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.

Question

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?

in progress 0
Thiên Di 6 months 2021-08-12T14:52:21+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-08-12T14:54:05+00:00

    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 .

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )