A wheel, starting from rest, rolls down a hill with a height of 1 m. Consider th

Question

A wheel, starting from rest, rolls down a hill with a height of 1 m. Consider the following three situations: The wheel rolls without slipping: the wheel slides down an icy hill (negligible friction): the wheel skids down a grassy hill (kinetic friction). (a) Rank the three situations according to the time it takes for the wheel to reach the bottom of the hill, soonest first. Explain. (b) Rank the three situations according to the rotational rate of the wheel at the bottom of the hill, highest rate first. Explain.

Explanation / Answer

Icy incline means no friction so minimum resistance or maximum speed down the incline.

Grassy hill refers that kinetic friction is into action, so ball will have some friction and will come down a little later than icy slope.

Rolling without slipping means, no translation, and friction is acting properly, so maximum time.

Conservation of energy : potential energy at h(1m) = mv2/2 +Iw2/2.

Translational kinetic energy + rolling kinetic energy.

If no friction acts on ball in any case, means translational motion +rolling motion :so least rotational rate

Hence, acc. To rotational rates :rolling without slipping> grassy hill>icy slope of hill.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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