MC 2004 No.4

The answer is C. (1) and (2) only.

For the block to be at rest, by Newton’s 1st law of motion, the resultant force acting on the block must be zero.

(1):

圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/A_Hepburn04Feb102026.jpg?t=1202646416


(2):

圖片參考：http://i182.photobucket.com/albums/x4/A_Hepburn_1990/A_Hepburn05Feb102026.jpg?t=1202646436



For (3): the maximum resultant by F1 and F2 = 3 + 5 = 8 N < 9 N

F1 + F2 < F3, so, there must be a resultant force acting on the block and the block must be accelerating, it cannot remain at rest.

By mathematical method, for the block to be at rest, net force acting on the block is zero, that is, the resultant force vectors can form a complete triangle.

However, in this case, F1, F2 and F3 cannot form a complete triangle since F1 + F2 < F3. By mathematics, this is not possible to draw a complete triangle. This implies in case (3), the block cannot remain at rest.