Question

A boy is swinging a yo-yo with mass 0.5 kg in a circle with radius 1.5 m at aspeed of 6 m/s. What is the tension in the string connecting the yo-yo to theboy's finger, disregarding the effect of gravity?O A. 20 NO B. 35 NO C. 9ND. 12 N

Answer 1

Given:

Mass, m = 0.5 kg

Speed, v = 6 m/s

radius, r = 1.5 m

Let's find the tension in the string.

To find the tension in the string, apply the formula:

`T=(m\omega^2)/(r)`

Where;

w is the angular velocity.

To find the angular velocity, apply the formula below:

`\begin{gathered} \omega=(v)/(r) \\ \\ \omega=\frac{6\text{ m/s}}{1.5} \\ \\ \omega=4\text{ rad/s} \end{gathered}`

The angular velocity is 4 rad/sec.

Now, find the centripetal acceleration:

`\begin{gathered} a=r\omega^2 \\ \\ a=1.5*4^2 \\ \\ a=24\text{ m/s}^2 \end{gathered}`

Now, to find the tension, we have:

`\begin{gathered} T=(mw^2)/(r)=ma \\ \\ T=0.5*24 \\ \\ T=12\text{ N} \end{gathered}`

Therefore, the tension in the string is 12 N.

ANSWER:

D. 12N