Stress, Strain, Tension, Compression, Elasticity
M o d u lu s o f e la s tic ity =
S tr e s s
S tra in
S tr a in = D e g re e o f D e fo rm a tio n =
S tr e s s =
F o rc e
A re a
c h a n g e in d im e n s io n
o rg in a l d im e n s io n
M e a s u r e d in P a (u n it o f P re s s u re ) 1 P a = 1 N /m 2
A re a = π r 2 = π (
D
2
)2
* * * * Y o u N E E D T H IS F O R # 2 a n d # 4
1.
The heels on a pair of women’s shoes have a radius of .5 cm at the bottom. If 30% of the weight of a woman 480N is
supported by each heel, find the stress on each heel. Stress = Force/area
2.
Find the diameter of an 18 m(L) long steel wire that will stretch no more than .009 m(ΔL) when a load (stress) of 3800
N is hung on the end of the wire. The Young’s Modulus for steel wire is 200 x 109 N/m2 . Y =
3.
F•L
Stress
=
Strain
A • ΔL
For safety in climbing mountaineers use a nylon rope that is 50 m long(L) and .01 m in diameter. When supporting a
900 N climber the rope stretches 1.6 m (ΔL) under tension. Find the Young’s Modulus(Y) for the nylon rope
Y=
F•L
Stress
=
Strain
A • ΔL
Stress, Strain, Tension, Compression, Elasticity
4.
The elastic limit of steel is 5.0 Pa (N/m2), find the minimum diameter a steel wire can to support a 700 N weight
without exceeding its elastic limit. Maximum Stress =
5.
Force
Minimum Area
The distortion of the earth’s crust is an example of sheer on a large scale. A particular rock has a sheer modulus of 1.5
x1010 Pa(N/m2)(Shear Modulus, S). What shear stress is applied when a 10 km layer (h) of rock is sheared a distance
F
of 5 m (Δx).
S =
S h e a r S tr e s s
F •h
= A =
Δx
S h e a r S tra in
A • Δx
h
Human bone has a Young’s Modulus of 14.5 x108 N/m2(Y). Under compression, it can withstand a stress of about 160
x 106 N/m2(stress) before breaking. Assuming a human adult thigh bone (femur) is about .5 m (L) long, how much
compression (ΔL) can the bone withstand before breaking.
F
F •L
Y= A =
ΔL
A • ΔL
L
6.
Stress, Strain, Tension, Compression, Elasticity
7.
A cylindrical aluminum pillar 7.00 high has a radius of 30.0 cm. If a 2000-kg sculpture is placed on top of the pillar,
by how much is the pillar compressed?
8.
A mass of 2.00 kg is supported by a copper wire of length 4.00 m and diameter 4.00 mm. Determine (a) the stress in
the wire and (b) the elongation of the wire.
9.
A uniform pressure of 5.00 × 104 Pa is exerted on a copper block having a volume of 10–3 m3. What is the change in
volume of the block?
10. During a tensile strength experiment, a small-diameter fiber is elongated by a force of 0.0250 N. The fiber has an
initial length of 0.200 m and stretches a distance of 4.00 × 1024 m. The Young’s modulus for the material being tested
is 7.60 × 1010 Pa. Determine the diameter of the fiber.