A box of mass $ 20 $ $ \text{kg} $ moves to the right on a horizontal frictionless surface with a speed of $ 4.0 $ $ \text{m/s} $. The box collides with and remains attached to one end of a spring of negligible mass whose other end is fixed to a wall. After the collision, the spring compresses a maximum distance of $ 0.50 $ $ \text{m} $, and the box then oscillates back and forth.

Question

A box of mass $ 20 $ $ \text{kg} $ moves to the right on a horizontal frictionless surface with a speed of $ 4.0 $ $ \text{m/s} $. The box collides with and remains attached to one end of a spring of negligible mass whose other end is fixed to a wall. After the collision, the spring compresses a maximum distance of $ 0.50 $ $ \text{m} $, and the box then oscillates back and forth.(a) Indicate whether the work done by the spring on the box from the moment the box first contacts the spring until the spring reaches maximum compression is positive, negative, or zero, and justify your answer.
, (b) Calculate the magnitude of the work done by the spring during the interval described above.
, (c) Calculate the spring constant of the spring.
, (d) Calculate the magnitude of the maximum acceleration of the box.
, (e) Calculate the frequency of oscillation of the box.
, (f) Sketch the kinetic energy $ K $ of the oscillating box as a function of position $ x $ for the range $ x = -0.50 $ $ \text{m} $ to $ x = +0.50 $ $ \text{m} $. Describe what your graph looks like.
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Jason · Accepted Answer

$\text{Negative}$
$160\,\text{J}$
$1.28\times10^{3}\,\text{N/m}$
$32\,\text{m/s^{2}}$
$1.27\,\text{Hz}$
$K(x)=160-640x^{2}$

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