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

Question

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?

Accepted Answer

$ 49 J $. Mechanical energy is the sum of kinetic and potential energies. At x = 5 m, U = 20 + (5 - 2)^2 = 29 J, so E = 20 J + 29 J = 49 J.

Solution

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