| 1. |
What is the maximum tension possible in a
1.00 mm diameter nylon tennis racquet string? If you want tighter
strings, what do you do to prevent breakage: go to thinner or thicker
strings? Why? Physics Charts - Ultimate Strengths of Materials
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Area =  r2
= ( 0.00100 m )2
= 3.14 x 10 -6 m 2
F
US tensile =
---
Solve for F.
A
F = A x US tensile
= 3.14 x 10 -6 m
2 x 500 x 10 6 N/m2 = 1570 N
If you have thicker strings, the area is
greater and the Force necessary for fracture is greater.
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| 2. |
If a compressive force of 3.0 x 10 4
N is exerted on the end of a 20. cm long bone of cross-sectional area
3.6 cm2, (a) will the bone break, and (b) if not, by how
much does it shorten? Physics Charts - Ultimate Strengths of Materials
Physics Charts - Elastic Moduli
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1 m = 100 cm
=> 1 m2 = 10000 cm2
Area = 0.00036 m2
F
US tensile =
---
Solve for F.
A
F = A x US tensile
= 0.00036 m2 x
130 x 10 6 N/m2 = 47000
N Force
required for fracture.
Since the applied force is less than the force
required for fracture, the bone will not break.
1
F
1
3.0 x 10 4 N
/\L = --- --- Lo =
----------------------- ------------------ 20. cm
= 0.11 cm
E A
15 x 10 9 N m -2
0.00036 m2
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| 3. |
(a) What is the minimum
cross-sectional area required of a vertical steel cable for which is
suspended a 320. kg chandelier? Assume a safety factor of
7.0. (b) If the cable is 7.5 m long, how much does
it elongate? Physics Charts - Ultimate Strengths of Materials
Physics Charts - Elastic Moduli
|
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US tensile x Safety Factor
= 500 x 10 6 N/m2 x 7.0
= 3.5 x 10 9 N/m2
F = mg = 320. kg x 9.80 m s
-2 = 3140 N
F
US tensile =
---
Solve for A.
A
F
3140 N
A = -------------- = ------------------------
= 9.0 x 10 -7 m2
US tensile
3.5 x 10 9 N m -2
1
F
1
3140 N
/\L = --- --- Lo =
------------------------ --------------------- 7.5 m
= 0.13 m
E A
200 x 10 9 N m -2 9.0
x 10 -7 m2
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| 4. |
A steel cable is to support an elevator
whose total loaded mass is not to exceed 3100 kg. If the
maximum acceleration of the elevator is 1.2 m s -2, calculate
the diameter of the cable required with a safety factor of
7.0? Physics Charts - Ultimate Strengths of Materials
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US tensile x Safety Factor
= 500 x 10 6 N/m2 x 7.0
= 3.5 x 10 9 N/m2
F = m (g +a) = 3100. kg x(
9.80 m s -2 + 1.2 m s -2 ) = 34000 N
F
US tensile =
---
Solve for A.
A
F
34000 N
A = -------------- = ------------------------
= 9.7 x 10 -6 m2
US tensile
3.5 x 10 9 N m -2
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