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Lesson: The Negative Mass Method

Worksheet • 19 Questions

Q1:

A uniform lamina is in the form of a rectangle 𝐴 𝐡 𝐢 𝐷 in which 𝐴 𝐡 = 6 4 c m and 𝐡 𝐢 = 2 4 0 c m . The corner 𝐴 𝐡 𝐸 , where 𝐸 is the midpoint of 𝐴 𝐷 , was cut off. The resulting lamina 𝐴 𝐢 𝐷 𝐸 was freely suspended from the vertex 𝐢 . Determine the size of the angle the side 𝐢 𝐡 makes to the vertical when the lamina is hanging in its equilibrium position stating your answer to the nearest minute.

  • A 1 6 5 7 β€² ∘
  • B 7 3 3 β€² ∘
  • C 8 2 2 4 β€² ∘
  • D 7 3 6 β€² ∘

Q2:

A uniform lamina 𝐴 𝐡 𝐢 𝐷 is in the form of a square of side length 51 cm. The points 𝐸 and 𝐹 are the midpoints of 𝐴 𝐡 and 𝐴 𝐷 , respectively. The corner 𝐴 𝐸 𝐹 has been folded over along the line 𝐸 𝐹 so that the point 𝐴 aligns with 𝑀 , the center of the square, as shown in the diagram. Determine the coordinates of the center of gravity of the lamina in this form.

  • A ο€Ό βˆ’ 1 7 1 6 , βˆ’ 1 7 1 6 
  • B ο€Ό 1 7 1 6 , 1 7 1 6 
  • C ο€Ό 8 5 1 6 , 8 5 1 6 
  • D ο€Ό βˆ’ 1 7 8 , βˆ’ 1 7 8 

Q3:

Find the coordinates of the centre of mass of the following figure, which is drawn on a grid of unit squares.

  • A ο€Ό 9 2 , 4 
  • B ( 9 , 8 )
  • C ο€Ό 2 7 9 2 2 , 4 
  • D ο€Ό 1 8 9 2 2 , 8 4 1 1 
  • E ο€Ό 9 2 , 1 2 4 1 1 
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