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    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
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    (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 v_1,v_2 be the velocities of A,B respectively after impact.

    In summary.

    Conservation of Momentum:

    Perpendicular to line of centres gives:

    v_1 = u\tan\theta

    Parallel to line of centres gives:

    \dfrac{u}{\cos\theta}=\lambda v_2

    Restitution equation gives:

    v_2+v_1\sin\theta=eu\cos\theta

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

    \dfrac{1}{\lambda\cos\theta}+   \dfrac{\sin^2\theta}{\cos\theta}  = e\cos\theta

    Multiply up, rearrange giving.

    \dfrac{1}{\lambda}=e\cos^2\theta - \sin^2\theta

    Now:
    Spoiler:
    Show

    e\cos^2\theta - \sin^2\theta\leq e\cos^2\theta - e\sin^2\theta

    =e\cos 2\theta

    \leq e

    PS: I won't accept you can't upload any working next time.
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    (Original post by ghostwalker)
    Let v_1,v_2 be the velocities of A,B respectively after impact.

    In summary.

    Conservation of Momentum:

    Perpendicular to line of centres gives:

    v_1 = u\tan\theta

    Parallel to line of centres gives:

    \dfrac{u}{\cos\theta}=\lambda v_2

    Restitution equation gives:

    v_2+v_1\sin\theta=eu\cos\theta

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

    \dfrac{1}{\lambda\cos\theta}+   \dfrac{\sin^2\theta}{\cos\theta}  = e\cos\theta

    Multiply up, rearrange giving.

    \dfrac{1}{\lambda}=e\cos^2\theta - \sin^2\theta

    Now:
    Spoiler:
    Show

    e\cos^2\theta - \sin^2\theta\leq e\cos^2\theta - e\sin^2\theta

    =e\cos 2\theta

    \leq e
    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.
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    (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
    • Thread Starter
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    (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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