Question

1. a 16-g ball at the end of a 1.4-m string is swung in a horizontal circle. it revolves every 1.09 s. what is the magnitude of the string’s tension? given: 16 g, 1.4 m, 1.09 s unknown:

Explanation:

Step1: Convert mass to kg

$m = 16\ \text{g} = 0.016\ \text{kg}$

Step2: Calculate angular velocity

$\omega = \frac{2\pi}{T} = \frac{2\pi}{1.09\ \text{s}} \approx 5.77\ \text{rad/s}$

Step3: Compute centripetal force (tension)

$T = m\omega^2r = 0.016\ \text{kg} \times (5.77\ \text{rad/s})^2 \times 1.4\ \text{m}$
First calculate $\omega^2$: $(5.77)^2 \approx 33.29$
Then $T = 0.016 \times 33.29 \times 1.4 \approx 0.74\ \text{N}$

Answer:

0.74 N