3. (36) In a physics experiment, an iron casting with an empty cavity is complet

Question

3. (36) In a physics experiment, an iron casting with an empty cavity is completely submerged in an open container of water. The casting is suspended by a cord connected to the ceiling of the laboratory. A schematic of the situation is shown below. The tension in the cord is T = 4000 N. The mass M of the casting is 600 kg. The density of iron (that is, a sample with no cavities) is 7870 kg/m3 . The density of water is assumed to exactly 1000 kg/m3. (a) (4) What is the volume VD of water displaced by the casting? (b) (22)What is the volume VC of the empty cavity? (c) (2) Suppose the cord breaks. Immediately after the cord breaks, what direction does the casting move, up or down? Circle one. (d) (8) What is the magnitude | a | of the acceleration while it moves ?

Please show all the steps and show the formula when solving.

Explanation / Answer

a)
Her the casting is in equilibrium.

so, Fnety = 0

B + T = m*g

rho_water*VD*g + T = m*g

VD = (m*g - T)/(rho_water*g)

= (600*9.8 - 4000)/(1000*9.8)

= 0.1918 m^3

b) VC = VD - V_casting

= 0.1918 - mass/density

= 0.1918 - 600/7870

= 0.1156 m^3

c) down

d) a = Fnet/m

= (m*g - B)/m

= g - B/m

= g - rho_water*VD*g/m

= 9.8 - 1000*0.1918*9.8/600

= 6.67 m/s^2

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