What that means is the atom is so radioactive that the nucleus is unstable.
Okay so yeah u have to minus then subtract then decide it it’s a method i was taught to do
Explanation:
It is given that,
Spring constant of the spring, k = 15 N/m
Amplitude of the oscillation, A = 7.5 cm = 0.075 m
Number of oscillations, N = 31
Time, t = 15 s
(a) Let m is the mass of the ball. The frequency of oscillation of the spring is given by :
![f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}](https://tex.z-dn.net/?f=f%3D%5Cdfrac%7B1%7D%7B2%5Cpi%7D%5Csqrt%7B%5Cdfrac%7Bk%7D%7Bm%7D%7D)
Total number of oscillation per unit time is called frequency of oscillation. Here, ![f=\dfrac{31}{15}=2.06\ Hz](https://tex.z-dn.net/?f=f%3D%5Cdfrac%7B31%7D%7B15%7D%3D2.06%5C%20Hz)
![m=\dfrac{k}{4\pi^2f^2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bk%7D%7B4%5Cpi%5E2f%5E2%7D)
![m=\dfrac{15}{4\pi^2\times 2.06^2}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B15%7D%7B4%5Cpi%5E2%5Ctimes%202.06%5E2%7D)
m = 0.0895 kg
or
m = 89 g
(b) The maximum speed of the ball that is given by :
![v_{max}=A\times \omega](https://tex.z-dn.net/?f=v_%7Bmax%7D%3DA%5Ctimes%20%5Comega)
![v_{max}=A\times 2\pi f](https://tex.z-dn.net/?f=v_%7Bmax%7D%3DA%5Ctimes%202%5Cpi%20f)
![v_{max}=0.075\times 2\pi \times 2.06](https://tex.z-dn.net/?f=v_%7Bmax%7D%3D0.075%5Ctimes%202%5Cpi%20%5Ctimes%202.06)
![v_{max}=0.970\ m/s](https://tex.z-dn.net/?f=v_%7Bmax%7D%3D0.970%5C%20m%2Fs)
![v_{max}=97\ cm/s](https://tex.z-dn.net/?f=v_%7Bmax%7D%3D97%5C%20cm%2Fs)
Hence, this is the required solution.
Answer:
(a) The equivalent spring constant is 598.485 N/m
(b) The work done is 46.926 J
Explanation:
From Hooke's law of elasticity
K (spring constant) = F/e
F is the range of force exerted = 237 - 0 = 237 N
e is the extension of bowstring = 0.396 m
K = F/e = 237/0.396 = 598.485 N/m
Work done = 1/2 Fe = 1/2 × 237 × 0.396 = 46.926 J