A 8.2 pound bucket about 3/4 full of water sits on a scale that reads 91.8 pound

ID: 3161125 • Letter: A

Question

A 8.2 pound bucket about 3/4 full of water sits on a scale that reads 91.8 pounds. A standard concrete block has two cores (as shown) and measures 7-5/8 x 7-5/8 x 15-5/8 inch on the outside. The block weighs 36.8 pounds and is lowered into the bucket and suspended by a rope that is attached to a spring scale. The block is completely in the water and no water spills out of the bucket. The spring scale reads 16.3 pounds after the concrete block is suspended in the water. Determine the following:

a.) The volume of the water.

b.) The weight density of the block.

c.) The material for the concrete block costs $2.60 per cubic foot. Determine the cost of a single block. ($)

d.) The reading of the scale the bucket rests on after the block is suspended.

e.) The concrete block is now suspended in a new liquid. The spring scale reading is 19.6 pounds. Determine the weight density of the new liquid.

Explanation / Answer

a) weight of water = 91.8 – 8.2

= 83.6 lb = 37.92 kg

Volume = mass/density,

density should be around 1000kg/m^3 in metric.

So volume = 37.92/1000

= 0.03792 m^3 = 10.02 gallons

b) Density equation is : Density = mass/volume,

so density = 36.8 lb / (7-5/8 x 7-5/8 x 15-5/8 inch)

density = 117.8 lb/ft^3 [Remember to convert inch^3 to ft^3.]

C) we know that the cost is 2.6 $/ft^3

Then we must find how many square feet of block we have.

We know it's weight density is

weight density = lb/ft^3

We have weight density = 117.8 lb/ft^3

We know how many lb of the block we have and we know the density, so we just need to clear ft^3

ft^3 = lb / weight density

ft^3 = 36.8 / 117.8

ft^3 = 0.31239 ft^3

We have the price:

2.60 $/ft3

So cost of block = (2.60)*(0.31239) = 0.8122 $

d) Let's remember that the block still weighs 36.8, it only seems lighter because the water is doing a force that cancels part of the weight.

In the air we have a that weight = 36.8

And the force dealt down to the scale will be the same force done up to cancel part of the weight,

In other words (flotation force=B)

B = W-T

= 36.8 - 16.3

= 20.5

Then the scale will read:

Scale = 8.2 lb + 20.5 lb = 28.7 lb

e) I will use once again the volume you found in your answer of weight density of the block:

We know that a volume of 0.31239 ft3 was displaced, and we can find how much this volume weights:

B = W-T = 36.8 – 19.6 = 17.2 lb

Density = W / V

= 17.2/ 0.31239

= 55.06 lb/ft^3

(OR)