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Problem 40 Medium Difficulty

A rocket blasts off from rest and attains a speed of 45 $\mathrm{m} / \mathrm{s}$ in 15 $\mathrm{s}$ , An astronatt has a mass of 57 $\mathrm{kg}$ . What is the astronaut's apparent weight during takeoff?

Answer

$7.3 \times 10^{2} N$

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Video Transcript

during the take off. There are two forces acting the after note. One force is the gravitational force. The weak force on the order force is the normal force exerted by the seat on that astronaut do the normal force. Then Newton's second law tells us the following the net force. Let me say that everything that is pointing up positive and everything that is pointing down is negative, then applying you don't second look that say's that the net force acting on the astronaut is echo streets, mess times its acceleration. But the net force is composed by two forces. The normal force and the weight force and the musicals to the mass times acceleration off the astronaut. What we call the apparent weight is the normal force, so they're after not apparent. Wait, which is It goes to the normal force is given by the mask off the astronaut times acceleration off the astronaut plus the weight force. So how can he calculates the weight force? Well, just remember that the weight forest is given by the mask off. The astronaut finds an explanation of gravity, and the acceleration of gravity is approximately 9.8 meters per second squared, then the weight force is. It goes to 57 times 9.8, so their parent weight is equals to mass off the astronaut times its acceleration plus 57 times 9.8. Now, why is the acceleration of the astronaut? It is the course to the acceleration off the rocket and acceleration off the rocket can be calculated using these information about its velocity and the time it took to think that velocity acceleration is it goes to the variation in velocity divided by the time it took. So these is equals to 45 divided by 15 and this is three meters per second squared. Therefore, the apparent weight is equals to 57 times three plus 57 times 9.8 and these give us on apparent weight off approximately 730 mutants.