Energy Needed to Maintain Velocity

[Riceman1974]

I know how to figure out how much energy is needed to acclerate to a certain speed. What I don't know is how much energy is needed to maintain that speed.

For example. I was watching the first Trek movie the other day, and Kirk orders the Enterprise to go to .5 light speed. So the Enterperise goes from 0 to 150M meters per second in like 5 seconds. I wondered how much force would be needed to do that, so I calculated:

F = M * A
The ship has a mass of 200,000 metric tons, so 200,000,000 kg * acceleration, which going from 0 to .5 light in 5 seconds would be 30,000,000 meters per second per second (i hope that's right).

That gave me 6*10^15 Newtons (damn!)

I then tried to see what this would be in joules, so I next calculated the distance traveled, using:

Distance = .5*Acceleration*Time^2
.5*30,000,000*(5^2)

That gave me 375,000,000 meters.

To then calculate joules, I used W(joules) = Force * Distance
6*10^15 * 375,000,000

That gave me 2.25*10^24 joules of energy needed to accelerate a 200,000 metric ton object to .5 light speed in 5 seconds (please correct me if I'm wrong).

My question, how many joules per second is needed to maintain that speed?

This is not homework. I'm just a nerd.

 

[PatPwnt]

0 Joules/sec are necessary, if you are traveling in a vacuum(space) see Newtons first law. Also, the energy required to get up the speed is a little more than you calculated because when you increase your speed, your mass increases as well, see special relativity / einstein. But, your method of calculations are right if you ignore special relativity ( I didnt actually do your calculations). You don't need to calculate the energy from force times d, you can use 1/2 m v^2 too. (would have been quicker, but same answer.)

 

[astrokreng]

To maintain a constant velocity, the object needs to have a net force of zero acting on it. Therefore, no additional energy is needed to maintain that speed. However, the object will continue to have kinetic energy, which is the energy associated with its motion. This kinetic energy can be calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

In this case, the object has a mass of 200,000,000 kg and a velocity of 150,000,000 meters per second. Plugging these values into the formula, we get a kinetic energy of 2.25*10^22 joules. This is the amount of energy that the object will have while maintaining a speed of .5 light speed.

To put this into perspective, the amount of energy needed to accelerate the object to this speed (2.25*10^24 joules) is much greater than the amount needed to maintain it (2.25*10^22 joules). This is because acceleration requires a continuous application of force, while maintaining a constant velocity only requires the initial energy input.

Also, keep in mind that this calculation does not take into account any external factors such as air resistance or other forces that may act on the object. These factors would require additional energy to counteract and maintain the speed.

In summary, to maintain a constant velocity, no additional energy is needed as long as there is no net force acting on the object. However, the object will continue to have kinetic energy associated with its motion.