??- 10.91 A 4.5 kg box slides down a 5.2-m-high frictionless hill, starting from

Question

??- 10.91 A 4.5 kg box slides down a 5.2-m-high frictionless hill, starting from rest, across a 1.9-m -wide horizontal surface, then hits a horizontal spring with spring constant 460 N/m. The other end of the spring is anchored against a wall. The ground under the spring is frictionless, but the 1.9-m-long horizontal surface is rough. The coefficient of kinetic friction of the box on this surface is 0.22 SubmitPre ious Ans Request Answer X Incorrect; Try Again; 5 attempts remaining Part D Including the first crossing, how many complete trips will the box make across the rough surface before coming to rest? SubmitPra vious Answers Request Answer × Incorrect: Try Again: 4 attempts remaining

Explanation / Answer

Each time box crosses rough surface it loses Wf:

over rough surface friction force extracts work from box energy total

Wf = FF x 1.9 {where Wf = work done by friction force of FF)

FF = (0.22) x normal force

normal force = box weight = mg = (4.5)(9.8) = 44.1 N

FF = (0.22)(44.1) = 9.702 N

Wf = (9.702)(1.9) = 18.43 J

Box starts with a total energy:

at top of frictionless hill the box has its TOTAL starting energy as P.E.

P.E. top = mgh {where m = 4.5, g = 9.8, h = 5.2)

P.E. top = (4.5)(9.8)(5.2) = 229.32 J {total energy at start}

Box can cross rough surface = 229.32/18.43 = 12.44 times

since question asks for "complete trips" answer is 12 times

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.