Answer:
Material K has a modulus of elasticity E=3.389× 10¹¹ Pa
Material H has a modulus of elasticity E=1.009 × 10⁹ Pa
Material K has higher value of modulus of elasticity than material H
Material K is stiffer.
Explanation:
Wire 1 material H
Length=L = 40 ft =12.192 m
Diameter= 3/8 in = 0.009525 m
Area= A= πr²,where r=0.009525/2 =0.004763
A=3.142*0.004763² =0.00007126 m²
Force, F= 225 lb= 225*4.45 =1001.25 N
Change in length =Δ L= 0.10 in = 0.00254
To find modulus of elasticity apply'
E=F*L/A*ΔL
E=1001.25*12.192/(0.004763*0.00254)
E= 1009027923.58 Pa
E=1.009 × 10⁹ Pa
For Wire 2 material K
Length=L= 40 ft =12.192 m
Diameter = 3/16 in = 0.1875 in = 0.004763 m
Area= πr² = 3.142 * (0.004763/2)² = 0.00000567154 m²
Force, F= 225 lb= 225*4.45 =1001.25 N
Change in length =Δ L= 0.25 in =0.00635 m
To find modulus of elasticity apply'
E=F*L/A*ΔL
E= (1001.25*12.192)/(0.00000567154 * 0.00635 )
E=338955422575 Pa
E=3.389× 10¹¹ Pa
Material K has a greater modulus of elasticity
The material with higher value of E is stiffer than that with low value of E.The stiffer material is K.
