A spring on Earth has a 0.500 kg mass suspended from one end and the mass is displaced by 0.3 m. What will the displacement of the same mass on the same spring be on the Moon, where the acceleration due to gravity is one sixth that of Earth
Question
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.