A 8.0 kg block of metal is suspended from a scale and immersed in water as in Fi

Question

A 8.0 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 ? 11.0 cm ? 11.0 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. The reading on the spring scale is 64.2 N.

Ftop
________ N Fbottom __________N

A 8.0 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 ? 11.0 cm ? 11.0 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. The reading on the spring scale is 64.2 N. What are the forces exerted by the water on the top and bottom of the block? (Take P0 = 1.0130 times 105 N/m2.)

Explanation / Answer

The absolute pressure at the level of the top of the block is

Pup=P+ P water g h

= 1.0130 105 + 10^3 x9.8 x 1.00 x10 ^-2m

=1.0179x 10^5 Pa

and that at the level of the bottom of the block is

Pbottom =P+ P water g h

= 1.0130 105 + 10^3 x9.8 x 17.00 x10 ^-2m

=1.0279x 10^5 Pa

Thus, the downward force exerted on the top by the water is

F PA top top =1.0179x 10^5 Pa (0.11)^2=1231.65N

and the upward force the water exerts on the bottom of the block is

F PA top top =1.0279x 10^5 Pa (0.11)^2=1243.75N

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