Show all the work for a,b and c. Please and thank you. You make a primitive yo-y
ID: 1468598 • Letter: S
Question
Show all the work for a,b and c. Please and thank you. You make a primitive yo-yo by wrapping a string several times around the edge of a solid disk of mass 0.300 kg and radius 4.00cm. You hold the end of the string stationary while releasing the disk with no initial motion. The string unwinds without slipping or stretching as the disk drops and rotates. Use energy considerations to find the speed of the center of mass of the solid disk after it has fallen 0.500 m. Using rotational dynamics, find the tension in the cord. What is the acceleration of the falling disk? Show that this is consistent with your answer to (a).Explanation / Answer
here,
mass of the disk , m = 0.3 kg
radius , r = 4 cm = 0.04 m
(a)
h = 0.5m
let the speed be v
using conservation of energy
0.5 * m * v^2 + 0.5 *I*w^2 = m*g*h
0.5 * m * v^2 + 0.5 * 0.5 * m*r^2 * ( v/r^2) = m*g*h
0.5 * v^2 + 0.25 * v^2= g*h
0.75 * v^2 = 9.8 * 0.5
v = 2.56 m/s
the speed of the centre of mass is 2.56 m/s
(c)
let the accelration be a
using third equation of motion
v^2 - 0 = 2*a*h
2.56^2 - 0 = 2*a*0.5
a = 6.55 m/s^2
the accelration of the centre of mass is 6.55 m/s^2
(b)
let the tension in the string be T
m*g - T = m*a
0.3 * 9.8 - 0.3 * 6.55 = T
T = 0.98 N
the tension in the string is 0.98 N