Center of Mass Concepts and Calculations

Explore the fundamental concept of center of mass, learn how to calculate it, and understand its significance in balancing objects. Dive into examples, equations, and practical demonstrations to enhance your understanding.

• Center of Mass
• Calculations
• Balancing Point
• Physical Concepts
• Mass Distribution

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Uploaded on Sep 24, 2024 | 1 Views

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Presentation Transcript

1. Center of Mass Basic Concept Calculating Demos

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

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

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

5. Finding the COM: Regular solids: COM is the center. Show how to find X Balances on COM: Trial and error meter stick irregular solid Sliding fingers meter stick meter stick with mass broom pointer 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

6. Finding the COM: Teeter Totter equation (derive) L m1 m2 X m2L m1+ m2 x =

7. Finding the COM: Teeter Totter equation in general: (weighted average!) m2 m3 m1 X1 X2 X3 xCOM=m1x1+ m2x2+ m3x3 m1+ m2+ m3

8. 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 xCOM=m1x1+m2x2+m3x3 m1+m2+m3 8.66 m from the left side

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

10. 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: X5kg = 0) 5 kg 2 kg 34.0 cm solution 9.71 cm

11. How far is the COM of the earth moon system from the center of the earth? Earth s mass: 5.97x1024 kg Moon s Mass: 7.36x1022 kg Earth-Moon Distance: 3.84x108 m (The earth s radius is 6.38x106 m. Is this COM closer to the center or the surface of the earth?) solution 4.68x106 m

12. 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

13. 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

14. 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

15. 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

16. COM Demos!!!!!!! Irregular solids Air Table/spin Stability Tip O Meter Miata Vs. 4Runner 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