Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

A 0.39Kg block on a horizontal frictionless surface is attached ot a spring whos

ID: 2008308 • Letter: A

Question

A 0.39Kg block on a horizontal frictionless surface is attached ot a spring whose force constant is a 570 N/m. The block is pulled from its equilibrium position at x = 0 m to a displacement x = +0.080 m and is released from rest. the block then executes simple harmonic motion along the x-axis (horizontal). when the displacement is x = 0.057 m, the kinetic energy of the block is closest to:

A) 0.90 J B) 1.1 J C) 1.0 J D) 0.84 J E) 0.95 J

The answer key says the answer is A, but I am lost on how to get there. Please show the algerbra and concepts involved. Thank You!

Explanation / Answer

PE at any point = 1/2 k x^2

Total E = 1/2 k A^2

KE = E - PE = 1/2 k (A^2 - x^2)

k = 570

A = 0.080

x = 0.057

Substitute to get:

KE = 0.898 J = 0.9 J (A)