An elastic (head-on) collisionoccurs between two objects. Object #1 has a mass o

Question

An elastic (head-on) collisionoccurs between two objects. Object #1 has a mass of 23.9 kgand is initially moving to the right with a speed of 3.97m/s. Object #2 has a mass of 13.71 kg and is initially movingto the left with a speed of 9.35 m/s. Following thecollision, object #2 is moving to the right with a speed of 7.16m/s.

(A)Determine the magnitude and direction of the velocity of object #1after the collision.   

(B) Whatis the impulse suffered by each object during the collision? Make sure you show a separate solution for each object.

(C) Ifduring the collision the objects remain in contact for 492.8milliseconds, determine the average force exerted by each object onthe other (remember what Newton’s Third Law tells us aboutthis interaction).

Explanation / Answer

Given : .                  m1   = 23.9   kg   ; u1 = 3.97   m /s   ;  v1 = ? .                  m2   = 13.71 kg ; u2 =   -9.35 m /s   ; v2 = 7.16 m/s . (a)           Velocity of   " m1" after collision is : .                   v1  =   [ u1 ( m1 - m2 ) + 2 m2 u2 ] / (m1 + m2 ) .                         =   [ 3.97 ( 23.9 - 13.71 ) - (2 * 13.71 * 9.35 ) ]/ ( 23.9 + 13.71 ) .                         =   - 5.74 m /s . Hence velocity is : 5.74 m /s  ; Direction is : Left . (b) .                 Impulse of first object is : .                    J1 = m1 ( v1 - u1 )   =   23.9 ( - 5.74 - 3.97 ) = --------- kg- m /s .                   Impulseof second object is : .                    J2 = m2 ( v2 - u2 )  =    13.71 ( 7.16 + 9.35) = --------- kg - m /s . (c) .                    Average force on Object one is : .                     F1   =   J1 / 0.4928 s  =   --------- N .                    Average force on Object two is : .                     F1   =   J2 / 0.4928 s  =   --------- N . Solve the above. . Hope this helps u! .                    J2 = m2 ( v2 - u2 )  =    13.71 ( 7.16 + 9.35) = --------- kg - m /s . (c) .                    Average force on Object one is : .                     F1   =   J1 / 0.4928 s  =   --------- N .                    Average force on Object two is : .                     F1   =   J2 / 0.4928 s  =   --------- N . Solve the above. . Hope this helps u! .                     F1   =   J2 / 0.4928 s  =   --------- N . Solve the above. . Hope this helps u!

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