Question

NASA conducted a study in which four people spent 22 hours each in a compartment attached to the end of a 28 foot arm the rotated with an angular speed of 10.0 rpm.

a) What centripetal acceleration did these volunteers experience? Express your answer in two significant figures.

b) What was their linear speed? Express your answer in two significant figures.

Answer 1

I realize for part a) that centripetal acceleration will be in m/s^2.
I tried \[2\pi \times28\times10\] and got 1759.29 and realized that was too big of a number. So I divided by 60 to get 29.3 but it's still the wrong answer. I also tried 2.9 wondering if there was something else, but it wasn't correct either.

For part b), I realize that is in m/s.
I tried \[10^{2}\div28\] and I got 3.6 which is also wrong.

Answer 2

Right track

want v^2/r or

a = r w^2 = (28 ft/ 3.28 ft /m) [(2 pi)(10/60)]^2

= 9.35 m/s^2, j un the acceleration of gravity, 9.8 m/s^2, but horizontal
= 9.4 ^2 two signif figs

velocity = r w = [(28 ft / 3.28 ft/m)] (2 pi )(10/60s) = 8.9 m/s

You should check my arithmetic, tho. Conversion to metric seems a problem.

Answer 3

That's seems to be right!
Thanks!