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PhysicsClassical Physics

A 20 kg Box on a Horizontal Frictionless Surface Attached to a Spring

The spring does negative 160 J of work, has k = 1280 N/m, produces a maximum acceleration of 32 m/s², and oscillates at about 1.27 Hz.

Question

A 20 kg20\,\mathrm{kg} box on a horizontal frictionless surface is moving to the right at 4.0 m/s4.0\,\mathrm{m/s}. The box hits and remains attached to one end of a spring of negligible mass whose other end is attached to a wall. The spring compresses a maximum distance of 0.50 m0.50\,\mathrm{m}, and the box then oscillates back and forth.

  1. From first contact until maximum compression, is the work done by the spring positive, negative, or zero? Justify.
  2. Calculate the magnitude of that work.
  3. Calculate the spring constant.
  4. Calculate the magnitude of the box's maximum acceleration.
  5. Calculate the oscillation frequency.

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Evidence boundary

The calculation uses the problem’s ideal frictionless surface and negligible-mass spring, treats the attachment as having no mechanical-energy loss, and takes 0.50 m as the oscillation amplitude from the uncompressed equilibrium position. It does not model damping, spring nonlinearity, or a real collision loss.