Matter & Interactions 2nd ed. Practice Problems
Aaron Titus | High Point University
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(N)=# of solutions
1540001     Final speed of a space probe with thrusters firing; application of the update form of the energy principle     1540001
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Question

 

In a 3-D computer game, a 5000-kg space probe in space (far from any significant interactions with planets or stars) has four thrusters that fire in the +x, –x, +y, and –y directions, respectively. As the space probe moves from to , there are two thrusters simultaneously firing with forces and respectively. If the initial speed of the space probe is 200 m/s, what is its final speed? State any assumptions that you make.


Figure: Thrusters on a spaceship firing in the +y and – x directions, respectively.

 



Solution

 

Define the system as the space probe, and apply the Energy Principle. Once we calculate the final kinetic energy of the system, then we can solve for its final speed.

Treat the space probe as a point particle that only has rest energy and kinetic energy.

Though the space probe presumably loses fuel, treat the space probe as an ideal particle whose mass is constant, the rest energy of the space probe doesn't change and cancels out in the energy principle.

Calculate the work done by the thrusters on the spaceship and substitute into the energy principle to get the kinetic energy. Be sure to convert km to m. The work done by thruster 1 is

The work done by thruster 2 is

The total work done by the thrusters on the space probe is

Substitute into the energy principle and solve for the final kinetic energy of the space probe. Because the probe's speed is nonrelativistic, use the nonrelativistic approximation for kinetic energy.

Because the work done on the space probe is negative, it is slowing down. As a result, the probe lost kinetic energy, exactly as expected. Use the final kinetic energy to calculate the final speed.

Note that the final speed (130 m/s) is less than the initial speed (200 m/s), exactly as expected since the work done on the space probe was negative. The space probe indeed slowed down.