Answer:
The displacement of the same mass on the same spring on the Moon is 0.05 m.
Explanation:
Given;
mass suspended from one end of the spring, m = 0.500 kg
displacement on the spring on Earth, x = 0.3 m
Apply Newton's second law of motion;
F = ma = mg
where;
m is mass on the spring
g is acceleration due to gravity
Also, apply Hook's law;
F = Kx
where;
K is force constant
x is extension or diplacement of the spring
Combine the two equations from the two laws;
mg = kx
when the spring in on Earth;
0.5 x 9.8 = 0.3k
4.9 = 0.3k
k = 4.9 / 0.3
k = 16.333 N/m
when the spring is on moon;
mg = kx
mass is the same = 0.5 kg
acceleration due to gravity on moon = ¹/₆ that of Earth = ¹/₆ x 9.8 m/s²
0.5 (¹/₆ x 9.8) = 16.333 x
0.8167 = 16.333 x
x = 0.8167 / 16.333
x = 0.05 m
Therefore, the displacement of the same mass on the same spring on the Moon is 0.05 m.
