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PHYS_2014_Homework_7_soln

PHYS_2014_Homework_7_soln - PHYS2014 Benton Fall 2010 OSU...

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PHYS2014 Fall 2010 Benton OSU Physics Dept. 7-1 Physics 2014: General Physics I Solutions to Homework Assignment 7 Due: Friday, 29 October 2010 at the beginning of your Recitation session. 1. Modern cars are designed with crumple zones to make them safer in case of head-on and rear- end collisions. During a head-on collision a crumple zone in the front section of a car collapses, absorbing much of the energy of the collision so that this energy is not transferred to the vehicle’s occupants. The collapse of the crumple zone has the effect of increasing the time over which the collision occurs. A 2000 kg car traveling at 30 m/s collides head on with a solid concrete wall. If the car has no crumple zones, the collision takes 0.23 s, while if the car does include crumple zones in its design the collision takes 1.1 s. a) By what amount is the average force of the concrete wall pushing against the car reduced during the collision by the inclusion of crumple zones? b) From what height would the car have to be dropped in order to have the same kinetic energy at the instant it impacted the ground? Solution: a) Recall the impulse momentum theorem from Lecture 15, slide 6: ( ) c c t t avg t J p F t dt F t = Δ = = Δ We can calculate the car’s impulse and then find the average force both with and without crumple zones. avg f i f i f i avg p F t p p p mv mv mv mv F t Δ = Δ Δ = = = Δ Note that v f = 0, so: i avg mv F t = Δ Car with crumple zones: m 2000kg 30 s 54545J 1.1s avg F = = Car without crumple zones: m 2000kg 30 s 260869J 0.23s 260869J 54545J 0.79 or 79% 260869J avg n cz n n F F F F F F = = Δ = = = The inclusion of crumple zones reduce the average force of the impact by 79%. That could be the difference between surviving a crash relatively unscathed versus major injury or death.
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PHYS2014 Fall 2010 Benton OSU Physics Dept. 7-2 b) We need to find the height for which the gravitational potential energy would be converted to the same value of kinetic energy as that when the car slams into the concrete wall. m 1 2 gh m = ( ) 2 2 2 2 30m s 45.9m 151 ft 2 2 9.8m s v v h g = = = = 2. Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide inelastically . The first asteroid, which is initially traveling towards the second asteroid at a speed of 40 m/s, is deflected by the collision at an angle of 30 ° relative to its original trajectory, while the second asteroid is deflected by an angle of 45 ° relative to the original trajectory of the first asteroid. a) What are the final speeds of the first and second asteroids? b) What fraction of the first asteroid’s original kinetic energy was lost as a result of the collision (i.e. does not appear as kinetic energy of the first or second asteroid after the collision)? Solution: Because this is an inelastic collision, we know that kinetic energy will not be conserved. Since angles are involved, we see that this must be a 2-D situation.
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