8. (25 points) A landing craft is in the process of landing on Mars, where the a

Question

8. (25 points) A landing craft is in the process of landing on Mars, where the acceleration of gravity is 0.385 that of Earth (g-9.81 m/s2 on earth). The craft has the following acceleration relative to the landing surface: a (1.96i+3.92j-19.62 k) m/s?. At this instant, an astronaut is raising a hand camera with a mass of 0.31 kg. If she is giving the camera an upward (vertical acceleration of 3 m/s'relative to the landing craft, what force must the astronaut exert on the camera at the instant of interest? Include the force due to gravity in your calculations. (Hint the force has i, j, and k components and gravity on Mars is 0.385 that of earth.)

Explanation / Answer

Let acceleration due to gravity at earth =g

Acceleration due to gravity at mars =x=0.385g

Vertical relative acceleration given to camera=3k

Vertical acceleration of spacecraft =19.62k m/s²

The astronaut has to overcome a vertical acceleration of 19.62k and provide an additional 3k m/s² acceleration, so

Net vertical acceleration on mars, x=3+19.62=22.62k m/s²

Acceleration wrt earth=g=x/0.385

Mass of camera =0.31 kg

Force wrt earth is

As force =mass x acceleration

We have

Force vertical =0.31*x/0.385=0.31*22.62/0.385=18.21k N.

Ad astronaut ptovides acceleration in k direction only, so force must be applied in k direction only.

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