MasteringPhysics: Chapters 108 11-Google Chrome https://session.masteringphysics
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MasteringPhysics: Chapters 108 11-Google Chrome https://session.masteringphysics.com/myct/itemView?assignmentProblemID-56099998 hys201-2016-Spring Chapters 10811 Problem 10.55 Problem 10.55 Part A A 41.0 g ball is fired horizontally with initial speed to toward a 110 g ball that is hanging motionless from a 1.00 m -long string The balls undergo a head-on, perfectly elastic collision, after which the 110 g ball swings out to a maximum angle 8mA What was vo? Express your answer with the appropriate units. 52.0° . ? Value Units Submit My Answers Give UpExplanation / Answer
KE of 110 g ball just after the collision = its gain of PE
=> (1/2) mv^2 = m * (9.81) * (1) (1 - cos52°)
=> 0.5*v^2=9.81*(1-cos(52)) =2.74 m/s
For elastic collision, both the linear momentum and KE are conserved.
If V = velocity of 41 g ball just after the collision,
By the law of conservation of linear momentum,
(0.041)V0 + 0 = (0.041) V + (0.11) * (2.74)
=> V0 - V = 7.35-------------( 1 )
By the law of conservation of KE,
(1/2) (0.041) V0^2 + 0 = (1/2) (0.041)V^2 + (1/2) (0.11) (2.74)^2
0.0205*(V0^2 - V^2 )=0.4129
=> V0^2 - V^2 = 20.14--------------- ( 2 )
Dividing eqn. ( 2 ) by ( 1 ),
V0 + V = 2.74----------( 3 )
Solving ( 1 ) and ( 3 ) for V0,
V0 = 5.045m/s.