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A particle of mass 0.0100 kg moves along the r-axis and is subject to a single conservative force that gives rise to the potential energy function U(z) = -[(2.50J/m*)r³ – (7.50 J/m²)z² + (5.00 J/m)x + 5.00 JJe¬(1.0/m)=, (1) (a) Find the force F(x) on the particle as a function of its position r. (b) Find the points at which the particle is in equilibrium, and classify these equilibrium positions as stable or unstable. Plot the graphs of F(x) and U(z). (You are allowed to draw these by hand, or use your preferred graphing software.) (c) You should find two stable equilibrium positions, r, and r2. Let 21 be the stable equilibrium

A particle of mass 0.0100 kg moves along the r-axis and is subject to a single conservative force that gives rise to the potential energy function U(z) = -[(2.50J/m*)r³ – (7.50 J/m²)z² + (5.00 J/m)x + 5.00 JJe¬(1.0/m)=, (1) (a) Find the force F(x) on the particle as a function of its position r. (b) Find the points at which the particle is in equilibrium, and classify these equilibrium positions as stable or unstable. Plot the graphs of F(x) and U(z). (You are allowed to draw these by hand, or use your preferred graphing software.) (c) You should find two stable equilibrium positions, r, and r2. Let 21 be the stable equilibrium

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A particle of mass 0.0100 kg moves along the r-axis and is subject to a single conservative force that gives rise to the potential energy function U(z) = -[(2.50J/m*)r* – (7.50 J/m²)z² + (5.00.J/m)x + 5.00 J]e-(1.00/m)». (1) (a) Find the force F(x) on the particle as a function of its position r. (b) Find the points at which the particle is in equilibrium, and classify these equilibrium positions as stable or unstable. Plot the graphs of F(r) and U(r). (You are allowed to draw these by hand, or use your preferred graphing software.) (c) You should find two stable equilibrium positions, ri and r2. Let 21 be the stable equilibrium position with lower potential energy, and zz be the stable equilibrium position with higher potential energy. If the particle moves from zi to r2, what is the average force it experiences? (d) If the particle is at z1, what speed should it have in order to have access to r2? (e) If the particle is at ra, what speed should it have to be able to escape the influence of the force (that is, to move to arbitrarily large z)?
Transcribed Image Text:A particle of mass 0.0100 kg moves along the r-axis and is subject to a single conservative force that gives rise to the potential energy function U(z) = -[(2.50J/m*)r* – (7.50 J/m²)z² + (5.00.J/m)x + 5.00 J]e-(1.00/m)». (1) (a) Find the force F(x) on the particle as a function of its position r. (b) Find the points at which the particle is in equilibrium, and classify these equilibrium positions as stable or unstable. Plot the graphs of F(r) and U(r). (You are allowed to draw these by hand, or use your preferred graphing software.) (c) You should find two stable equilibrium positions, ri and r2. Let 21 be the stable equilibrium position with lower potential energy, and zz be the stable equilibrium position with higher potential energy. If the particle moves from zi to r2, what is the average force it experiences? (d) If the particle is at z1, what speed should it have in order to have access to r2? (e) If the particle is at ra, what speed should it have to be able to escape the influence of the force (that is, to move to arbitrarily large z)?
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