As shown in the figure below, a box of mass m = 7.00 kg is sliding across a hori
ID: 1449896 • Letter: A
Question
As shown in the figure below, a box of mass m = 7.00 kg is sliding across a horizontal frictionless surface with an initial speed v= 3.80 m/s when it encounters a spring of constant k = 2550 N/m. The box comes momentarily to rest after compressing the spring some amount x_c. Determine the final compression x_c of the spring. Can you write an expression for the initial kinetic energy of the box in terms of its mass and initial speed? What is the final kinetic energy of the box? How is the change in kinetic energy related to the initial and final kinetic energy? Since only conservative forces are acting on the system (box and spring) is energy conserved? How is the change in spring potential energy related to the change in kinetic energy of the box? How is the compression of the spring related to the change in potential energy of the spring and the spring constant?Explanation / Answer
0.5kx2 = 0.5mv2
=> x=sqrt(mv2/k) = sqrt(7*3.82/2550) = 0.1991 m = 19.91 cm
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