Essential Calculus Early Transcendentals 2nd Edition James Stewart
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MULTIPLE CHOICE
1. 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
ANS: B PTS: 1 DIF: Medium REF: 7.6.25
MSC: Bimodal NOT: Section 7.6
2. 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
ANS: C PTS: 1 DIF: Medium REF: 7.6.27
MSC: Bimodal NOT: Section 7.6
3. 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
ANS: B PTS: 1 DIF: Medium REF: 7.6.28
MSC: Bimodal NOT: Section 7.6
4. 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
ANS: C PTS: 1 DIF: Medium REF: 7.6.31
MSC: Bimodal NOT: Section 7.6
5. The masses are located at the point . Find the moments and and the center of mass of the system. ;
e.
ANS: B PTS: 1 DIF: Medium REF: 7.6.37
MSC: Bimodal NOT: Section 7.6
6. Find the centroid of the region bounded by the graphs of the given equations.
d. ANS: B PTS: 1 DIF: Medium REF: 7.6.44
MSC: Bimodal NOT: Section 7.6
7. Find the centroid of the region bounded by the given curves.
b.
c.
d.
e.
ANS: B PTS: 1 DIF: Medium REF: 7.6.45
MSC: Bimodal NOT: Section 7.6
8. Find the centroid of the region bounded by the given curves.
a.
b.
c.
d.
e. None of these
ANS: D PTS: 1 DIF: Medium REF: 7.6.46
MSC: Bimodal NOT: Section 7.6
NUMERIC RESPONSE
1. 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 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/ .)
ANS:
PTS: 1 DIF: Medium REF: 7.6.33a
MSC: Numerical Response NOT: Section 7.6
2. Find the coordinates of the centroid for the region bounded by the curves , x = 0, and y = .
ANS:
PTS: 1 DIF: Medium REF: 7.6.39
MSC: Numerical Response
3. Find the exact coordinates of the centroid.
NOT: Section 7.6
ANS:
PTS: 1 DIF: Medium REF: 7.6.41
MSC: Numerical Response
NOT: Section 7.6
4. Calculate the center of mass of the lamina with density =
ANS:
PTS: 1 DIF: Medium REF: 7.6.47
MSC: Numerical Response
NOT: Section 7.6
5. Find the center of mass of a lamina in the shape of a quarter-circle with radius with density = .
ANS:
PTS: 1 DIF: Medium REF: 7.6.48
MSC: Numerical Response
NOT: Section 7.6
6. 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.
ANS:
PTS: 1 DIF: Medium REF: 7.6.51
MSC: Numerical Response
SHORT ANSWER
NOT: Section 7.6
1. 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.)
ANS:
a. 1497.6 lb
b. 499.2 lb
c. 374.4 lb
PTS: 1 DIF: Medium REF: 7.6.15 MSC: Short Answer
NOT: Section 7.6
2. Find the center of mass of the system comprising masses mk located at the points Pk 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)
ANS:
PTS: 1 DIF: Easy REF: 7.6.38 MSC: Short Answer
NOT: Section 7.6