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December 22, 2014

December 22, 2014

Posted by **MIKE** on Friday, January 25, 2013 at 4:30pm.

1 /6 g.

Find the reading of the spring scale on the moon.

Find the period for vertical oscillations of the spring on the moon.

This question has been really bugging me! Can someone please provide the work and answer so I can work backwards to learn this!? THANK YOU VERY MUCH FOR YOUR TIME !!!

- physicss -
**Damon**, Friday, January 25, 2013 at 4:51pmon earth we are given that

W = m g = 9.81 m

= 17.1 N

so m = 17.1/9.81 = 1.74 kg

F = m a

in static case a = 0 so

m g - k x = 0

x = m g/k

.044 = 17.1/k

so

k = 389 Newtons/meter

on moon

Gmoon = g/6 = 9.81/6 = 1.64 m/s^2

mg moon = (1/6) mg earth = 17.1/6

stretch moon = stretch earth/6 = 4.4/6 = .733 cm

for period, we have m and g moon and k

m = 1.74 kg

g = 1.64 m/s^2

k = 389 N/m

for spring and mass

if

x = sin 2 pi t/T

v = (2 pi/T) cos 2 pi t/T

a = - (2 pi/T)^2 sin 2 pi t/T = -(2 pi/T)^2 x

F = - k x = m a

-k x = -m (2 pi/T)^2 x

so

(2 pi/T)^2 = k/m

2 pi/T = sqrt (k/m)

T = 2 pi sqrt (m/k)

so

T on moon = 2 pi sqrt(1.74/389)

By the way, k and m are the same on earth and moon. The period of the spring/mass system has nothing to do with g and is the same on earth and moon. That would NOT be true for a pendulum.

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