1 - Estimate the number of cars that drive into Manhattan on a typical work week
ID: 1549967 • Letter: 1
Question
1 - Estimate the number of cars that drive into Manhattan on a typical work weekday.
Estimate the number of cars that enter Manhattan on an average size bridge or tunnel in a typical day and then multiply by the number of bridges and tunnels.
2 - From the equation for impulse in which the force times the time for stopping is constant (SEE THE ATTACHED SLIDE ON IMPULSE) give and discuss at least three examples (that are not on the slide) where you want the stopping time to be long (so that the force is small) and three examples where you want the stopping time to be short (so that the force is large).
Explanation / Answer
2. Stopping time is long (so that the force is small) :
Example 1 : Air bags in cars are designed with impulse, or momentum change principles. When a driver gets into an accident their momentum carries them forward into the steering wheel. By putting an airbag in the car, a smaller force is exerted over a longer period of time to change the momentum of the driver to a stop.
Example 2 : If you have ever competed in an egg toss competition and done well, you were putting impulse into action. In order to reduce the amount of force on the egg so it doesn't break when you catch it, you move your hands in the same direction as the egg as you catch it. This action increases the amount of time you apply force on the egg and the amount of force acting on the egg to change its momentum is reduced so the egg will not break.
Example 3 : If you jump to the ground from any height, you bend your knees upon impact, extending the time of collision and lessening the impact force.
Stopping time is short (so that the force is large) :
Example 1 : Air bags in cars are designed with impulse, or momentum change principles. When a driver gets into an accident their momentum carries them forward into the steering wheel. Without the airbag in the car, a large force is exerted over a short time causing more damage to the driver.
Example 2 : When a hammer hits a nail, the change of momentum of the hammer occurs in a very short time during which the nail is driven into the wood. So the hammer has a very rapid loss of momentum caused by the force of the nail acting on the hammer. This force, which is equal & opposite to the force of the hammer acting on the nail, must be very large to cause the rapid change of momentum of the hammer. So the impulse which drives the nail into the wood is a large force acting for a short time.
Example 3 : Eggs are packed in soft, shock absorbing boxes so that when they suddenly stop or start moving, they do not get cracked. A moving egg with a certain amount of momentum requires a force to stop it moving. If the force acts for a short time (in hard box), then the force on the egg will be large and will crack it.
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