A 9.0 kg block of metal is suspended from a scale and immersed in water as in Fi

Question

A 9.0 kg block of metal is suspended from a scale and immersed in water as in Figure P9.30. The dimensions of the block are 12.0 cm ? 8.0 cm ? 8.0 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water.

(b) What is the reading of the spring scale?
N

THANK YOU!!

Ftop 651.45 N Fbottom 655.8  N A 9.0 kg block of metal is suspended from a scale and immersed in water as in Figure P9.30. The dimensions of the block are 12.0 cm ? 8.0 cm ? 8.0 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. * 10^5 N/m^2.) F top 651.45 N F bottom 655.8 N (b) What is the reading of the spring scale? N (a) What are the forces exerted by the water on the top and bottom of the block? (Do not ignore the effect of the air above the water. Take P0 = 1.0130

Explanation / Answer

Archimedes principal says the buoyant force on an object is exactly
equal to the volume of the water displaced. So, the buoyant force is
V = 10.3cm x 10.3cm x 12cm = 1273 cm^3. Since 1 cc of water weighs 1 g, the weight of the block, less the buoyancy is the weight that will register on the scale, or

b) 11.1 kg - 1.273 kg = 9.827 kg
a) they give us air pressure in N/m^2, we want to convert to cm^2
or 1.013 x 10^5 N/m^2 /(100 cm/M)^2 = 10.13 N/cm^2, to that air pressure, we want to add the pressure of the water. Water weighs 1 g per cubic centimenter, so it puts a pressure of 1g per square centimeter for every centimeter of height. Convert g to N by multiplying by Gravity = 9.8 m/s^2 so the pressure of water is
9.8 N/cm^2 for every cm below the surface. Then, Force = Pressure * Area

Ftop = (9.8*5 + 10.13)*10.3^2 = 6273.1N
Fbottom = (9.8*(5+12) + 10.13)*10.3^2 = 18749.3 N

c) Fbottom - Ftop = 18749.3 - 6273.1 = 12476.3 N
In the preamble we showed the volume was 1273 cm^3 and that water weighs 1g/cc for a weight of 1273 g. We convert that to Newtons by multiplying by gravity - 9.8 m/sec^2 or
1273 * 9.8 = 12475.5 which is within rounding error of equalling 12476.3N

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