The mattress of a water bed is 2.00 m long by 2.00 m wide and 27.0 cm deep. (A)

Question

The mattress of a water bed is 2.00 m long by 2.00 m wide and 27.0 cm deep. (A) Find the weight of the water in the mattress. (B) Find the pressure exerted by the water on the floor when the water bed rests in its normal position. Assume the entire lower surface of the bed makes contact with the floor (A) Find the weight of the water in the mattress. Conceptualize Think about carrying a jug of water and how heavy it is. Now imagine a sample of water the size of a water bed. We expect the weight to be relatively large. Categorize This example is a substitution problem. Find the velume of the water fiing the Fe(2.00 m) (2.00 m) ??.27m). 1.08 m, of density and ar " pr·(1,000 kg/m?)( 1.06 m? 1.0830k density of fresh mater bed of the bed: Afg . (1.08 x 10,9) (9,80 m/s? which is approximately 2381 lb. (A regular bed, including mattress, box springs, and metal frame, weighs approximately 300 lb.) Because this load is so great, it is best to place a water bed in the basement or on a sturdy, well supported floor. (B) Find the pressure exerted by the water on the floor when the water bed rests in its normal position. Assume the entire lower surface of the bed makes contact with the floor with the fleor s 4.00m2, Use the the definiblion of Calculate the pressure exerted by the water bed on the floor if the bed rests on its side. Pa Need Help? Show My Work (Required) What steps or reasoning did you use? Your work counts towards your score.

Explanation / Answer

a)

After multiplication we get,

Weight of the bed = Mg= 10584 N

b)

Pressure exerted by water on floor will be 10584/4 = 2646 N/m^2

Now when the bed rests on it's side the area in contact in ground will change and the weight will remain the same.

The area will now become

A=2×0.27=0.54 m^2

So the pressure in this case will be

P=10584/0.54=19600 N/m^2

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