The space probe Deep Space 1 was launched on October 24, 1998. Its mass was 474

Question

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 705 m/s (1580 mi/h), assuming that the probe started from rest and that the mass remained nearly constant?

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 705 m/s (1580 mi/h), assuming that the probe started from rest and that the mass remained nearly constant? t = days the tolerance is +/-2%

Explanation / Answer

for this we can apply v = u + at

so t = (v - u ) /a,   v is final velocity, u is initialvelocity,a isacceleration

we have given v = 705 m/s , u = 0 and

we know that a = F/ m (F = ma Newton's secondlaw )

so time t = (v - u ) /a

= ( 705 - 0)/ ( F/m )

= m ( 705 - 0) / F -----(1)

WHERE m = 474 kg

F = 56mN = 56*10-3 N

t = 474* 705/0.056 =5967321 s

t =1 day = 8.61 *10 4 s

t =69 days

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