# Collisions

 Q:     A 150 lb. man belly flops off a 20 foot diving board into a swimming pool.  Assuming the pool has 5 feet of water in it, and the man stops moving downward at 10 inches, what is the average force on the man by the water? A:     When the man reaches the water he will have obtained a speed of which satisfies mgh = .5 mv2, in this case h = 20 feet.  As he is slowed down by the water, by the average force , he will have and average speed of  = v / 2.  the time it takes him to stop from the speed v is therefore t = l / = 2l / v, where l = 10 inches is the depth until the man stops.  From F t = p = mv we obtain     or about 1.8 tons  or  16,014 N. Q:    I was told that the panels and bumpers on cars are purposefully built to crumple when they are in an accident.  Why would the car companies do this, is it just for the money? A:    Yes, our society decided that every effort should be directed toward saving lives (drivers and car passengers) but not vehicles.  That's why seatbelts and airbags have been developed and installed in all new vehicles.  Both seatbelts and airbags allow an increase in the stopping time for the drivers and passengers involved in collisions.  If the car body also crumples during the collision, this will add to an increase of the stopping time.  The more the stopping time is increased the more the collision force is decreased (collision force (F) multiplied by stopping time (t) is a constant equal to the mass of the vehicle (m) multiplied by the speed (v) before collision: F t = mv).   Use of seatbelts and airbags is currently mandated by law.  Loss of vehicles is tolerated.  Certainly it results in stimulating the car manufacturing industry.

## References

### Equations

Impulse-Linear Momentum Theorem
 pf - pi   =  p = J
Elastic Collision - One Dimension
Inelastic Collision - One Dimension m1 v  = (m1 + m2 ) V
m1 v1  +  m2 v2 = (m1 + m2 ) V
Motion of the Center of Mass
Nuclear Reactions and Decay Q = - m c2

# Mechanics List of Topics

 Measurements Newton's Laws Potential Energy and Conservation of Energy Rotation of Rigid Bodies Elasticity Vectors Forces and Fields Linear Momentum Angular Momentum Mechanical Oscillations Motion of Point-Mass Objects in One Dimension The Gravitational Field Collisions Torque Mechanical Waves Motion of Point-Mass Objects in Two and Three Dimensions Kinetic Energy and Work Circular Motion of Point-Mass Objects Equilibrium Sound

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