Problem

$\bullet$$\bullet$ Force during a jump. An averag…

06:09

Problem 20 Medium Difficulty

$\bullet$$\bullet \mathrm{A} 75,600 \mathrm{N}$ spaceship comes in for a vertical landing.
From an initial speed of $1.00 \mathrm{km} / \mathrm{s},$ it comes to rest in 2.00 $\mathrm{min}$ .
with uniform acceleration. (a) Make a free-body diagram of
this ship as it is coming in. (b) What braking force must its
rockets provide? Ignore air resistance.

Answer

a.see DIAGRAM
b.$-64,260 \mathrm{N}$

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Physics 101 Mechanics

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Video Transcript

So in this case you have no a spaceship that's decelerating. A zit approaches the now the planet. So you're free body diagram as two forces First, the force of gravity point outwards the weight and then the force of the braking force applied by the spacecraft going upwards. So remember that velocity will velocity will decrease from one kilometers per second, Teo to zero. And the velocity is is acting downwards because facial was moving downwards. So let's go ahead and do some calculations. So part be, the first thing I should do is find the mass way were given the weight, but not the mass of the spacecraft. Simply wait as mass times gravity, gravitational acceleration, some masses W over G. And so wait is 77,000 our groups, 75,600 new rules canned. That's divided by that 0.8 meters per second squared Asai units. So mass is 7,714 kilograms. Okay, and then we just want to use Newton's second law to find the fort and breaking for us. But the problem here is we need acceleration. And for that, of course, we're assuming constant acceleration, motion and we're using this following equation Emotion. So these of lie since the supply uh, he calls b the initial why velocity plus acceleration, the wind direction times the time So acceleration, wider years, The difference in gloss initial final velocities over time initial velocity are sorry. Final glass it was Your aunt comes to rest but initial velocity of my exactly downwards. So we're taking way implicitly assume here that upwards is positive and downward is negative. So when it's acting download, that should be a big So it's negative. One kilometers per second time is two minutes Now we gotta convert these one Kilometer is 1,000 meters, so that's a negative. 1,000 meters per second. Two minutes is a 60 seconds. So this is two times 60 seconds and so we end up with positive eight points to three meters per second squared. So acceleration is actually acting upwards. That acceleration is like upwards, which helps it stabilized as our great concert to not crash into the planet with by just the force of gravity. And we're going to find what force is required to do that. And so the force would be computed than that force is from Newton's second law, so we compute for mass and acceleration. And so we have that breaking for us, minus the weight equals mass times. Acceleration of it was found. The breaking forest is make plus mass times acceleration. Cancer rate is 75,000 600. Mittens uh plus Mass. 7714 kilos times acceleration. A pointy tio meters per second squared, plus a medic celebration, by the way signals. And so we get breaking force needed of 1.4 times 10 to the 540 thousands, and that's that's a

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