Modern cars are designed with crumple zones to make them safer in case of head-on andrear-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’soccupants. The collapse of the crumple zone has the effect of increasing the time over which thecollision occurs. A 2000 kg car traveling at 30 m/s collides head on with a solid concrete wall. If the carhas no crumple zones, the collision takes 0.23 s, while if the car does include crumple zones in itsdesign the collision takes 1.1 s. a) By what amount is the average force of the concrete wall pushingagainst the car reduced during the collision by the inclusion of crumple zones? b) From what heightwould the car have to be dropped in order to have the same kinetic energy at the instant it impactedthe ground?2. Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide inelastically. Thefirst asteroid, which is initially traveling towards the second asteroid at a speed of 40 m/s, is deflectedby the collision at an angle of 30deg relative to its original trajectory, while the second asteroid isdeflected by an angle of 45deg relative to the original trajectory of the first asteroid. a) What are the finalspeeds of the first and second asteroids? b) What fraction of the first asteroid’s original kinetic energywas lost as a result of the collision (i.e. does not appear as kinetic energy of the first or second asteroidafter the collision)? 30o 45o
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?
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 30deg relative to its original trajectory, while the second asteroid is
deflected by an angle of 45deg 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)?
30o
45o
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