Physics · The potential energy of a spring, conservation of mechanical energy, conservative and non-conservative forces

A single conservative force \) acts on a particle that moves along the x-axis. T

A single conservative force \( F(x) \) acts on a \( 1.0-k g \) particle that moves along the x-axis. The potential energy \( U(x) \) is \( \operatorname{given} \operatorname{by} U(x)=20+(x-2)^{2} \) where \( x \) is in meters. At \( \boldsymbol{x}=\mathbf{5 . 0} \mathrm{m}, \) the particle has a kinetic energy of 20 J.What is the mechanical energy of the system?

  • A. \( 35 J \)
  • B. \( 64 J \)
  • C. \( 86 J \)
  • D. \( 49 J \)

Step-by-step solution

The potential energy at x = 5.0 m is U(5) = 20 + (5-2)^2 = 20 + 9 = 29 J. The kinetic energy is given as 20 J. Mechanical energy is the sum of kinetic and potential energies: E = K + U = 20 J + 29 J = 49 J.
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