1 Two lumberjacks, Sven and Buttercup like nothing better than to cover themselv

Question

1 Two lumberjacks, Sven and Buttercup like nothing better than to cover themselves in Velcro and run at top speed toward one another, colliding in the forest. If Sven has a mass of 80 0 ka and runs at a speed of 6.0 m/s while Buttercup has a mass of 100.0 kg and also runs at a speed of 6.0 m/s before the collision, a) Calculate the velocity of the two lumberjacks after they collide and stick together b) Determine whether energy was conserved in this collision. If it was not, determine what percentage of the original energy remains after the collision.

Explanation / Answer

a)

Let

m1 = 80 kg

m2 = 100 kg

before the collsion,

u1 = 6 m/s

u2 = -6 m/s

Let V is the speed with which they move after the collision

Apply, m1*u1 + m2*u2 = (m1+m2)*V

80*6 + 100*(-6) = (80 + 100)*v

V = (80*6 + 100*(-6))/(80 + 100)

= -0.67 m/s (in the direction of 100 kg Buttercup)

b) It is a completely inelastic collision. so, energy is not conserved.

KI = 0.5*m1*u1^2 + 0.5*m2*u2^2

= 0.5*80*6^2 + 0.5*100*6^2

= 3240 J

KF = 0.5*(m1+m2)*V^2

= 0.5*(80+100)*0.67^2

= 40 J

KF/KI = 40/3240

= 0.0123

KF = 1.23 % of KI

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