Far out in space, a 100,000-kg rocket and a 200,000-kg rocket are docked at opposite ends of a motionless 90m-long tunnel. the tunnel is rigid and has much less mass than the rockets. the rockets start their engines simultaneously, each providing 50,000n of constant thrust in opposite directions. a. find the center of mass, as measured from rocket 1b. what is the moment of inertia of the system, assuming the rockets can be treated as point masses? c. find the net torque on the system about the center of massd. what is the angular acceleration of the system? e. what is the structure's angular velocity after 30.0 seconds?

a)

b) I =

c) N*m

d) a =

e) W= 0.25 rad/s

Explanation:

a) we know that:

where is the ubicaton of the center of mass, the mass of the first rocket, its distances with the rocket 1, the mass of the second rocket and its distance with the rocket 1. So, replacing values, we get:

So, the center of mass is at 60m from the rocket 1.

b) we know that:

where I is the moment of inertia, is the mass of the rocket 1, its distance from the center of mass, the mass of the second rocket and the distance between the rocket 2 and the center of mass. So, replacing values, we get:

I =

c) We know that:

T = Fr

where T is the net torque, F is the force and r is the distance between the rocket and the radius. Then:

Replacing values, we get:

50,000N(60m)+50,000N(30m) = T

N*m

d) We know that:

T = Ia

where T is the net torque, I the moment of inertia and a is the angular aceleration. So, replacing values, we get:

solving for a:

a =

e) Finally, using:

W = at

where W is the angular velocity, a is the angular aceleration and t is the time.

Then, replacing values. we get:

W = ()(30s)

W = 0.25 rad/s

come closer and become far apart and become steam/gas

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

-it's clean and sustainable

-resources of geothermal energy range from the shallow ground to hot water and hot rock found a few miles beneath the earth's surface, and down even deeper to the extremely high temperatures of molten rock called magma

-almost everywhere, the shallow ground or upper 10 feet of the earth's surface maintains a nearly constant temperature between 50° and 60°f (10° and 16°c)

-geothermal heat pumps can tap into this resource to heat and cool buildings

-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

-in the winter, the heat pump removes heat from the heat exchanger and pumps it into the indoor air delivery system

-in the summer, the process is reversed, and the heat pump moves heat from the indoor air into the heat exchanger

-the heat removed from the indoor air during the summer can also be used to provide a free source of hot water