Question

THIS IS ALL ONE QUESTION, PLEASE ANSWER ALL PARTS!

a)We have a crate of mass 29.6 kg on an inclined surface, with a coefficient of kinetic friction 0.144. Instead of pushing on the crate, you let it slide down due to gravity. What must the angle of the incline be, in order for the crate to slide with an acceleration of 6.62 m/s^2?

b)Consider a non-rotating space station in the shape of a long thin uniform rod of mass 8.10 x 10^6 kg and length 1116 meters. Rocket motors on both ends of the rod are ignited, applying a constant force of F = 8.37 x 10^5 N to each end of the rod as shown in the diagram, causing the station to rotate about its center. If the motors are left running for 1 minutes and 33 seconds before shutting off, then how fast will the station be rotating when the engines stop?

c)This time we have a non-rotating space station in the shape of a long thin uniform rod of mass 8.87 x 10^6 kg and length 581 meters. Small probes of mass 8564 kg are periodically launched in pairs from two points on the rod-shaped part of the station as shown, launching at a speed of 3364 m/s with respect to the launch points, which are each located 162 m from the center of the rod. After 20 pairs of probes have launched, how fast will the station be spinning?

This is all one question !

Answer #1

This time we have a non-rotating space station in the shape of a
long thin uniform rod of mass 1.88 x 10^6 kg and length 1447
meters. Small probes of mass 9779 kg are periodically launched in
pairs from two points on the rod-shaped part of the station as
shown, launching at a speed of 3576 m/s with respect to the launch
points, which are each located 412 m from the center of the rod.
After 17 pairs of probes...

Question 7
This time we have a non-rotating space station in the shape of a
long thin uniform rod of mass 3.73 x 10^6 kg and length 1428
meters. Small probes of mass 7553 kg are periodically launched in
pairs from two points on the rod-shaped part of the station as
shown, launching at a speed of 4962 m/s with respect to the launch
points, which are each located 384 m from the center of the rod.
After 13 pairs...

A.) Consider a non-rotating space station in the shape of a long
thin uniform rod of mass 4.20 x 10^6 kg and length 953 meters.
Rocket motors on both ends of the rod are ignited, applying a
constant force of F = 4.40 x 10^5 N to each end of the rod as shown
in the diagram, causing the station to rotate about its center. If
the motors are left running for 1 minutes and 26 seconds before
shutting off,...

A.) Consider a non-rotating space station in the shape of a long
thin uniform rod of mass 4.96 x 10^6 kg and length 530 meters.
Rocket motors on both ends of the rod are ignited, applying a
constant force of F = 4.99 x 10^5 N to each end of the rod as shown
in the diagram, causing the station to rotate about its center. If
the motors are left running for 1 minutes and 28 seconds before
shutting off,...

Consider a non-rotating space station in the shape of a long
thin uniform rod of mass 6.65 x 10^6 kg and length 574 meters.
Rocket motors on both ends of the rod are ignited, applying a
constant force of F = 9.48 x 10^5 N to each end of the rod as shown
in the diagram, causing the station to rotate about its center. If
the motors are left running for 2 minutes and 21 seconds before
shutting off, then...

A.) This time we have a crate of mass 27.8 kg on an inclined
surface, with a coefficient of kinetic friction 0.283. Instead of
pushing on the crate, you let it slide down due to gravity. What
must the angle of the incline be, in order for the crate to slide
with an acceleration of 3.12 m/s^2?
B.) Different situation now. You re out in space, on a rotating
wheel-shaped space station of radius 841 m. You feel planted firmly...

PART 1: This time we have a crate of mass 26.5
kg on an inclined surface, with a coefficient of kinetic friction
0.168. Instead of pushing on the crate, you let it slide down due
to gravity. What must the angle of the incline be, in order for the
crate to slide with an acceleration of 4.44 m/s^2?
A) 21.6 degrees
B) 50.4 degrees
C) 28.8 degrees
D) 36.0 degrees
PART 2: Different situation now. You re out in
space,...

Now we have a rod-shaped space station of length 1407 m and mass
4.47 x 10^6 kg, which can change its length (kind of like an
old-fashioned telescope), without changing its overall mass.
Suppose that the station is initially rotating at a constant rate
of 2.35 rpm. If the length of the rod is reduced to 2.35 m, what
will be the new rotation rate of the space station?
3.86 rpm
8.37 rpm
2.32 rpm
6.44 rpm

(PLEASE COMPLETE ALL PARTS OF THE QUESTION)
A uniform thin rod of mass m = 2.9 kg and
length L = 1.9 m can rotate about an axle through its
center. Four forces are acting on it as shown in the figure. Their
magnitudes are F1 = 5.5 N,
F2 = 2.5 N, F3 = 11 N and
F4 = 19.5 N. F2 acts a
distance d = 0.23 m from the center of mass.
A) Calculate the magnitude τ1...

A space station in the shape of a uniform disk (mass
6.42x105 kg, radius 150 m) rotates with period 33.6
seconds. There are also 809 astronauts (whom you can treat as point
particles) working inside the space station, each of mass 199 kg,
and all standing on the outside rim and rotating with the station.
Now, all the astronauts move to a conference room at the very
center of the space station. Find the new period of the rotation of...

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