A 80-kg halfback on a football team runs head-on into a 120-kg opponent at an in

Question

A 80-kg halfback on a football team runs head-on into a 120-kg opponent at an instant when neither has his feet on the ground. The halfback is initially going west at 10 m/s , and his opponent is initially going east at 4.37 m/s. The collision is totally inelastic. Suppose that the positive x axis is directed to the west.

A) If the collision takes 0.257s, what are the x components of the accelerations of each player? (ahalfbackx, aopponentx)

B) How much kinetic energy is converted to incohenrent energy during the collision? (Kinitial - Kfinal)

Explanation / Answer

Force= change of momentum/ time = m*(dv)/t ; dv- velocity change

A) Since the collision is totally inelastic, both get sticked together

From conservation of linear momentum, m1v1+ m2v2= Mv ; M=m1+m2

80*10 +120*(-4.37)= 200*v ; v=1.378 ms-1

change of momentum(dp) ,,

for halfback ; dp= 80*(1.378-10) ; Fx= dp/t= -2683.9 N

for opponent : dp= 120*(1.378-(-4.37)) : Fx= dp/t=2683.9 N

B) Kinetic energy= m1v12/2 + m2v22/2

Kinitial= 5145.814 J

Kfinal= Mv2/2 = 189.888 J

Kinitial-Kfinal= 4955.926 J

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