further mechanics collision question. Watch

Mr. sypherPB
Badges: 4
Rep:
?
#1
Report Thread starter 3 weeks ago
#1
A smooth sphere S of mass m is moving
with speed (u) on a smooth horizontal
plane. The sphere S collides with another
smooth sphere T, of equal radius to S
but of mass km, moving in the same
straight line and in the same direction
with speed (Au), O < A < 0.5 .The coefficient
of restitution between S and Tis e.
Given that S is brought to rest by the impact,

a) Show that e= (1+kA)/k(1-A)
b)Deduce that k>1 .

Please help with part b. i have gotten close to it but i m not sure many thanks. p.s. instead of A its suppose to be lamda but thats effort.
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#2
Report 3 weeks ago
#2
(Original post by Mr. sypherPB)
A smooth sphere S of mass m is moving
with speed (u) on a smooth horizontal
plane. The sphere S collides with another
smooth sphere T, of equal radius to S
but of mass km, moving in the same
straight line and in the same direction
with speed (Au), O < A < 0.5 .The coefficient
of restitution between S and Tis e.
Given that S is brought to rest by the impact,

a) Show that e= (1+kA)/k(1-A)
b)Deduce that k>1 .

Please help with part b. i have gotten close to it but i m not sure many thanks. p.s. instead of A its suppose to be lamda but thats effort.
Use the condition e &lt; 1 and go from there. Rearrange the inequality for k and reach the conclusion.
0
reply
Mr. sypherPB
Badges: 4
Rep:
?
#3
Report Thread starter 3 weeks ago
#3
(Original post by RDKGames)
Use the condition e &lt; 1 and go from there. Rearrange the inequality for k and reach the conclusion.
i did this but i don't know wht the conclusion is or where i m suppose to deduce the fact that k>1. obv k is greater than 1 as mass cant be 0.
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#4
Report 3 weeks ago
#4
(Original post by Mr. sypherPB)
i did this but i don't know wht the conclusion is or where i m suppose to deduce the fact that k>1. obv k is greater than 1 as mass cant be 0.
What do you get after rearranging for k?
0
reply
Mr. sypherPB
Badges: 4
Rep:
?
#5
Report Thread starter 3 weeks ago
#5
e < 1
1+kA < k-kA
1/(1-2A) < k

< is the less than or equal to sign
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#6
Report 3 weeks ago
#6
(Original post by Mr. sypherPB)
obv k is greater than 1 as mass cant be 0.
Tbh I’m not sure where you are pulling this sentence from. It doesn’t make sense.

(Original post by Mr. sypherPB)
e < 1
1+kA < k-kA
1/(1-2A) < k
Looks good.

What is the lower bound of 1/(1-2A) ??

You are given that 0 < A < 0.5 so use it.

< is the less than or equal to sign
No, the inequality is strict.

You can’t have e=1 since this collision is not perfectly elastic.
1
reply
Mr. sypherPB
Badges: 4
Rep:
?
#7
Report Thread starter 3 weeks ago
#7
0 < (A)< 0.5
0<(1-2A)<1
now how do i deduce that k>1. from here i got to this bit.
btw i really appreciate your help it means a lot. Not a lot of further maths forum that i have seen in student room so really appreciate your help.
1
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#8
Report 3 weeks ago
#8
(Original post by Mr. sypherPB)
0 < (A)< 0.5
0<(1-2A)<1
now how do i deduce that k>1. from here i got to this bit.
btw i really appreciate your help it means a lot. Not a lot of further maths forum that i have seen in student room so really appreciate your help.
That result is two steps away.

I asked for the lower bound of 1/(1-2A) so can you figure it from what you have at the moment??
0
reply
Mr. sypherPB
Badges: 4
Rep:
?
#9
Report Thread starter 3 weeks ago
#9
(Original post by RDKGames)That result is two steps away.

I asked for the lower bound of 1/(1-2A) so can you figure it from what you have at the moment??

I dont know what you mean by lower bound?
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#10
Report 3 weeks ago
#10
(Original post by Mr. sypherPB)
I asked for the lower bound of 1/(1-2A) so can you figure it from what you have at the moment??

I dont know what you mean by lower bound?
Really...? The lower bound is a value which bounds the function from below. Can you figure out for what value the function \dfrac{1}{1-2A} is always greater??

If not, then perhaps I can rephrase my question to: "Find the range of f(A) = \dfrac{1}{1-2A} when the domain is 0 &lt; A &lt; 0.5" which hopefully you know how to do from your Pure aspect of A-Level Maths.
0
reply
Mr. sypherPB
Badges: 4
Rep:
?
#11
Report Thread starter 3 weeks ago
#11
(Original post by RDKGames)
Really...? The lower bound is a value which bounds the function from below. Can you figure out for what value the function \dfrac{1}{1-2A} is always greater??

If not, then perhaps I can rephrase my question to: "Find the range of f(A) = \dfrac{1}{1-2A} when the domain is 0 &lt; A &lt; 0.5" which hopefully you know how to do from your Pure aspect of A-Level Maths.
umm so would it not be f(a) greater or equal to 1
Last edited by Mr. sypherPB; 3 weeks ago
0
reply
RDKGames
  • Community Assistant
Badges: 20
Rep:
?
#12
Report 3 weeks ago
#12
(Original post by Mr. sypherPB)
umm so would it not be f(A)> 1
Exactly. So 1 is what you'd call the lower bound. (well it's not precisely that, but I'm not gonna go into it)

The point of all that is this:

k &gt; \dfrac{1}{1-2A} and now we know that  \dfrac{1}{1-2A} &gt; 1

So the conclusion immediately follows.
1
reply
Mr. sypherPB
Badges: 4
Rep:
?
#13
Report Thread starter 3 weeks ago
#13
(Original post by RDKGames)
Exactly. So 1 is what you'd call the lower bound. (well it's not precisely that, but I'm not gonna go into it)

The point of all that is this:

k &gt; \dfrac{1}{1-2A} and now we know that  \dfrac{1}{1-2A} &gt; 1

So the conclusion immediately follows.
oh wow! never thought to even bring in some of normal a level maths in this. You are very smart. thank you so much. the answers at the back jumped straight to the conclusion.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Birmingham
    Postgraduate Open Day Postgraduate
    Wed, 20 Mar '19
  • King's College London
    Postgraduate Taught Courses - Arts & Sciences - Strand Campus Postgraduate
    Wed, 20 Mar '19
  • University of East Anglia
    All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
    Wed, 20 Mar '19

Where do you need more help?

Which Uni should I go to? (50)
15.11%
How successful will I become if I take my planned subjects? (28)
8.46%
How happy will I be if I take this career? (63)
19.03%
How do I achieve my dream Uni placement? (51)
15.41%
What should I study to achieve my dream career? (39)
11.78%
How can I be the best version of myself? (100)
30.21%

Watched Threads

View All