a 0.343-kg mass slides on a frictionless floor with a speed of 1.56 m/s. the mass strikes and compresses a spring with a force constant of 43.4 n/m.

part a
how far does the mass travel after contacting the spring before it comes to rest?

part b
how much time does it take for the spring to stop the mass?

Question

a 0.343-kg mass slides on a frictionless floor with a speed of 1.56 m/s. the mass strikes and compresses a spring with a force constant of 43.4 n/m.

part a
how far does the mass travel after contacting the spring before it comes to rest?

part b
how much time does it take for the spring to stop the mass?

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Conservation of Energy", "Spring Compression", "Simple Harmonic Motion Period" ], "new_concepts": [], "current_concepts": [ "Conservation of Energy", "Spring Compression", "Simple Harmonic Motion Period" ] } ## Calculate the maximum spring compression $$ \begin{aligned} E_i &= E_f \ \frac{1}{2} m v^2 &= \frac{1}{2} k A^2 \ A &= v \sqrt{\frac{m}{k}} \ A &= 1.56 \times \sqrt{\frac{0.343}{43.4}} \approx 0.13869\text{ m} \end{aligned} $$ ## Calculate the time to stop the mass $$ \begin{aligned} T &= 2\pi \sqrt{\frac{m}{k}} \ t &= \frac{T}{4} = \frac{\pi}{2} \sqrt{\frac{m}{k}} \ t &= \frac{\pi}{2} \sqrt{\frac{0.343}{43.4}} \approx 0.13969\text{ s} \end{aligned} $$ ## Question 1 $A =$ 0.139 m ## Question 2 $t =$ 0.140 s { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Simple Harmonic Motion" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the maximum spring compression

Calculate the time to stop the mass

Answer:

Question 1

Question 2