Question

A spring with spring constant 15 N/m hangs from the ceiling. A ball is attached to the spring and allowed to come to rest. It is then pulled down 7.5 cm and released. The ball makes 31 oscillations in 15 s 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

Answer:

1)m=89.01 g

2)V(max) = 97.3 cm/s

Explanation:

Given that

K= 15 N/m

The maximum amplitude ,A=7.5 cm = 0.075 m

Given that 31 oscillations in 15 seconds ,this means that frequency f

f=\dfrac{31}{15}

f=2.066 Hz

lets take mass of the ball = m kg

$f=\dfrac{1}{2\pi}\times \sqrt{\dfrac{K}{m}}$

$m=\dfrac{1}{4\times \pi^2}\times{\dfrac{K}{f^2}}$

$m=\dfrac{1}{4\times \pi^2}\times{\dfrac{15}{2.066^2}}$

m=0.08901 kg

m=89.01 g

The maximum speed

V(max)= ω x A

ω = 2π f= 2 x π x 2.066 = 12.98 rad/s

V(max) = 12.98 x 0.075 =0.973 m/s

V(max) = 97.3 cm/s