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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?

Sagot :

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 .

lhmarianateixeira

In this exercise we have to use the knowledge of springs to calculate the distance from it, that way:

A)d=3.24 cm

B)d=4.9 cm

So, before starting the calculations, we have to organize the values ​​and put everything in function of a single unknown such as:

[tex]k_1 * 0.34 * 10^{-2} m = m_1 g_1\\ k_1 = 294 .11 m_1 g_1\\49 m_1 g = 294 .11 m_1 g_1\\g = 6.0022 g_1\\k_1 *0 .54 * 10^{-2} m = m_2 g_1\\k_1 = 185.18 m_2 g_1\\294 .11 m_1 g_1 = 185.18 m_2 g_1\\1.588 m_1 = m_2[/tex]

A) By calculating the distance we find that:

[tex]k1_1 * d = m_2 g\\185.18 m_2 g_1 d =m_2 g\\185.18 d g_1 = g\\185.18 d g_1 = 6.0022 g_1\\d = 0.03241 m= 3.24 cm[/tex]

B) So now calculating the distance from the lab to the moon, so:

[tex]k_2* 0.013 = m_2 g_1\\k_2 = 76.92 m_2 g_1\\k_2 d_1 = m_1 g\\76.92 m_2 g_1 d_1 = m_1 g\\76.92 m_2 g_1 d_1 = m_16.0022 g_1\\76.92 m_2 d_1 = m_1 6.0022\\12.815 * 1.588 m_1 * d_1= m_1\\d_1 = 0.049 m = 4.9 cm[/tex]

See more about springs at brainly.com/question/4433395

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