How Much Mass Converts to Energy to Accelerate the Enterprise to 0.1c?

[pinkerpikachu]

The fictional starship Enterprise obtains power by combining matter and antimatter, achieving complete conversion of mass into energy. If the mass of Enterprise is approximately 5 X 10⁹ kg, how much mass must be converted into kinetic energy to accelerate it from rest to one tenth the speed of light?

of course, E=mc² but I don't have the energy so I can't solve for m? What other ways can I approach this problem

the answer in the back of the book is 2.5 X 10⁷ kg

 

[pinkerpikachu]

nevermind! totally solved my own problem!

 

[nlightner]

There are a few different ways to approach this problem. One way is to use the equation E=mc2 to calculate the total energy required for the Enterprise to accelerate to one tenth the speed of light. From there, you can calculate the amount of mass that needs to be converted into energy by solving for m. Another approach is to use the kinetic energy equation, KE=1/2mv2, to calculate the kinetic energy required for the acceleration and then convert that energy back into mass using E=mc2. Whichever method you use, the important thing to remember is that mass and energy are interchangeable and can be converted into each other through the famous equation E=mc2.