91影视

The maximum acceleration of the satellite is a = 5g

The mass of the satellite is m = 1160 kg

The speed of a satellite relative to orbiting space is v = 2.5 m/s

The principle of centripetal acceleration is used to find the compression of spring and the force constant of spring. The compression of the spring will be the same as the radius of the orbiting space.

The compressed distance of the spring is given as:

$$\begin{gathered} a=\frac{v^2}{x} \\ 5g=\frac{v^2}{x} \end{gathered}$$

Here, g is the gravitational acceleration and its value is $9.8鈥�m/s^2$, x is the compressed distance for spring.

Substitute all the values in the above equation and we get,

$$\begin{gathered} 5\left(9.8鈥�\frac{m}{s^2}\right)=\frac{\left(2.5鈥�{\displaystyle \frac{m}{s^2}}\right)}{x} \\ x=0.128鈥�m \end{gathered}$$

Therefore, the compressed distance of spring is 0.128 m.

The force constant of the spring is calculated as:

kx = ma

kx = 5mg

Here, a is the acceleration of the elevator

Substitute all the values in the above equation, and we get,

$$\begin{gathered} k(0.128鈥�m)=5(1160鈥�kg)\left(9.8鈥�\frac{m}{s^2}\right) \\ k=4.46脳{10}^5鈥�N/m \end{gathered}$$

Therefore, the force constant of the spring is $4.46脳{10}^5鈥�N/m$.