Question

Consider the following diamond-shaped 2D object.

(1, 0) (0,-1) (2,-1) (1,-2)

Answer the following prompts regarding the object:

Part 1: What is the tangential normal vector of the upper right panel (whose center is indicated as X)? Assuming the ordering of vertices ordered in counter-clockwise direction.

A.)(-1/sqrt(2),1/sqrt(2))

B.)(1/sqrt(2),1/sqrt(2))

C.)(-1/sqrt(2),-1/sqrt(2))

D.)(1/sqrt(2),-1/sqrt(2))

Part 2: What is the outward normal vector of the lower right panel (whose center is indicated as P)?

A.)(-1/sqrt(2),1/sqrt(2))

B.)(1/sqrt(2),1/sqrt(2))

C.)(-1/sqrt(2),-1/sqrt(2))

D.)(1/sqrt(2),-1/sqrt(2))

Part 3: Under hydrostatic condition (no waves), what is the vector sum of the forces acting on all the panels? The dimension of the object out of the plane (perpendicular to the screen) is 1m. All coordinates shown below are in meters as well. Gravitational constant as g = 10 m/s^2; Round to nearest integer.

Answer 1

normal. tangential Diet AB-0 Àto B from trangle rule. (0,-1) origin o OB a ê 1 Anonton AB= 2. Now I Å - 2² - (1-2) x+y yo Now AB is the tangetial vector. Hence normal to this vector say , must satisfy AB N = 0 Hence only option (b) and (C) satisfy this condition. It is also clear that the loop encloses the origin as, as we move from c to A only the x-componet changes 2) Sinilarly as we move from A to B only & Hence the normal, must be pericking away from the origin. quadrant 2. and is Bob QL z Vz 4. A) / 2 1 - 1 2) as the tangential rector and outwardo B) († 17) is the normal rector do For lower right pand tangential rector DÁ Bh.-08+ = A * -NW, 78-8-23, 07?a zî-9 Da=-osto Ä - - + 2ŷta ĝe å tŷ. DÀ = tangential rector = htŷ . If y be the outward normal, N, DAZO .. Ng must be in and or 4th quadrant: Basto Aus is either (A) or (D) As clear from fig., Ans is in 4th anadsant hence Aus= 'D. In the absence of waves presst exeats the same force. in all direction. since area of all walls are equall heale net hooreno outward normats components in the 1st ar Tx ABS