I\'m not sure where to even start: 19) The nearest stars, apart from the Sun, ar

Question

I'm not sure where to even start:

19) The nearest stars, apart from the Sun, are light-years awayfrom Earth. If we are to investigate these stars, our space shipswill have to travel at an appreciable fraction of the speed oflight.

(a) You are in charge of estimating the energy required toaccelerate a 10,000-kg capsule from rest to 10 percent of the speedof light in one year. What is the minimum amount of energy that isrequired? Note that at velocities approaching the speed of light,the kinetic energy formula (1/2)mv2 is not correct.However, it gives a value that is within 1% of the correct valuefor speeds up to 10% of the speed of light.

(b) Compare your estimate to the amount of energy that the UnitedStates uses in a year (about 5 x 1020 J).

(c) Estimate the minimum average power required of the propulsionsystem.

Explanation / Answer

reletivcistic kineticnenergy of the particle                         E = (p^2c^2 +mo^2 c^4)              p = mv                 = mo * v                 givenv = 0.1c                = 1 / (1-v^2 /c^2)                  = 1.00503
                         E^2 = m^2(0.1c)^2 *c^2 + mo^2*c^4 .                            E^2 = mo^2c^4 [(1.00503^2)(0.01) + 1 ]                 mo = 10,000 kg                    c = 3*10^8 m/sec                from the above relation plugging the known values in the aboveequation we can solve for energy E . b) the percentage of energy when compared to the UnitedStates uses in a year will be = E / 5*10^20J c)average power needed P = E / 1 yr                                            P = E / 365*24*3600sec .        

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