RE: Physics Question

From: Colin Hales (
Date: Fri Feb 22 2002 - 18:18:57 MST

Sir Isaac will do here. Assume that the system brings the rear car to rest
at a constant deceleration and that no energy is lost in crumpling the lead
F*deltaT = M * deltaV (a kludged/averaged F = ma). Also assuming the
incoming detritus was brought to rest in 1 car length (say 5meters).

Converting oldeworlderubbishunits to real units that the rest of the world
:-) poke poke...
stationary object = 1364 kg
stationary person = 100 kg
moving object = 1818kg @ 56km/hr (= 15.5m/sec)
Time to halt the incoming vehicle = 5/15.5 = .323sec
Average force applied by the incoming car to the combined stationary mass =
The average work done by this on the stationary mass is 70254 * 5 = 351270
This was imparted in .323 second, meaning an power of 1.089MW applied for
.323 seconds.
The person would receive 100/1464 of this = 24028 joules (~74kW!). Hug 74
single bar radiator elements for .323 secs and see how you look afterwards.

Assuming that the person's contact period with the car is somewhere under
.323 seconds then the energy imparted would be less. When the DeltaV of
objects becomes equal you would disconnect from the lead vehicle and leave
the system. The overall conservation of momentum would mean this occurs at
0.179 secs (roughly when the speeds are equal) when the crumpling car/human
combo has travelled 0.5*(70254/1464)*(.179)^2 (constant acceleration from
rest) = 0.768m (right at the beginning of the 5m crash distance)

Energy Imparted in this time approx 70254*0.768 = 53961 joules or an average
power of 30kW and assuming this is converted all to kinetic enrgy E =
0.5mv^2 the person would be travelling at 118km/hr = 75mph after an
acceleration of 183m/sec^2 for 0.179 seconds or 18.7G! This energy of 70254
joules would be converted to heat as the person came to rest, being smashed
up in the process. During this period your cortex would be sloshing around
inside your skull like a sock full of custard.

Ouch. If I'm 50% wrong on this it's still OUCH. Thank you Sir Isaac.


> -----Original Message-----
> From:
> []On Behalf Of Jerome
> Sent: Friday, 22 February 2002 5:56 AM
> To:
> Subject: Physics Question
> Suppose I am stepping out of the seat of a high, stopped
> vehicle (a 3000
> pound mini-van), which is stopped on ice.
> Suppose, further, that I have placed one foot outside the van, on the
> ground, and have begun standing on that leg, when:
> The van I am climbing out of is struck from behind by a 4000
> pound car
> traveling at, say 35 miles per hour. The car striking the
> van comes to
> rest, imparting it's energy to the van, which quickly comes
> up to a high
> (~35 mph?) speed. Since my torso is still in the doorway,
> the rear leading
> edge of the door frame strikes me in the back at whatever
> speed the car is
> traveling, accelerating my 220 pound body like the blow from
> a giant hammer
> (the impact zone between the door frame and my back being
> about 1 inch by 8
> inches). Luckily for me, the impact was felt about 2 inches
> to the right
> of my spine, so I was only badly hurt, but not paralyzed.
> My physics question is: how does one characterize the energy
> transfer that
> occurred here? I'm especially interested in being able to
> say how much
> energy was in the blow that I received.
> Thanks!
> - Jerome

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