Deck 7: Extension F: Differential Equations

Question 1

Find the centroid of the region bounded by the given curves.

A)
B)
C)
D)
E) None of these

Answer 1

Question 2

Find the exact coordinates of the centroid.

Answer 2

Question 3

Find the centroid of the region shown,not by integration,but by locating the centroids of the
rectangles and triangles and using additivity of moments.

Answer 3

Question 4

A vertical plate is submerged in water (the surface of the water coincides with the x-axis).Find the force exerted by the water on the plate.(The weight density of water is 62.4 lb/ft³.)

A) 62.4 lb
B) 436.8 lb
C) 873.6 lb
D) 124.8 lb

Question 5

The masses are located at the point Find the moments and and the center of mass of the system. ;

A)
B)
C)
D)
E)

Question 6

A trough has vertical ends that are equilateral triangles with sides of length 2 ft.If the trough is filled with water to a depth of 1 ft,find the force exerted by the water on one end of the trough.Round to one decimal place.(The weight density of water is 62.4 lb/ft³.)

A) 31.2 lb
B) 62.4 lb
C) 12.0 lb
D) 6.0 lb

Question 7

Find the center of mass of the system comprising masses m_k located at the points P_k in a coordinate plane.Assume that mass is measured in grams and distance is measured in centimeters.
m₁ = 3,m₂ = 4,m₃ = 5
P₁ (-3,5),P₂ (3,4),P₃ (-4,1)

Question 8

You are given the shape of the vertical ends of a trough that is completely filled with water.Find the force exerted by the water on one end of the trough.(The weight density of water is 62.4 lb/ft³.)

A) 332.8 lb
B) 1331.2 lb
C) 2662.4 lb
D) 665.6 lb

Question 9

Find the center of mass of a lamina in the shape of a quarter-circle with radius with density =

Question 10

A swimming pool is 10 ft wide and 36 ft long and its bottom is an inclined plane,the shallow end having a depth of 1 ft and the deep end,12 ft.If the pool is full of water,find the hydrostatic force on the shallow end.(Use the fact that water weighs 62.5 lb/ )

Question 11

Find the centroid of the region bounded by the given curves.

A)
B)
C)
D)
E)

Question 12

You are given the shape of the vertical ends of a trough that is completely filled with water.Find the force exerted by the water on one end of the trough.(The weight density of water is 62.4 lb/ft³.)

A) 208 lb
B) 1040 lb
C) 104 lb
D) 520 lb

Question 13

Find the centroid of the region bounded by the graphs of the given equations.

A)
B)
C)
D)

Question 14

An aquarium is 4 ft long,3 ft wide,and 2 ft deep.If the aquarium is filled with water,find the force exerted by the water (a)on the bottom of the aquarium,(b)on the longer side of the aquarium,and (c)on the shorter side of the aquarium.(The weight density of water is 62.4 lb/ft³.)

Question 15

Calculate the center of mass of the lamina with density =

Question 16

Find the coordinates of the centroid for the region bounded by the curves ,x = 0, and y = 72