Question

A spring scale being used to measure the weight of an object reads 17.1 N when it is used on earth. The spring stretches 4.40 cm under the load. The same object is weighed on the moon, where gravitational acceleration is
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 !!!

Answer 1

on 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.