Consider the motion of a 1.00-kg particle that moves with potential energy given by
U(x) = (-2.00 J∙m) /x + (4.00 J∙m²) /x². Suppose the particle is moving with a speed of 3.00 m/s when it is located at x = 1.00 m. What is the speed of the object when it is located at x = 5.00 m?

Question

Quizplus · Accepted Answer

We can use conservation of mechanical energy to solve this problem. The total mechanical energy of the particle is given by: E = K + U where K is the kinetic energy and U is the potential energy. At x = 1.00 m, the particle has a kinetic energy of: K = (1/2)mv^2 = (1/2)(1.00 kg)(3.00 m/s)^2 = 4.50 J and a potential energy of: U = (-2.00 J*m)/x + (4.00 J*m*²)/x² = (-2.00 J*m)/(1.00 m) + (4.00 J*m*²)/(1.00 m*²) = 2.00 J So, the total mechanical energy at x = 1.00 m is: E = K + U = 4.50 J + 2.00 J = 6.50 J At x = 5.00 m, the potential energy of the particle is: U = (-2.00 J*m)/x + (4.00 J*m*²)/x² = (-2.00 J*m)/(5.00 m) + (4.00 J*m*²)/(5.00 m*²) = 0.20 J Therefore, the kinetic energy at x = 5.00 m is: K = E - U = 6.50 J - 0.20 J = 6.30 J and the speed is: v = ²(2K/m) = ²(2(6.30 J)/(1.00 kg)) = 3.67 m/s Therefore, the answer is D, 3.67 m/s.

Consider the Motion of a 1