You move a 210 g cup across the room from your 113 cm tall counter top table to the top cabinet shelf at a height of 160 cm. You carry it a horizontal distance 4.6 m across the room to get there. You can carry the cup any one of three possible paths: - Falh 0: Carry lhe cup horizontally until you get to lhe cupboard and then raise iI vertically up to the shelf. - Falh R: Raise the cup vertically lo the height of lhe shelf and then carry it horizontally to the self. - Falh 5: Bring Ihe cup from the countenop to Ihe shelf in a slraighi. line motion from its initial position Io its final position in one molion. I. Paths Write the vectors for each path of motion. (a) Write the vectors for each phase of path Q m%=E:::j?+C:::ji (ii) qi = :G + 2 (b) Write the vectors for each phase of path R: cn=[::::19+E::::ji mg: (C) Write the vector for the path S: %=K::::H+K:::ji II. Distances Write the distances for each path of motion. (a) Write the distance for each phase of path Q mm=K:::j (Wm=C:::j (b) Write the total distance for path Q q=E:::3 (c) Write the distance for each phase of path R m = :I mm:E:::j (d) Write the total distance for path R (e) Write the total distance for path 5 III. Directions Write the unit vectors for each path of motion. (a) Write the direction for each phase of path Q mo=C:::j?+C:::ji (ii) Elli ::9 + i:|i (b) Write the direction for each phase of path R: m f. = E? + 2 mo=::::W+E:::j (c) Write the direction for the path 5: IV. Force (a) What is the weight of the cup? W=E:::j?+C:::ji (b) Write the component of the weight directed along each path segment. Mew-e: (ii) qui = W ' Elii = i:i (iii) w\" : W - Pi : \\:| (W) wril : W ' i'ii : :l > comm-h: V. Work Find the work done by gravity along each path. m w = S cm wk : S cm ws = |:|