A space probe is built with a mass of 1700 pound-mass [lb_m] before launch on Ea

Question

A space probe is built with a mass of 1700 pound-mass [lb_m] before launch on Earth. The probe is powered by four ion thrusters, each capable of generating 225 millinewtons [mN] of thrust. Using Newton's second law, the acceleration (a) of the craft is equal to the force (F) divided by the mass (m): a = F/m The velocity (v) of an object increases as an object accelerates. If the object starts at rest, the final velocity is given by the acceleration multiplied by the length of time the acceleration is applied to the object (t): v = at = Ft/m Using this equation, how many weeks will the thrusters have to operate for the probe, initially at rest, to reach a velocity of 420 miles per minute [mi/min]? You may assume the initial velocity of the probe is zero miles per minute [0 mi/min].

Explanation / Answer

From the Newton second law accleration of hte probe is

a= F/m = 4 ( 225 * 10^-3 N)/1700 pound mass ( 0.45359237 kilograms/ pound mass) = 1.167 * 10^-3 m/s^2

v= Ft/m

t= vm/F

= 420 mi/min (26.8224 meters / second/ mi/min) ( 1700 pound mass ( 0.45359237 kilograms/ pound mass)/4 ( 225 * 10^-3 N)

=9652039.21 s

convert seconds to weeks

t= 15.959 weeks

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