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March 26, 2017

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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?

  • Physics - ,

    (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

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