Question

I need help with these 2 questions.

A=2 B=5 C=1 D=9 E=5 F=9

Date: Problem 1 A wire of un-stretched length to and diameter D is used to suspend a block of weight w. The wire, of unknown composition, has a Young's modulus of Y. la.) Assuming the wire obeys Hooke's law, what is the force constant k of the wire? 1b) What would the weight w have to be to stretch the wire by a given Δ Given values fill in): 10 = 80.0 + 20A + 2B D = 0.500 + C/10 + D/100 Y = 6.0 + E + F/10 A1 = 0.40 + C/5 + A/ 10 Formulas: cm x 1010 Pa = Answers: la.) k- lb.) w =

Answer 1

Solution

From Hooks law

F = Kx

K = F / x

in this case

K = W / dl

By the definition of young modulus

Y = stress / strain

stress =Y( lo / dl)

stress =( 6+E + F / 10 ) (80+20A+2B) / (0.40+C / 5 + A/10 )

stress =( 6+5+ 9/10) (80+20*2 + 2*5) / (0.40 + 1/5 + 2/10)

stress = 1933.75 pa

W / A = 1933.75

w = 1933.75( 3.14 * ( D/ 2)² )

W = 1517.9 ( 0.500+ C/10+D / 100)(10^-6)

W = 1517.9 ( 0.500+ 1/10+9/100)(10)^-6

b) W = 0.0010 N

a) force constant will be = K = w / dl = 0.0010 / (0.40+ C / 5 + A/10)

K = 0.0013(10)³ N / m

K = 1.309 N / m

Question 2

Speed could be found by building up the following relationship

m2 V² / r = G m1 m2 / r²

V² = Gm₁ / r

V = ( G m1 / r)^1/2

V =( 6.67 * 10^-11) (100+2E+20F) / (1+A/2+D/20)

V = (6.67 * 10^-11)((100+2*5 + 20*9) / (1+1+9/20)

V = 7.8 * 10^-9 m / s

Time period = T = 2pi / w

T = 2pi / v / r

T = 2pir / V

T = 2(3.14)(1+A/2+D/20) / 7.8* 10^-9

T = 805128205 (1+1+9/20)

T = 1972564102.56 s