Question

A spring with spring constant 18 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 6.5 cm and released. The ball makes 19 oscillations in 18 s seconds.

Answer 1

Answer with Explanation:

We are given that

Spring constant=k=18 N/m

Amplitude,A=6.5 cm=$6.5\times 10^{-2}m$

1m=100 cm

Number of oscillations=N=19

Time=t=18 s

Frequency=Number of oscillations per second=$\nu=\frac{19}{18}=1.06 Hz$

Frequency=$\nu=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$

$\nu^2=\frac{1}{4\pi^2}\times \frac{k}{m}$

$m=\frac{k}{4\pi^2\nu^2}=\frac{18}{4\times (3.14)^2\times (1.06)^2}=0.41 kg$

1kg=1000g

$m=0.41 \times 1000=410 g$

Mass of the ball=410 g

Maximum speed of the ball=$A\omega=A(2\pi\nu}$)

Maximum speed of the ball=$v_{max}=6.5\times 10^{-2}\times 2\times 3.14\times 1.06=0.43m/s$

Hence, the maximum speed of the ball=0.43 m/s