Answer:
The distance is 0.9681 m.
Explanation:
Given that,
Length = 0.95 m
Mass of block = 7.9 kg
Stretches spring length = 1.06 m
another mass = 1.3 kg
Magnitude of restoring force acting in the spring equal to the magnitude of applied force
![F_{rest}=F_{ap}](https://tex.z-dn.net/?f=F_%7Brest%7D%3DF_%7Bap%7D)
![F = mg](https://tex.z-dn.net/?f=F%20%3D%20mg)
We need to calculate the spring constant
Using Hook's law,
![F_{r}=kx](https://tex.z-dn.net/?f=F_%7Br%7D%3Dkx)
![k=\dfrac{F}{x}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7BF%7D%7Bx%7D)
Put the value into the formula
![k=\dfrac{mg}{x}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7Bmg%7D%7Bx%7D)
Put the value into the formula
![k=\dfrac{7.9\times9.8}{1.06-0.95}](https://tex.z-dn.net/?f=k%3D%5Cdfrac%7B7.9%5Ctimes9.8%7D%7B1.06-0.95%7D)
![k=703.81\ N/m](https://tex.z-dn.net/?f=k%3D703.81%5C%20N%2Fm)
We need to calculate the distance
Using formula of spring constant
![x=\dfrac{mg}{k}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7Bmg%7D%7Bk%7D)
Put the value into the formula
![x=\dfrac{1.3\times9.8}{703.81}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B1.3%5Ctimes9.8%7D%7B703.81%7D)
![x=0.0181\ m](https://tex.z-dn.net/?f=x%3D0.0181%5C%20m)
We need to calculate the total distance
Using formula of distance
![d=x+l](https://tex.z-dn.net/?f=d%3Dx%2Bl)
![d=0.0181+0.95](https://tex.z-dn.net/?f=d%3D0.0181%2B0.95)
![d=0.9681\ m](https://tex.z-dn.net/?f=d%3D0.9681%5C%20m)
Hence, The distance is 0.9681 m.