question 4
10 pts
consider a spring-loaded grappling harpoon gun. the spring in the gun is compressed by 0.75 m, and is supposed to launch the 1.50 kg harpoon with a final velocity of 265 m/s.
what is the spring constant of the harpoon gun in newtons per meter?

question 5
10 pts
the actual speed of the harpoon gun when fired is only 240 m/s. how much energy is lost (in joules) from the system due to nonconservative work?

Question

question 4
10 pts
consider a spring-loaded grappling harpoon gun. the spring in the gun is compressed by 0.75 m, and is supposed to launch the 1.50 kg harpoon with a final velocity of 265 m/s.
what is the spring constant of the harpoon gun in newtons per meter?

question 5
10 pts
the actual speed of the harpoon gun when fired is only 240 m/s. how much energy is lost (in joules) from the system due to nonconservative work?

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Conservation of Energy", "Elastic Potential Energy", "Nonconservative Work" ], "new_concepts": [], "current_concepts": [ "Conservation of Energy", "Elastic Potential Energy", "Nonconservative Work" ] } ## Calculate the spring constant for Question 4 $$ \begin{aligned} &m = 1.50\text{ kg},\quad x = 0.75\text{ m},\quad v = 265\text{ m/s}\ &\frac{1}{2} k x^2 = \frac{1}{2} m v^2 \implies k = \frac{m v^2}{x^2}\ &k = \frac{1.50 \times 265^2}{0.75^2} = 187266.67\text{ N/m} \approx 187267\text{ N/m} \end{aligned} $$ ## Calculate the energy lost for Question 5 $$ \begin{aligned} &v_{\text{actual}} = 240\text{ m/s}\ &E_{\text{initial}} = \frac{1}{2} k x^2 = \frac{1}{2} \times 187266.67 \times 0.75^2 = 52668.75\text{ J}\ &E_{\text{final}} = \frac{1}{2} m v_{\text{actual}}^2 = \frac{1}{2} \times 1.50 \times 240^2 = 43200\text{ J}\ &E_{\text{lost}} = E_{\text{initial}} - E_{\text{final}} = 52668.75 - 43200 = 9468.75\text{ J} \approx 9469\text{ J} \end{aligned} $$ ## Question 4 187267 ## Question 5 9469 { "subject": "Natural Science", "question_type": "Multi-part", "knowledge_point": [ "Natural Science", "Physics", "Conservation of Energy" ] }

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Question

Explanation:

Calculate the spring constant for Question 4

Calculate the energy lost for Question 5

Answer:

Question 4

Question 5