Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Astronaut X of mass 50kg floats next to Astronaut Y of mass 100kg while in space, as shown in the figure. The positive direction is shown. Astronaut X applies a force against Astronaut Y such that the kinetic energy of each astronaut as a function of time is shown in the graph. What is the change in momentum of the two-astronaut system and the change in momentum of each astronaut from immediately before the force was applied to immediately after the force was applied?

Astronaut X Of Mass 50kg Floats Next To Astronaut Y Of Mass 100kg While In Space As Shown In The Figure The Positive Direction Is Shown Astronaut X Applies A Fo class=

Sagot :

Answer:

C

Explanation:

The change in momentum of x has to be the opposite of the change in momentum of Y because the momentum is just transferred from one to another. But I'm still trying to figure it out how to calculate.

The change in momentum of the system is zero, change in momentum of astronaut X is -100 Kg·m/s and change in momentum of astronaut Y is 100 Kg·m/s.

To find the correct statement among all other options, we need to know more about the conservation of linear momentum.

What is linear momentum?

Linear momentum of an object is the product of its mass and velocity of it.

What is conservation of linear momentum?

In the absence of net external force, the linear momentum of a system remains constant.  

How does the conservation of linear momentum apply to find the linear momentum of the two-astronaut system?

  • The two astronaut system includes the both astronauts X and Y. When the astronaut X was applying force on astronaut Y, there is no external force on the system.
  • Here we can not take the force applied by astronaut X as external force because the astronaut X is a part of the system.
  • Since, there is no external force acting on the system, so the linear momentum of the system both before and after the force applied by astronaut X is zero.
  • Therefore, the change in momentum of the two astronaut system is 0.

How do we find linear momentum from kinetic energy?

  • Kinetic energy = 1/2 × mass × velocity².
  • So, 2 × mass × kinetic energy = ( mass × velocity )² = momentum²
  • Or momentum = [tex]\sqrt{2 × mass × kinetic energy }[/tex]

What is the change in linear momentum of astronaut X?

  • Before the force applied by astronaut X, astronaut X was  constant with respect to astronaut Y. So its linear momentum is 0.
  • After the application of force, the astronaut X has kinetic energy  100 J. So its momentum is [tex]\sqrt{2 × 50 × 100 }[/tex] or 100 Kg·m/s.
  • So, change in linear momentum of astronaut X is -100 Kg·m/s. Negative sign due to the motion of astronaut X along the opposite direction that of astronaut Y.

What is the change in linear momentum of astronaut Y?

  • Similarly, astronaut Y was at constant before the application of force. So, its linear momentum is 0.
  • After the force applied by astronaut X, the astronaut Y has kinetic energy 50J. So, its linear momentum is  [tex]\sqrt{2 × 100 × 50}[/tex] or 100 Kg·m/s.
  • So, change in linear momentum of astronaut Y is 100 Kg·m/s.

Thus, we can conclude that option (c) is correct.

Learn more about linear momentum here:

https://brainly.com/question/7538238

#SPJ2

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.