Yo-yo Physics Questions? Please help!?

[匿名]

2017-02-14 3:14 pm

Pictures of the problem:
https://anonimag.es/image/JT9hAR9
https://anonimag.es/image/JT9hARp

Someone please help me? I missed this question by now, but I need an explanation and the right answers so I could find out what to do:

A. Assume: Drag(friction) is negligible.
Given g = 9.81 m/s^2. The density of a large Yo-yo like solid is uniform throughout. The Yo-yo like solid has a mass of 2.1 kg. A cord is wrapped around the stem of the Yo-yo like solid and attached to the ceiling. The radius of the stem is 3m and the radius of the disk is 7m. Calculate the moment of inertia about the center of mass(axis of rotation). Answer in units of kg*m^2.

ANSWER: 44.9327

B. What is the vertical acceleration of the center of mass of the Yo-you? Answer in units of m/s^2.

C. What is the magnitude of the torque the cord exerts on the center of mass of the Yo-Yo? Answer in units of Nm

D. The Yo-Yo is released from rest at height h. Find the velocity v of the center of mass of the disk at the height ∆h = 19 m. Answer in units of m/s.

回答 (1)

NCS

2017-02-15 2:10 am

✔ 最佳答案

NOW I see, by virtue of the second image, how to calculate the moment of inertia.

If the 7 m disks are each ℓ wide and the 3 m disk is 2ℓ wide, then the
3 m disk has volume V3 = 2ℓ*π(3m)²
and the 7 m disks have volume V7 = 2ℓ*π(7m)²
for a total volume V = 2ℓπ[(3m)² + (7m)²] = 2ℓπ*58m²

so V3 accounts for (3²/58)*2.1kg = 0.326 kg
and V7 accounts for (7²/58)*2.1kg = 1.774 kg

Armed with this knowledge, the total moment of inertia is
I = ½[0.326kg*(3m)² + 1.774kg*(7m)²] = 44.9 kg·m²

B) If we consider that the yo-yo is rotating not about its center but about the point at which the string leaves the stem, then by the parallel axis theorem
I = Ic + mr² = 44.9kg·m² + 2.1kg*(3m)² = 63.8 kg·m²

torque = I*α = T*R
where T is the tension, so
63.8kg·m² * α = T*R

But α = a/R
and T = m(g - a), so
63.8kg·m² * a/3m = 2.1kg*(9.81m/s² - a)*3m
which solves to
a = 2.24 m/s² ◄

C) T = 2.1kg * (9.81 - 2.24)m/s² = 15.9 N ◄

D) v = √(2ah) = √(2 * 2.24m/s² * 19m) = 9.23 m/s ◄

Hope this helps!

參考: http://www.wolframalpha.com/input/?i=63.8+*+a%2F3+%3D+2.1*(9.81+-+a)*3

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