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# M4 help!!! Rep awarded

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1. Despite having no problem with oblique impacts, I can't seem to solve the following question.I am unable to upload any working.However, I did the usual the perpendicular components remain unchanged,use the law of restution etc , but I did set the intial velocity of sphere A as usintheta and its velocity aftr impact as v1sin(90-theta).I then tried to eliminate variables and solve for 1 in terms of lambda and e , then substituted this into the inequality lambda>1

Heres the question:
A smooth sphere,of mass m and radius a, moves on a horizontal table with speed u and collides with a smooth stationary sphere B, of mass lambdam(lambda>1) and radius a.Before impact the direction of motion of A makes an acute angle theta with the lines of centres.As a result of the impact A is deflected through a right angle.The coefficent if restution between the spheres is e
Show that e>1/lambda
Any help would be greatly appreciated
2. (Original post by Sapereaude45)
Despite having no problem with oblique impacts, I can't seem to solve the following question.I am unable to upload any working.However, I did the usual the perpendicular components remain unchanged,use the law of restution etc , but I did set the intial velocity of sphere A as usintheta and its velocity aftr impact as v1sin(90-theta).I then tried to eliminate variables and solve for 1 in terms of lambda and e , then substituted this into the inequality lambda>1

Heres the question:
A smooth sphere,of mass m and radius a, moves on a horizontal table with speed u and collides with a smooth stationary sphere B, of mass lambdam(lambda>1) and radius a.Before impact the direction of motion of A makes an acute angle theta with the lines of centres.As a result of the impact A is deflected through a right angle.The coefficent if restution between the spheres is e
Show that e>1/lambda
Any help would be greatly appreciated
Let be the velocities of A,B respectively after impact.

In summary.

Conservation of Momentum:

Perpendicular to line of centres gives:

Parallel to line of centres gives:

Restitution equation gives:

Sub'ing previous into that last equation, dropping the u, gives:

Multiply up, rearrange giving.

Now:
Spoiler:
Show

PS: I won't accept you can't upload any working next time.
3. (Original post by ghostwalker)
Let be the velocities of A,B respectively after impact.

In summary.

Conservation of Momentum:

Perpendicular to line of centres gives:

Parallel to line of centres gives:

Restitution equation gives:

Sub'ing previous into that last equation, dropping the u, gives:

Multiply up, rearrange giving.

Now:
Spoiler:
Show

PS: I won't accept you can't upload any working next time.
Brilliant thanks for the help-one if the most helpful on the site.Ive confident I'll be needing your help again in the future
Sorry for the lack of working on my part, I did try uploading a picture howver it wouldn't show due to an error.For future reference how do I show my working in the same way you have?As I have seen others use the same format before.
4. (Original post by Sapereaude45)
For future reference how do I show my working in the same way you have?As I have seen others use the same format before.
It's call LaTex, and in one form or another is a widely used typesetting tool for mathematics, and documents in general. And used on this website by anyone serious about their maths (apart from one person I know of). It's well worth learning.

There is a maths starter guide in the "useful resources" widget, but I'll include the link just in case - see here
5. (Original post by ghostwalker)
It's call LaTex, and in one form or another is a widely used typesetting tool for mathematics, and documents in general. And used on this website by anyone serious about their maths (apart from one person I know of). It's well worth learning.

There is a maths starter guide in the "useful resources" widget, but I'll include the link just in case - see here
I'll be sure to use this in future.

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