Block of massM= 4kgrides on a horizontal plane. The region of the plane withx <0 is frictionless and that withx >0 has friction. The coefficient of kinetic friction between the block and the plane (where >0) isμK= 0.3. Initially, the block is pressed against a spring with force constantk= 24N/mand held there with the spring compressed0.5mfrom its relaxed length. The block and compressed spring are well to the left of the origin, i.e.,x0<0. The block is suddenly released and is propelled by the spring towardx= 0.( a) (i) Determine the pre-release kinetic energy of the block.(ii) Determine the pre-release spring potential energy of the block.(iii) Determine the pre-release total mechanical energy ofthe block.
(b) (i) Determine the total mechanical energy of the block just as it separates from the spring(as it passes the point where the end of the spring resides when it is relaxed).(ii) Determine the potential energy of the block when the spring is relaxed.(iii) Determine the kinetic energy of the block while it moves towardx= 0.
(c) (i) Determine the kinetic energy of the block as it reachesx= 0.(ii) Determine the magnitude of the force of kinetic friction exerted on the block once itpassesx= 0.(iii) How much energy must the block lose during the time interval from its passage by the origin to its coming to rest at xf? (iv) Determine the position, xf, at which the block stops.

where are the vectors ?

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:

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-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

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-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

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it is a negative acceleration