8) (a) The shape in (a) below is cut from a uniform sheet of material. Each square of side 2 cm has a mass of 10 g. Locate the center of mass with respect to the origin. (b) Repeat (a) for the shape in (b). (a) (b)

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8) (a) The shape in (a) below is cut from a uniform sheet of material. Each square of side 2 cm has a mass of 10 g. Locate the center of mass with respect to the origin. (b) Repeat (a) for the shape in (b) Show all work please
**Physics Problem Flow Chart**

1. **Draw a Picture**
   - Label which directions are positive (x- and y-), and label relevant quantities on the diagram.

2. **Draw a Second Picture...**
   - If you have BEFORE/AFTER situations, force additions, vector component diagrams.

3. **Identify Explicitly Given Values**
   - Write all given actual numbers in terms of variables. For previously calculated values, use values before rounding for sig figs.

4. **Identify Implicitly Given Values**
   - Wording that implies specific values: e.g., “at rest”, “comes to a stop”, “dropped”, “smooth surface”, “constant velocity”.

5. **Identify Required Quantity and Type of Problem**
   - Look for keywords like “when”, “how far”, “how fast”, etc. Get type of problem from quantities given/sought.

6. **Calculate/Convert Easily Derived Quantities**
   - For example, the x- and y-components of velocity/force vectors, or the force of gravity given the mass.

7. **Find Relevant Equation(s)**
   - One that links the given quantities to the quantity you need to find.

8. **Find a Second Equation...**
   - If you’re missing a quantity needed to use an equation. Draw up a plan on how to link the equations & quantities.

9. **Solve for the Quantity Without Using Numbers**
   - First, cancel any quantities that are zero. Use algebra to isolate the quantity you need on one side of the equals sign. Check with dimensional analysis.

10. **Sub in Numbers on Paper**
    - Make sure units of each number are correct before you substitute in values into the equations.

11. **Use Calculator to Find Value**
    - Use as few presses of the “=” or “ENTER” button as possible. Keep extra sig figs until next step.

12. **Write Conclusion Statement with Correct Sig Figs**
    - In plain English with correct units.
Transcribed Image Text:**Physics Problem Flow Chart** 1. **Draw a Picture** - Label which directions are positive (x- and y-), and label relevant quantities on the diagram. 2. **Draw a Second Picture...** - If you have BEFORE/AFTER situations, force additions, vector component diagrams. 3. **Identify Explicitly Given Values** - Write all given actual numbers in terms of variables. For previously calculated values, use values before rounding for sig figs. 4. **Identify Implicitly Given Values** - Wording that implies specific values: e.g., “at rest”, “comes to a stop”, “dropped”, “smooth surface”, “constant velocity”. 5. **Identify Required Quantity and Type of Problem** - Look for keywords like “when”, “how far”, “how fast”, etc. Get type of problem from quantities given/sought. 6. **Calculate/Convert Easily Derived Quantities** - For example, the x- and y-components of velocity/force vectors, or the force of gravity given the mass. 7. **Find Relevant Equation(s)** - One that links the given quantities to the quantity you need to find. 8. **Find a Second Equation...** - If you’re missing a quantity needed to use an equation. Draw up a plan on how to link the equations & quantities. 9. **Solve for the Quantity Without Using Numbers** - First, cancel any quantities that are zero. Use algebra to isolate the quantity you need on one side of the equals sign. Check with dimensional analysis. 10. **Sub in Numbers on Paper** - Make sure units of each number are correct before you substitute in values into the equations. 11. **Use Calculator to Find Value** - Use as few presses of the “=” or “ENTER” button as possible. Keep extra sig figs until next step. 12. **Write Conclusion Statement with Correct Sig Figs** - In plain English with correct units.
**Problem 8: Center of Mass Calculation**

(a) The shape in diagram (a) is cut from a uniform sheet of material. Each small square has a side length of 2 cm and a mass of 10 grams. Determine the center of mass of this shape with respect to the origin.

(b) Repeat the process for the shape in diagram (b).

**Diagrams Explanation:**

- **Diagram (a):**
  - The shape consists of an L-shaped figure formed by six squares. 
  - Three squares are aligned vertically, and three more are aligned horizontally to form the base of the 'L'.

- **Diagram (b):**
  - This shape also consists of an L-shaped figure formed by six squares.
  - Three squares are stacked vertically, and three squares are aligned horizontally to form the right side of the 'L'.
Transcribed Image Text:**Problem 8: Center of Mass Calculation** (a) The shape in diagram (a) is cut from a uniform sheet of material. Each small square has a side length of 2 cm and a mass of 10 grams. Determine the center of mass of this shape with respect to the origin. (b) Repeat the process for the shape in diagram (b). **Diagrams Explanation:** - **Diagram (a):** - The shape consists of an L-shaped figure formed by six squares. - Three squares are aligned vertically, and three more are aligned horizontally to form the base of the 'L'. - **Diagram (b):** - This shape also consists of an L-shaped figure formed by six squares. - Three squares are stacked vertically, and three squares are aligned horizontally to form the right side of the 'L'.
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