ELASTICITY

QUESTION 2nd WEEK

QUESTION 1 ;

1. A load of 100 lb is applied to the lower end of a steel rod 3 ft long and 0.20 in a diameter, How much will the rod stretch?

ANSWER 1 ;

1. Y = F/A ÷ ∆ L/L
= (3 ft)(100 lb) ÷∏ (0.1in ²) (3.3 X 10 ⁷lb /in ²)

= 2.9 X 10 ⁻⁴ ft or ∆ L = 3.5 x 10⁻³ in



QUESTION 2 ;


2. A solid metal cylinder has r = 0.60cm and L = 8.0cm. Its mass is 77g. Find the density of the metal.


ANSWER 2 ;


2. The cylindrical volume is ∏r L= ∏(0.60)²(8.0) = 9.05cm ³ and density is p = m / V
= 71 / 9.05 = 7.85g / cm ³= 7850 kg / m ³


QUESTION 3 ;

3. Find the density and specific gravity of ethyl alcohol if 63.3 g occupies 80.0 mL.


ANSWER 3 ;

3. p = density = mass / volume = 63.3 g / 80.0 mL
= 0.791 g / mL = 791 kg / m³
specific gravity = density of alcohol / density of water
= 791 kg / m³ ÷ 1000 kg / m³
= 0.791

QUESTION 4 ;

4. Give a 2.0 m length of steel wire with 1.0 mm diameter, about how much will the wire stretch under a 5.0 kg load?
Y = 195000 M Pa.


ANSWER 4 ;

4. Since tensile modulus is stress / strain, we have ∆ L/L = (F/A) /Y = (5(9.8) )/( ∏ (5 X 10ˉ⁴) ²(195 x 10⁹) )
= 3.2 x 10ˉ⁴ and ∆L = 6.4 x 10 ˉ⁴ m


QUESTION 5 ;

5. What increase in pressure is required to decrease the volume of 200L of water by 0.004 percent? Find ∆ V.
( B = 2100 M Pa)

ANSWER 5 ;

5. ∆V = 0.00004( 200L) = 0.008L
= ∆ p = B ( - ∆ V / V )
= (2100 M Pa) (0.008 / 200 L) = 0.084 M Pa = 84 k Pa.