Enter a number. Enter anumber. Enter anumber. F top Enter a number. 1 N F bottom
ID: 1744482 • Letter: E
Question
Enter a number. Enter anumber. Enter anumber. Ftop Enter a number. 1 N Fbottom Enter anumber. 2 N A 9.9 kg block of metal is suspended from a scale and immersed in water, as in the figure below. The dimensions of the block are 12.0 cm multiplied by8.4 cm multiplied by8.4 cm. The 12.0 cm dimension is vertical, and the top of the block is 5.00 cm below the surface of the water. (a) What are the forces exerted by the water on the top and bottom of the block? Take P0 =1.0130 x 10^5 N/m^2. (b) What is the reading of the spring scale? Enter a number. 3 N (c) Show that the buoyant force equals the difference between the forces at the top and bottom of the block.Explanation / Answer
(a)
the absolute pressure at the level of the top of theblock will be
Ptop = Po +water g htop
=(1.0130 105 N/m2) + (103 kg /m3) (9.80 m / s2) (5.0 x 10-2m)
=......... Pa
at the level of the bottom of the block will be
Pbottom = Po +water g hbottom
=(1.0130 105 N/m2) + (103 kg /m3) (9.80 m / s2) (17.0 x 10-2m)
=......... Pa
so the downward force exerted on the top by the waterwill be
Ftop = Ptop A
= Ptop(0.084 m)2
=........ N
the upward force the water exerts on the bottom of theblock is
Fbottom = Pbottom A
= Pbottom(0.084 m)2
=........ N
(b)
so the scale reads the tension in the T in the cordsupporting the block
as the block is in equilibrium we can write
Fy = T + Fbottom - Ftop -m g
=0
T = ....... N
(c)
according to the archimedes principle the buoyantforce on the block equals the weight of the
displaced water so we can write
B = (water Vblock) g
= ......... N
compare the answer with answer in part (a)
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