Two manned satellites approaching one another

[Mariesa Yeoman]

Homework Statement

I have tried this several times, though I am going wrong someplace along the way. I have tried using these equations below but I cannot seem to get anywhere with it. I left the attempts below so that you may see what I have done, and maybe someone can tell me what I am doing wrong ?

Two manned satellites approaching one another at a relative speed of 0.100 m/s intend to dock. The first has a mass of 2.00 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite.
(a) Calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.
(b) What is the loss of kinetic energy in this inelastic collision?
(c) Repeat both parts, in the frame of reference in which the second satellite was originally at rest.
final velocity
(d) loss of kinetic energy = ?

Homework Equations

p1 + p2 = p′1 + p′2
m1 v1 + m2 v2 = m1 v′1 + m2 v′2 .
To solve for v' is m1 * v1 = m1+m2 * v'
v1= initial velocity
v' = final velocity
m1 = 2000kg
m2 = 7500 kg

The Attempt at a Solution

Attempt 1:
With the equation m2*v^2+m1+0 = (m1 +m2) * v ----> 7500kg * 0.100m/s + 0 = (9500kg) * v'
Attempt 2:
m1 * v1 = (m1 +m2)* v' rearranged to solve for v' ---> v' = m1 / m1+m2 * v1 =
plugging in my values led me to ---> v' = 2000kg / 2000kg + 7500kg *(v1) =0.02105263158 or 0.0210
I will leave the list here, I have many other attempts, since they are wrong I will spare you those details! Thank you for your help.

 

[kuruman]

It is difficult to figure out what you are doing if you do not use parentheses to group quantities together.
For example v' = m1 / m1+m2 * v1 interpreted as stated would be $$v'=\frac{m_1}{m_1}+m_2v_1.$$ I am sure that's not what you meant to write. So please use parentheses or, even better, learn to use LaTeX (click on the link next to the question mark lower left above "Forums" link)

 

[Mariesa Yeoman]

No it is not what I meant. also none of what you have written is what I intended.
Let me be perfectly clear:
v' = m1 / (m1 + m2) * v1 This is the equation I attempted to use, NONE of these equations are giving me the correct answer. The chapter is on elastic and inelastic equations, and I have listed all the information (using the template given by the site). This is the first time someone has had any issue understanding the question. I am sorry you didn't get it. I feel your message was borderline rude? I am just on here trying to learn this stuff like many others. We are not all savvy to the level that the advisors are and sometimes do not have perfectly written questions, because we haven't learned. Hopefully, someone out there WILL be able to help me and if you cannot that's okay! It's not a problem, just leave it for someone else to answer?
Have a wonderful rest of your day,
M

 

[kuruman]

No it is not what I meant. also none of what you have written is what I intended.
Let me be perfectly clear:
v' = m1 / (m1 + m2) * v1 This is the equation I attempted to use, NONE of these equations are giving me the correct answer. The chapter is on elastic and inelastic equations, and I have listed all the information (using the template given by the site). This is the first time someone has had any issue understanding the question. I am sorry you didn't get it. I feel your message was borderline rude? I am just on here trying to learn this stuff like many others. We are not all savvy to the level that the advisors are and sometimes do not have perfectly written questions, because we haven't learned. Hopefully, someone out there WILL be able to help me and if you cannot that's okay! It's not a problem, just leave it for someone else to answer?
Have a wonderful rest of your day,
M

My intention is to help you, not to be rude. You also have to understand that all of us here spend time to provide help freely because we believe in what we are doing. Before helping you however, I need to understand what's on your mind and what you did. Therefore it is not rude to ask for clarifications or to explain to you why what you posted is not clear. You are not expected to be savvy, just be clear. So let's try again, and if you are not satisfied with my help, you can always fire me.

You say you used the equation v' = m1 / (m1 + m2) * v1 which would be better written as v1=m1*v1/(m1+m2). Then it is clear that v1 multiplies the numerator in the fraction. That's fine. That's the correct equation to use but how did you use it and for what part? You do not mention that anywhere so I have to guess that it is for part (a), but if it's for part (a) what is v1? The problem specifies that the first satellite has mass m1 = 2000 kg. So you write the equation m1 v1 + 0 =(m1+m2)v'. Saying so assumes that v2 = 0. Part (a) asks you to find the final velocity in the frame of reference in which satellite 1 was initially at rest. If it's initially at rest and its mass is 2000 kg, then its initial momentum should be 2000*0 = 0, no? It's satellite 2 that's moving in that frame.

You also say "This is the equation I attempted to use, NONE of these equations are giving me the correct answer." What other equations did you use? You do not say, so how can anyone point out to you whether they are correct and/or whether you have used them correctly? I hope you understand now the importance of being as clear as you can to help us help you. We are not mind readers. As for me, like I said, you can always fire me.

 

[Celso]

I can't see why your second attempt is wrong, except for the fact that the velocity should be negative, since the positive direction is directed from the second satellite towards the first, and our frame of reference is that in which the first satellite is at rest.
The ratio of kinetic energy between then and before the colision is given by $\frac{KE_{f}}{KE_{i}} =\frac{ \frac{1}{2}(m_{1}+m_{2})[\frac{m_{1}}{m_{1}+m_{2}}v_{1}]^2}{\frac{1}{2}m_{1}v_{1}^2}=\frac{m_{1}}{m_{1}+m_{2}}$