Question

A 0.30 kg yo-yo consists of two solid disks of radius 5.10 cm joined together by a massless rod of radius 1.0 cm and a string wrapped around the rod. One end of the string is held fixed and is under constant tension T as the yo-yo is released.(a) Find the acceleration of the yo-yo............ m/s2(b) Find the tension T.............. N

Answer 1

Answer:

0.70046 m/s²

2.732862 N

Explanation:

g = Acceleration due to gravity = 9.81 m/s²

m = Mass of yo-yo = 0.3 kg

R = Radius of rolling disk = 5.1 cm

r = Radius of rod = 1 cm

For a rolling disks the acceleration is given by

$a=\frac{g}{1+\frac{R^2}{2r}}\\\Rightarrow a=\frac{9.81}{1+\frac{0.051^2}{2\times 0.01^2}}\\\Rightarrow a=0.70046\ m/s^2$

The acceleration of the yo-yo is 0.70046 m/s²

The tension in the string will be

$T=m(g-a)\\\Rightarrow T=0.3\times (9.81-0.70046)\\\Rightarrow T=2.732862\ N$

The tension in the string is 2.732862 N