A cube with 25-cm-long sides is sitting on the bottom of an aquarium in which th
ID: 2866021 • Letter: A
Question
A cube with 25-cm-long sides is sitting on the bottom of an aquarium in which the water is one meter deep. (Round your answers to the nearest whole number. Use 9.8 m/s^2 for the acceleration due to gravity. Recall that the weight density of water is 1000 kg/m^3.) (a) Estimate the hydrostatic force on the top of the cube. N (b) Estimate the hydrostatic force on one of the sides of the cube. N Point-masses mi are located on the x-axis as shown. Find the moment M of the system about the origin and the center of mass bar x. M = bar x =Explanation / Answer
1.
(a)
P = ?gd
? = 1000 kg/m3 and g = 9.81 m/s2
F = PA = pressure x area
At the top, d = 0.75m
F = 1000 kg/m3 (9.81 m/s2) (0.75m) (0.25m)2
F = 459.844 N
(b)
On the sides,
dF = ?g y dA .............. however, dA = 0.25 dy
dF = ?g (0.25) y dy
F = 1000 (9.81)(0.25) ? y dy ... from 0.75 to 1
= 1000 (9.81)(0.25) (y2/2) ...... from 0.75 to 1
= 1000 (9.81)(0.25) (1/2 - (0.75)2/2)
= 536.484 N
2.
(a)
M = 12 * (-3) + 19 * 2 + 21 * 8
M = 170
(b)
m = 12 + 19 + 21 = 42
XCM = M/m = 170/42
XCM = 4.05 m