Before a collision, a player of mass m moves with velocity v and therefore has momentum p = mv. If after the collision his velocity is zero, then his momentum after the collision is also zero. His momentum changes by an amount pafter - pbefore = Dp = -mv during the collision. If, for example a player of mass m = 120 kg moves with a speed of v = 5 m/s before the collision, then the magnitude of the momentum change is Dp = 600 kgm/s.
A momentum change requires a force. For the momentum to change by an amount Dp, a force F must act for a time Dt such that.Dp = FDt. A small force acting for a long time can change the momentum by the same amount as a large force acting for a short time.
Pads are designed to increase the collision time and therefore reduce the force acting on the player during a collision which changes his momentum by an amount Dp. If a pad doubles the collision time, it decreases the force by a factor of 2.
Experiment:
A cart rolls down an inclined track and collides with a wood block at the end of the track. The wood block is padded with another block made of metal, wood, or foam. An acceleration sensor measures the accelerationas a function of time during the collision and a computer displays the output of the acceleration sensor. The interaction force F is proportional to the acceleration, F = ma. The table below shows the output of the acceleration sensor under different collision conditions.
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| (a) The cart collides with an
aluminum block. The magnitude of the maximum measured acceleration
is ~22 m/s2. The collision lasts for ~0.09 s.
Aluminum block --> |
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| (a) The cart collides with a
wood block. The magnitude of the maximum measured
acceleration is ~21 m/s2. The collision lasts for ~0.1
s.
Wood block --> |
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| (a) The cart collides with a
high-density foam block. The magnitude of the maximum measured acceleration is
~17 m/s2. The collision lasts for ~0.12 s.
A block of high-density foam --> |
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| (a) The cart collides with
another foam block. This type of foam is used for packing
fragile materials for shipping. The magnitude of the maximum measured
acceleration is ~14 m/s2. The collision lasts for ~0.15
s. A block of packing foam --> |
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The experiment clearly shows that the foam padding increases the collision time and therefore reduces the interaction force and the resulting acceleration.
Increasing the time interval during which the momentum of an occupant of a car changes from some initial value to zero is also they way to reduce injuries in car accidents. Let us look at a particular accident. A 800 kg car driving at 60 miles/h or 26.8 m/s looses traction in a curve and hits the wall of a house. When it hits, it has slowed down to 40 miles/h or 17.9 m/s. It breaks through the wall and comes to rest in the living room, 2 m from the wall.
For the car's speed to decrease from 17.9 m/s to 0 over a distance of 2 m the magnitude of its average acceleration must be 80 m/s2 = 8.2 g with g = 9.8 m/s2. This will take 0.22 s. The momentum of a driver with m = 60 kg changes 60 kg * 17.9 m/s = 1074 Ns to zero in 0.22 s. The average force acting on the 60 kg driver over the 0.22 s time interval is F = ma = 4806 N if he wearing a seat belt and is securely strapped into his car seat. This is probably a survivable accident.
If the driver does not wear a seatbelt, he will initially keep on moving forward at 17.9 m/s. In 0.1 s he will have covered a distance of approximately 1.8 m. The distance the car has covered in 0.1 s is approximately 1.4 m. If he sits initially 40 cm from the steering wheel, then his body will slam into the wheel and his head will slam into the windshield after approximately 0.1 s. The car has slowed down, and the car's speed after 0.1 s is approximately 9.9 m/s, so the driver slams into the steering wheel with a relative speed of 17.9 m/s - 9.9 m/s = 8 m/s = 18 miles/h. If after an additional 0.02 s he travels with the speed of the car, v = 8.3 m/s, then his momentum has changed from p = 60 kg *17.9 m/s to p = 60 kg * 8.3 m/s in 0.02 s. This requires a force F = Dp/Dt = 28800 N and an acceleration of 49 g. Now the accident is probably no longer survivable. Wearing a seat belt increases the collision time for the driver and therefore reduces the force acting on him during the collision.
