Space travel is fraught with hazards, not the least of which are the many side e

Question

Space travel is fraught with hazards, not the least of which are the many side effects of prolonged weightlessness, including weakened muscles, bone loss, decreased coordination, and unsteady balance. If you are fortunate enough to go on a trip to Mars, which could take more than a year each way, you might be a bit "weak in the knees" by the time you arrive. This could lead to problems when you try to take your first "small step" on the surface. To counteract these effects, NASA is looking into ways to provide astronauts with "portable gravity" on long space flights. One method under consideration is the human- powered centrifuge, which not only subjects the astronauts to artificial gravity, but also gives them aerobic exercise. The device is basically a rotating, circular platform on which two astronauts lie supine along a diameter, head-to-head at the center, with their feet at opposite rims, as shown in the accompanying photo. The radius of the platform in this test model is 6.25 ft. As one astronaut pedals to rotate the platform, the astronaut facing the other direction can exercise in the artificial gravity. Alternatively, a third astronaut on a stationary bicycle can provide the rotation for the other two. The figure shows the centripetal acceleration (in gs) produced by a rotating platform at four different radii. Notice that the acceleration increases as the square of the angular speed. Also indicated in the figure(Figure 1) are acceleration levels corresponding to 1, 3, and 5 gs. It is thought that enhanced gravitational effects may be desirable since the astronauts will experience the artificial gravity for only relatively brief periods of time during the flight.

1) Rank the four curves shown in the figure in order of decreasing radius. Rank curves from largest to smallest. To rank items as equivalent, overlap them.

https://session.masteringphysics.com/problemAsset/1123855/3/Walker4e.ch10.Pr112.jpg

2) What angular speed (in rpm) must the platform in this test model have to give a centripetal acceleration of 5.00 gs at the rim?

A) w=48.5 rpm

B) w=36.2 rpm

C) w= 26.1 rpm

D) w=5.07 rpm

3) The platform in the test model have to give a centripetal acceleration of 5.00 gs at the rim. Which of the curves shown in the figure corresponds to the test model?

4) Estimate the radius corresponding to curve 4.

A) 0.03 ft

B) 0.3 ft

C) 3 ft

D) 6 ft

Explanation / Answer

1)for same angular speed higher the acceleration higher the radius

so 1>2>3>4

2) a = w^2*R

so w = sqrt(a/R)

for a = 5g

w = sqrt(5*32.2/6.25)=5.08rad/s =5.08/(2pi)*60 rpm=48.47rpm

c) according to answer of question 2 we need acceleration 5g at w =48.47rpm

so curve 3 satisfies the condition.

d)the radius should be near 6.25 feet as discussed above.

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