Open-Response Homework Problem 10.6 A dump truck is sitting at the top of a hill

Question

Open-Response Homework Problem 10.6 A dump truck is sitting at the top of a hill. and its parking brake disengages. It rolls down a hill and collides with an empty, stationary car. The car sticks to the grill of the truck and the two continue moving forward. The dump truck has mass (mt = 4000kg) and is travelling at 36 km/hr when it hits the car. The car has mass (mc = 1000kg). (a)[2 pt(s)___________] What is the speed of the truck/car immediately after the collision? (b)[2 Pt(s)_] What is the momentum of the truck/car in the frame of reference of a jogger approaching the collision at 2 (opposite the trucks initial velocity)? (c)[2 pt(s)_____] How fast, and in which direction, would the jogger have to run for the momentum of the system to appear to him to be zero? (d)[2 pt(s) ] What are the momenta of the car and truck prior to the collision in the center of mass frame?

Explanation / Answer

Mass of truck Mt =4000Kg

Velocity of truck Vt = 36km/hr=10m/s

Mass of car Mc =1000Kg

Let the combined velocity be V

Conservation of momentum

Initial momentum = final momentum

V (Mt+Mc) = Vt Mt + Vc Mc

V(5000)= 36X4000 +0X1000

V= 28.8 Km/hr =8m/s

V with respect to jogger = 28.8 +2 =30.8Km/hr

So momentum seen by him = 30.8X5000=154000kg-km/hr=90000kg m/s

Jogger has to run at 28.8Km/hr=8m/s away from the truck so it would appear that momentum is zero

Vf velocity of centre of mass frame =4000X36/5000=28.8 km/hr=8m/s

Momentum of truck in centre of mass frame=(36-28.8)X4000=28800kg-km/hr=8000kgm/s

Momentum of car in centre of mass frame= -28.8X1000=-28800kg-km/hr=8000kgm/s

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