91影视

• The circumference of the circular path 鈥渞鈥� is 0.94 m .
• The length of the cord 鈥淟鈥� is 0.9 m .
• The mass of bob 鈥渕鈥� is 0.04 kg .

The problem deals with Newton鈥檚 second law of motion, which states that the acceleration of an object is dependent upon the net force acting upon the object and the mass of the object.

Calculate the angle made by the cord.

Use Newton鈥檚 second law of motion to calculate the tension in the cord. After calculating the tension, calculate the velocity of the bob and the time required to complete one revolution.

The radius of the circular path R,

$R=\frac{r}{2\mathrm{蟺}}=\frac{0.94\mathrm{m}}{2\mathrm{蟺}}=0.15\mathrm{m}$

The angle cord makes with horizontal:

$胃={\cos }^{-1}\left(R/L\right)={\cos }^{-1}\left(0.15\mathrm{m}/0.94\mathrm{m}\right)=80掳$

To calculate tension, apply Newton鈥檚 second law of motion in a vertical direction:

$T\sin 胃=mg$

Substitute the values in the above expression, and we get,

$$\begin{gathered} T=\frac{\left(0.04\mathrm{kg}脳9.8\mathrm{m}/{\mathrm{s}}^2\right)}{\sin \left(80掳\right)} \\ =0.4\mathrm{N} \end{gathered}$$

Thus, the tension in the string is 0.4 N.

To calculate the velocity of bob, apply Newton鈥檚 second law of motion horizontal direction:

$$\begin{gathered} T\cos 胃=\frac{m{v}^2}{R} \\ v=\sqrt{\frac{R脳T\cos 胃}{m}} \end{gathered}$$

Substitute the values in the above expression, and we get,

$$\begin{gathered} v=\sqrt{\frac{\left(0.15\mathrm{m}\right)脳\left(0.4\mathrm{N}\right)\cos \left(80掳\right)}{0.04\mathrm{kg}}} \\ =0.49\mathrm{m}/\mathrm{s} \end{gathered}$$

To calculate the time to complete one revolution:

$$\begin{gathered} t=\frac{0.94\mathrm{m}}{0.49\mathrm{m}/\mathrm{s}} \\ =1.9\mathrm{s} \end{gathered}$$

Thus, the period of motion is 1.9 s.