An astronaut has two springs: Spring A and Spring B. She also has two metal blocks that she can hang from the springs: Block X and Block Y. At her lab in Orlando, Florida, she hangs Block X from Spring A and sees that Spring A stretches 2.04 cm as a result. Later, at a research station on the moon, she hangs block X from spring A and finds that Spring A only stretches 0.34 cm. Then (still on the moon) she hangs block Y from Spring A and sees that spring A stretches 0.54 cm.
1) How much would spring A stretch if Block Y were hanging from it back in the lab in Orlando?
2) On the moon, when Block Y is hanging from Spring B, Spring B stretches a distance of 1.3 cm. In Orlando, how much would Spring B stretch when Block X is hanging from it?
Answer:
Explanation:
Let the spring constant of spring A and B be k₁ and k₂ . Mass of box X and Y be m₁ and m₂ .
Force created in spring which is stretched by d is kd where k is spring constant .
At her lab in Orlando, Florida,
k₁ x .0204 m = m₁ g where g is acceleration due to earth’s gravity
k₁ = 49 m₁ g
At a research station on the moon
k₁ x .34 x 10⁻² m = m₁ g₁ where g₁ is acceleration due to gravity at moon
k₁ = 294 .11 m₁ g₁
49 m₁ g = 294 .11 m₁ g₁
g = 6.0022 g₁
At a research station on the moon
k₁ x .54 x 10⁻² m = m₂ g₁
k₁ = 185.18 m₂ g₁
294 .11 m₁ g₁ = 185.18 m₂ g₁
1.588 m₁ = m₂
1 )
At her lab in Orlando, Florida,
k₁ x d = m₂ g , where d is the new stretch that is to be calculated .
185.18 m₂ g₁ d =m₂ g
185.18 d g₁ = g
185.18 d g₁ = 6.0022 g₁
d = .03241 m
= 3.24 cm .
2 )
At a research station on the moon
when Block Y is hanging from Spring B
k₂ x .013 = m₂ g₁
k₂ = 76.92 m₂ g₁
At her lab in Orlando, Florida,
Spring B stretch when Block X is hanging from it
k₂ d₁ = m₁ g
76.92 m₂ g₁ d₁ = m₁ g
76.92 m₂ g₁ d₁ = m₁ 6.0022 g₁
76.92 m₂ d₁ = m₁ 6.0022
12.815 x 1.588 m₁ x d₁ = m₁
d₁ = .049 m
= 4.9 cm .