Timothy A. Philpot - Mechanics of materials _ an integrated learning system-John Wiley (2017)

pRoBLEmS
p17.12 A 19 mm diameter steel [E = 200 GPa] rod is required
to absorb the energy of a 25 kg collar that falls h = 75 mm, as shown
in Figure P17.12/13. Determine the minimum required rod length L
so that the maximum stress in the rod does not exceed 210 MPa.
B
p17.15 As seen in Figure P17.15/16, collar D is released from rest
and slides without friction downward a distance h = 300 mm, where it
strikes a head fixed to the end of a compound rod ABC. Rod segment
(1) is made of aluminum [E 1 = 70 GPa] and has a length L 1 = 800 mm
and a diameter d 1 = 12 mm. Rod segment (2) is made of bronze [E 2 =
105 GPa] and has a length L 2 = 1,300 mm and a diameter d 2 = 16 mm.
What is the allowable mass for collar D if the maximum normal stress
in the aluminum rod segment must be limited to 200 MPa?
C
L
m
Collar
L 2
(2)
p17.13 In Figure P17.12/13, a 500 mm long steel [E = 200 GPa]
rod is required to absorb the energy of a 16 kg mass that falls a
distance h. If the diameter of the rod is 10 mm, what is the maximum
drop height h so that the maximum stress in the rod does not
exceed 210 MPa?
p17.14 A weight W = 4,000 lb falls from a height h = 18 in. onto
the top of a 10 in. diameter wooden pole, as shown in Figure P17.14.
The pole has a length L = 24 ft and a modulus of elasticity E = 1.5 ×
10 6 psi. For this problem, disregard any potential buckling effects.
Calculate
(a) the impact factor n.
(b) the maximum shortening of the pole.
(c) the maximum compressive stress in the pole.
A
FIGURE p17.12/13
Weight W
B
h
h
L 1
(1)
p17.16 Collar D shown in Figure P17.15/16 has a mass of
11 kg. When released from rest, the collar slides without friction
downward a distance h, where it strikes a head fixed to the end of a
compound rod ABC. Rod segment (1) is made of aluminum [E 1 =
70 GPa] and has a length L 1 = 600 mm and a diameter d 1 = 12 mm.
Rod segment (2) is made of bronze [E 2 = 105 GPa] and has a length
L 2 = 1,000 mm and a diameter d 2 = 16 mm. If the maximum normal
stress in the aluminum rod segment must be limited to 250 MPa,
determine the largest acceptable drop height h.
p17.17 In Figure P17.17, the 12 kg mass is falling at a velocity
v = 1.5 m/s at the instant it is h = 300 mm above the spring-and-post
A
B
FIGURE p17.15/16
v
Collar D
h
h
L
k
B
L
A
FIGURE p17.14
A
FIGURE p17.17
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