A rod extending between x = 0 and x = 14.0 cm has uniform cross-sectional area A = 9.00 cm 2 . Its density increases steadily between its ends from 2.70 g/cm 3 to 19.3 g/cm 3 . (a) Identify the constants B and C required in the expression ρ = B + Cx to describe the variable density. (b) The mass of the rod is given by m = ∫ all material ρ d V = ∫ all x ρ A d x = ∫ 0 14 .0 cm ( B + C x ) ( 9.00 cm 2 ) d x Carry out the integration to find the mass of the rod.
A rod extending between x = 0 and x = 14.0 cm has uniform cross-sectional area A = 9.00 cm 2 . Its density increases steadily between its ends from 2.70 g/cm 3 to 19.3 g/cm 3 . (a) Identify the constants B and C required in the expression ρ = B + Cx to describe the variable density. (b) The mass of the rod is given by m = ∫ all material ρ d V = ∫ all x ρ A d x = ∫ 0 14 .0 cm ( B + C x ) ( 9.00 cm 2 ) d x Carry out the integration to find the mass of the rod.
A rod extending between x = 0 and x = 14.0 cm has uniform cross-sectional area A = 9.00 cm2. Its density increases steadily between its ends from 2.70 g/cm3 to 19.3 g/cm3. (a) Identify the constants B and C required in the expression ρ = B + Cx to describe the variable density. (b) The mass of the rod is given by
m
=
∫
all material
ρ
d
V
=
∫
all x
ρ
A
d
x
=
∫
0
14
.0 cm
(
B
+
C
x
)
(
9.00
cm
2
)
d
x
Carry out the integration to find the mass of the rod.
A 1000-kg object hangs from the lower end of a steel rod 5.0 m long that is suspended vertically. The diameter of the rod is 0.80 cm and Young's modulus for the rod is 210,000 MN/m2. What is the elongation of the rod due to this object?
Group of answer choices
a. 0.12 cm
b. 0.46 cm
c. 0.047 cm
d. 1.2 cm
e. 1.8 cm
A cylindrical aluminum rod, with an initial length of 0.8000 m and radius 1000.0 mm, is clamped in place at one end and then stretched by a machine pulling parallel to its length at its other end. Assuming that the rod’s density (mass per unit volume) does not change, find the force magnitude that is required of the machine to decrease the radius to 999.9 mm. (The yield strength is not exceeded.)
Chapter 1 Solutions
Physics For Scientists And Engineers, Technology Update, Loose-leaf Version
Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)
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