An approximate expression for the force exerted by first rope is F = -kx + bx^2

Question

An approximate expression for the force exerted by first rope is F = -kx + bx^2 - cx^3, k = 230 N/m, b = 3.9 N/m^2, c = 2.0N/m^3 and  x is the stretch. Take U = 0 at x = 0.

a) Find the energy stored in strectching the rope 2.60m.

U = ___________

b) A second rope exerts a force given by F = -kx + bx^2, where k = 230 N/m, b = 3.9 N/m^2 and x is the stretch. By what percentage does your result for the first rope differ from that for second rope?

% = ___________

*I got -45.7 for "a" which is incorrect. Please show all work!

Explanation / Answer

force constant k=F/x=-k+bx-cx^2=-233.38 N/m

a) energy stored in strectching the rope 2.60m.

U=(1/2)*k*x^2=-788.82 J

B) for second rope force constnt k=F/x=-k+bx=-219.86 N/m

U=(1/2)*k*x^2=-743.126 J

percentage does your result for the first rope differ from that for second rope

=[(U2-U1)/U2]*100=5.79 %

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.