Question

to get a flat uniform cylindrical satellite spinning at the correct rate, scientists fire 4 tangential rockets. suppose that the satellite has a mass of 3600 kg and a radius of 4m, and that the rockets each add a mass of 250 kg. what is the steady force required of each rocket if the satellite is to reach 32 rpm in 5 min starting from rest.

Answer 1

Answer:

The steady force required of each rocket is 31.36 N

Explanation:

Given that,

Mass of satellite = 3600 Kg

Radius = 4 m

Mass of rocket = 250 kg

Time = 5 min

Angular velocity = 32 rpm

We need to calculate the moment of inertia

Using formula of moment of inertia

$I=\dfrac{1}{2}Mr^2+4mr^2$

Where, M = mass of satellite

r = radius

m = mass of rocket

Put the value into the formula

$I=\dfrac{1}{2}\times3600\times4^2+4\times250\times4^2$

$I=44800\ kg-m^2$

We need to calculate the angular acceleration

Using formula of angular acceleration

$\alpha=\dfrac{\omega}{t}$

Where, $\omega$ = angular velocity

t = time

Put the value into the formula

$\alpha=\dfrac{2\pi\times32}{3600\times5}$

$\alpha=0.0112\ rad/s^2$

We need to calculate the steady force required of each rocket

Using formula of torque

$\tau=I\alpha$

$4rF=I\alpha$

$F=\dfrac{I\alpha}{4r}$

Put the value into the formula

$F=\dfrac{44800\times0.0112}{4\times4}$

$F=31.36\ N$

Hence, The steady force required of each rocket is 31.36 N