Question

A spring with spring constant 17.0 N/m hangs from the ceiling. A ball is suspended from the spring and allowed to come to rest. It is then pulled down 4.00 cm and released. The ball makes 35.0 oscillations in 18.0 seconds.
1) What is its the mass of the ball?
Express your answer using two significant figures.
m = _____ g

2) What is its maximum speed?
Express your answer using two significant figures.

= _____ cm/s

Answer 1

Explanation:

Given that,

Spring constant of the spring, k = 17 N/m

It is then pulled down 4.00 cm and released, A = 4 cm = 0.04 m

The ball makes 35.0 oscillations in 18.0 seconds.

The time required to complete one oscillation is :

$T=\dfrac{18}{35}=0.514\ s$

Angular velocity,

$\omega=\dfrac{2\pi }{T}\\\\\omega=\dfrac{2\pi }{0.514}\\\\\omega=12.22\ rad/s$

(1) The relation between spring constant, angular velocity and mass is given by :

$\omega^2=\dfrac{k}{m}\\\\m=\dfrac{k}{\omega^2}\\\\m=\dfrac{17}{(12.22)^2}\\\\m=0.11\ kg$

(2) The maximum speed is given by :

$v=A\omega\\\\v=0.04\times 12.22\\\\v=0.49\ m/s$