1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Oblique collision of two bodies undergoing projectile motion

  1. Sep 22, 2015 #1

    Sujith Sizon

    User Avatar
    Gold Member

    Q) two identical smooth balls are projected from points O and A on the horizontal ground with the same speed of projection the angle of projection in each case is 30 The distance between O and A is 100m . The balls collide in mid air And return to their respective points of projection if coefficient of restitution is 0.7 find the speed of projection of either ball (m/s) correct to nearest integer ?

    Question figure
    CyYWJ.jpg

    My Attempt :

    Taking ##y## as the height from the ground to the point where the masses collide and ##\alpha## as the angle made by the final velocity vector with the horizontal .

    Using projectile equation ie : ##y=x\tan\theta\left[1-\frac{x}{R}\right]##

    For the case when it is projected and reaches a height ##y##

    ##y=\frac{50}{\sqrt{3}}\left[1-\frac{50\times 20}{\sqrt{3}u^{2}}\right]##

    For its return path considering a projectile motion from height ##y## with velocity vector making an angle ##\alpha## with the horizontal we get

    ##y=50\tan\alpha\left[1-\frac{50\times g}{v^{2}\sin2\alpha}\right]##

    The from coefficient of restitution formula we get

    ##e\rightarrow0.7=\frac{2v\cos\alpha}{2u\cos30}##

    SSySB.jpg

    Now assuming that my procedure so far is appropriate i need one more equation so that i can find ##u## and ##v##

    SOLVED (thanks to TSny)

    Conserving momentum along tangential component we will have
    ##2mu\sin30 = 2mv\sin\alpha##
     
    Last edited: Sep 22, 2015
  2. jcsd
  3. Sep 22, 2015 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Welcome to PF!

    What happens to the vertical component of velocity of each smooth ball during the collision?
     
  4. Sep 22, 2015 #3

    Sujith Sizon

    User Avatar
    Gold Member

    It changes but we cant conserve momentum along vertical because of gravitational force acting, right ?
     
  5. Sep 22, 2015 #4

    TSny

    User Avatar
    Homework Helper
    Gold Member

    You can forget about the effect of gravity during the very small time interval of the collision. The only important forces during the collision are the large contact forces between the two balls. (This is sometimes called the "impulse approximation" for collisions.)
     
  6. Sep 22, 2015 #5

    Sujith Sizon

    User Avatar
    Gold Member

    Which Impulse force ? the velocity changes only due to collision right ?
     
  7. Sep 22, 2015 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes. To a good approximation, the only force that causes a change in velocity of one of the balls during the collision is the impulsive contact force from the other ball.
     
  8. Sep 22, 2015 #7

    Sujith Sizon

    User Avatar
    Gold Member

    Okay so this impulse contact force will be along horizontal right (along the surface of contact) , then we will have to find its value( of Impulse contact force) also , how will we find that ?

    Im guessing J= Change in momentum along horizontal,
    ##J=mu\cos30 - mv\cos\alpha##
     
    Last edited: Sep 22, 2015
  9. Sep 22, 2015 #8

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes, for smooth surfaces the contact force will be horizontal (perpendicular to the surfaces of the balls at the point of contact). You do not need to determine the contact force; the coefficient of restitution gives you everything you need to know about the effect of the contact force on the horizontal components of velocity of the balls. You have already taken care of this in your equations. But, you have not yet used important information that you can deduce about the vertical components of velocity.
     
  10. Sep 22, 2015 #9

    Sujith Sizon

    User Avatar
    Gold Member

    So you are asking me to conserve momentum along vertical as
    ##2mu\sin30 = 2mv\sin\alpha##
    But then it will mean that there is no change in its vertical component of velocity , but there should be right , only the would it be able to reach back to its initial position right ?
     
  11. Sep 22, 2015 #10

    Sujith Sizon

    User Avatar
    Gold Member

     
  12. Sep 22, 2015 #11

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes, that's right. Without a vertical component of force, the balls do not change their vertical component of velocity during the collision.
    I'm not sure why you believe this.
     
  13. Sep 22, 2015 #12

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Your third figure looks good to me. :smile:
     
  14. Sep 22, 2015 #13

    Sujith Sizon

    User Avatar
    Gold Member

    oh okay because coefficient of restitution which is amount of change in speed only along impact axis so along tangential component it ought not to change and because of impulse approximations we are neglecting gravitational force , well then i will have my equation , thanks for your time .
     
  15. Sep 22, 2015 #14

    TSny

    User Avatar
    Homework Helper
    Gold Member

    OK, sounds good.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Oblique collision of two bodies undergoing projectile motion
Loading...