. 0, 4. 6, 5. 3, 6. 1, 7. 3, 9. 0, 11. 5, 15. 7, 24. 0, 49. 0) Hallway Kneeling/Pencil a you-cubit from your knees/hands behind back/nose to pencil Toes/Nose against wall/stand on toes Butt against wall, pick up pencil without bending knees Two footlengths from wall/Head against wall/Pick up chair/Pause/Then stand up