A spring has an unstretched length of 9.8 cm. The potential energy stored in the spring is V when the spring is streched to a length of 11.8 cm. What is the stretched length of the spring when its potential energy is 2.2 V? What compressed length will result in a potential energy of 2.3 V?
(1)
x₁=11.8-9.8 = 2 cm
V=kx₁²/2
2.2V =kx₂²/2
2.2V/V = 2kx₁²/2 kx₂²
2.2= x₁²/ x₂²
x=sqrt{2.2•2²} =2.97 cm
L=9.8+2.97 =12.77 cm
(2)
x=sqrt{2.3•2²} =3.03 cm
L=9.8-3.03=6.77 cm