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Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal pieces of width 2cm and are laid along xy plane as shown. the centre of mass has coordinates?
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Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal piece...
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Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal piece...
Given information:
- Metal sheet dimensions: 14cm * 2cm
- The sheet is cut into 2 equal pieces of width 2cm each.
- The pieces are laid along the xy plane.
Objective:
To find the coordinates of the center of mass of the metal sheet.
Solution:
1. Finding the Mass of the Metal Sheet:
- The mass of an object is directly proportional to its volume.
- Since the metal sheet is of uniform thickness, the volume will be directly proportional to the area.
- The area of the metal sheet can be calculated as the product of its length and width.
- Area = Length * Width = 14cm * 2cm = 28cm^2
- Since the metal sheet is of uniform thickness, the mass of the metal sheet can be considered proportional to its area.
2. Finding the Center of Mass of Each Piece:
- Since the metal sheet is cut into two equal pieces, each piece will have half the mass of the entire sheet.
- Therefore, each piece will have a mass of 0.5 * (mass of the metal sheet).
- The center of mass of each piece will be at its geometric center.
- The geometric center of a rectangle is the midpoint of its sides.
- Since the width of each piece is 2cm, the x-coordinate of the center of mass of each piece will be at x = 1cm.
3. Finding the Center of Mass of the Metal Sheet:
- The x-coordinate of the center of mass of the metal sheet will be the weighted average of the x-coordinates of the center of mass of each piece.
- Since both pieces have the same x-coordinate (1cm), the x-coordinate of the center of mass of the metal sheet will also be 1cm.
- The y-coordinate of the center of mass of the metal sheet will be the same as the y-coordinate of the center of mass of each piece.
- The y-coordinate of the center of mass of each piece can be calculated using the formula: y = (mass1 * y1 + mass2 * y2) / (mass1 + mass2)
- Since both pieces have the same mass (0.5 * mass of the metal sheet), the y-coordinate of the center of mass of the metal sheet will be equal to the y-coordinate of the center of mass of each piece.
- The y-coordinate of the center of mass of each piece will be at y = 1cm.
Therefore, the coordinates of the center of mass of the metal sheet will be (1cm, 1cm).
- Metal sheet dimensions: 14cm * 2cm
- The sheet is cut into 2 equal pieces of width 2cm each.
- The pieces are laid along the xy plane.
Objective:
To find the coordinates of the center of mass of the metal sheet.
Solution:
1. Finding the Mass of the Metal Sheet:
- The mass of an object is directly proportional to its volume.
- Since the metal sheet is of uniform thickness, the volume will be directly proportional to the area.
- The area of the metal sheet can be calculated as the product of its length and width.
- Area = Length * Width = 14cm * 2cm = 28cm^2
- Since the metal sheet is of uniform thickness, the mass of the metal sheet can be considered proportional to its area.
2. Finding the Center of Mass of Each Piece:
- Since the metal sheet is cut into two equal pieces, each piece will have half the mass of the entire sheet.
- Therefore, each piece will have a mass of 0.5 * (mass of the metal sheet).
- The center of mass of each piece will be at its geometric center.
- The geometric center of a rectangle is the midpoint of its sides.
- Since the width of each piece is 2cm, the x-coordinate of the center of mass of each piece will be at x = 1cm.
3. Finding the Center of Mass of the Metal Sheet:
- The x-coordinate of the center of mass of the metal sheet will be the weighted average of the x-coordinates of the center of mass of each piece.
- Since both pieces have the same x-coordinate (1cm), the x-coordinate of the center of mass of the metal sheet will also be 1cm.
- The y-coordinate of the center of mass of the metal sheet will be the same as the y-coordinate of the center of mass of each piece.
- The y-coordinate of the center of mass of each piece can be calculated using the formula: y = (mass1 * y1 + mass2 * y2) / (mass1 + mass2)
- Since both pieces have the same mass (0.5 * mass of the metal sheet), the y-coordinate of the center of mass of the metal sheet will be equal to the y-coordinate of the center of mass of each piece.
- The y-coordinate of the center of mass of each piece will be at y = 1cm.
Therefore, the coordinates of the center of mass of the metal sheet will be (1cm, 1cm).
Community Answer
Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal piece...
Com for system or cut pieces?
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Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal pieces of width 2cm and are laid along xy plane as shown. the centre of mass has coordinates?
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Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal pieces of width 2cm and are laid along xy plane as shown. the centre of mass has coordinates? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal pieces of width 2cm and are laid along xy plane as shown. the centre of mass has coordinates? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal pieces of width 2cm and are laid along xy plane as shown. the centre of mass has coordinates?.
Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal pieces of width 2cm and are laid along xy plane as shown. the centre of mass has coordinates? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal pieces of width 2cm and are laid along xy plane as shown. the centre of mass has coordinates? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Metal sheet 14cm * 2 cm of uniform thickness is cut into 2 equal pieces of width 2cm and are laid along xy plane as shown. the centre of mass has coordinates?.
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