Can you please answer each part and show complete work? Trying to understand all
ID: 1838320 • Letter: C
Question
Can you please answer each part and show complete work? Trying to understand all concepts for exam.
The figure is an end view of a flat, cylindrical satellite, radius R = 3.5 m & mass M = 2, 750 kg, which engineers are testing. It's moment of inertia is I = (0.57)MR^2. There are four rocket engines, arranged 90 degree apart, at radius R. When fired simultaneously, they exert four equal forces F = 1150 N tangent to the circle as shown. They give the satellite an angular acceleration alpha. Assume that the 4 forces F are only ones producing torques about the axis of rotation. Calculate: The total (net) torque tau_net exerted by the four rocket engines. The angular acceleration alpha of the satellite. The tangential acceleration at a_tan of a point on the rim. What Physical Principle did you use to find the angular acceleration in part b? The satellite starts from rest & has an angular velocity omega = 12 rad/s after the rockets have been firing for a time t. Calculate: Calculate the time t & the velocity v of a point on the rim at that time.Explanation / Answer
Here ,
I = 0.57 M * R^2
I = 0.57 * 2750 * 3.5^2
I = 19202 Kg.m^2
F = 1150 N
a) for the net torque
net torque exerted =4 * F * R
net torque exerted = 4 * 1150 * 3.5 N.m
net torque exerted = 16100 N.m
b) let the angular acceleration of the satellite is a
Using second law of motion
Tnet = I * a
16100 = 19202 * a
a = 0.838 rad/s^2
the angular acceleration of satellite is 0.838 rad/s^2
c)
atan = a * R
atan = 0.838 * 3.5 m/s^2
atan = 2.934 m/s^2
the tangential acceleration is 2.934 m/s^2
d)
We used Second law of motion to find the angular acceleration
e)
w = 12 rad/s
let the time is t
t = w/a
t = 12/0.838 = 14.32 s
the time taken is 14.32 s
velocity = w * R
velocity = 12 * 3.5 m/s
velocity = 42 m/s
the velocity of a point on the rim is 42 m/s