Question 1 The space probe Deep Space 1 was launched on October 24, 1998. Its ma

Question

Question 1

The space probe Deep Space 1 was launched on October 24, 1998. Its mass was 474 kg. The goal of the mission was to test a new kind of engine called an ion propulsion drive. This engine generated only a weak thrust, but it could do so over long periods of time with the consumption of only small amounts of fuel. The mission was spectacularly successful. At a thrust of 56 mN how many days were required for the probe to attain a velocity of 765 m/s (1710 mi/h), assuming that the probe started from rest and that the mass remained nearly constant?

Explanation / Answer

From newton's second law net Force Fnet = m*a

m is the mass of the probe = 474 kg

a is the accelaration = (v-u)/t

v is the final velocity = 765 m/s

u is the initial velocity = 0 m/s

t is the required time = ?

Given that net force = thrust = 56*10^-3 N

accelaration a = Fnet /m = (56*10^-3)/(474) = 1.18*10^-4 m/s^2

but a = (v-u)/t = (765-0)/t = 765/t

765/t = 1.18*10^-4

t = 765/(1.18*10^-4) = 6483050 S

t = 6483050/(24*60*60) = 75 days

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