Please show work. Thank you A yo-yo is made of two solid cylindrical disks, each
ID: 1469664 • Letter: P
Question
Please show work. Thank you
A yo-yo is made of two solid cylindrical disks, each of mass 0.055 kg and diameter 0.079 m , joined by a (concentric) thin solid cylindrical hub of mass 0.0054 kg and diameter 0.011 m . Use conservation of energy to calculate the linear speed of the yo-yo when it reaches the end of its 1.0 m long string, if it is released from rest. Express your answer using two significant figures. What fraction of its kinetic energy is rotational? Express your answer using two significant figures.Explanation / Answer
(a)
total mass of yo-yo:
m = 2(0.055 kg) + 0.0054 kg
m = 0.1154 kg
moment of inertia of yo-yo:
I = 2(1/2)(0.055 kg)(0.079/2 m)^2 + (1/2)(0.0054 kg)(0.011/2 m)^2
I = 8.58*10-5 kg-m^2
(gravitational potential energy) = (rotational kinetic energy) + (linear kinetic energy)
mgh = (1/2)I^2 + (1/2)mv^2
mgh = (1/2)(I)(v/r)^2 + (1/2)mv^2
mgh = (1/2)(I/r^2 + m)v^2
Use the radius of the hub for r since the tension in the string is what is imparting torque on the hub during motion.
(0.1154 kg)(9.81 m/s^2)(1.00 m) = (1/2)(8.58*10-5 kg-m^2/(0.011/2 m)^2 + 0.1154 kg)v^2
= 1.13207 = 1.47588v^2
v^2 = 1.13207 / 1.47588
v = 0.87 m/s
(b)
(rotational kinetic energy) / (total energy) =
(1/2)I^2 / (mgh) =
(1/2)(I)(v/r)^2 / (mgh) =
{(1/2)(8.58*10^-5 kg-m^2)[(0.87 m/s) / (0.011/2 m)]^2} / [(0.1154 kg)(9.81 m/s^2)(1 m)] =
= 0.95 or 95%