Question

A driver of a box van is going too fast on a wet slippery bridge and accidentally drives off it and lands in the river below (density of river water  = 1000 kg/m3 ). When the van first lands in the water it floats with a submergence depth of h (m) (See sketch of van on left in Fig 1a). The van can be represented in an idealized form of a rectangular cube submerged by the depth h (m) (See sketch of cube on right in Fig 1a). The cube has the following dimensions: length Lvan = 4m, height Hvan = 2m and width Wvan = 1m. The van has a mass of 5000 kg (Since the cube is a representation of the van, it has the same mass as the van). Figure 1a Side view of the van (left) and the cube representing the van (right) floating in the river In your exam booklet answer the following: (a) What is the weight of the van? Include your units. [2 marks] (b) At what depth (h (m)) does it float? [ 6 marks] QUESTION 1B 17 marks (allow 20 minutes) The van from question 1A has sunk (See van on left in Fig 1b). The driver is very strong and knows that he/she can exert a force on the door of F = 2 kN to get out and swim to safety. The driver can apply that force at the handle, 0.5m in the horizontal from the hinges on the door, thus creating a moment. The van door can be represented in an idealized form of a rectangle (See idealised door on right in Fig 1b). You can assume that the van is filled with air and slowly letting in water. The density of the river water can be considered as:  = 1000 kg/m3 . The idealised door has dimensions: Ldoor = 0.5m; Hdoor = 1.5m. Figure 1b Side view of the van (left) after it sunk; idealised representation of the van door (right) In your exam booklet answer the following: (a) Draw the hydrostatic pressure acting on the door when the van is sitting on the river bottom (depth = 4m). Label the magnitudes of pressure. [2 marks]. (b) What is the depth (yp) at which the hydrostatic pressure force is acting? [3 marks] (c) If the van settles on the river bottom that has a depth of 4 m (see Fig 1b for dimensions), can the driver open the door? Explain your reasoning with specific calculations. Use your understanding of moments and forces. [9 marks] (d) Considering what you know about hydrostatic forces acting on submerged bodies what could the driver do to help their situation [HINT: consider net forces on the door, what would make it easier for them to open the door]? Explain your answer. Note, you don’t have to have answered part (a-c) to complete (d). No calculations are required but can be used to justify your reasoning. [3 marks]

1m. The van has a mass of s same mass as the van). (Since the cube w arepresentation f thie an,it has the Actual Representao the van ealized Representation of the van 4 m 4 m Im h ( 1 m Side view of the van (left) and the cube representing the van (right) floating in Figure la the river kg/m3 The idealised door has dimensions: 0.5m; Hdoor # 1.5m. Actual Representatio van door Idealized Representation of the van door 0.5 m 0.5 m 2 m 0.25 m 1.5 m Side view of the van (left) after it sunk; idealised representation of the van door Figure 1b (right) In your exam booklet answer the following:

Answer 1

SOoD 2.2Sro .i -.ae, 3 DooTSm ue Df Ah From Surface o uati) -3.0625ทา-

o. -tlyctxosttic(Pre-teg K.),A.an EP) (Io 9,8x3) top vien b Dcor ke Moment about hive Aa2s+ nge ___Exo.se一Pxo.25 2 ドー22.031. an appl. 5o he won't be able to get out o Von ot Umai derth d) He Con break one ol window ta alla waler insicle the_van. Ss Allo uwaeer to Come Inšid theNe pveabue On doos usill be zeyo due to Submergence on Side. S Nou Can easity apenhecloox Scanned With