Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

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

We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.