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Car Contents Collision
Name: Leo M.
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: 9/12/2004
Question:
This is a question about objects in a car accident. Say
a car travelling at 60kmph hits a brick wall. Inside the car is a tissue
box that weighs say 1 kilo. The tissue box keeps moving from the rear
window of the car and hits the driver in the head. What would be the
weight of the tissue box and how would I calculate other items?
Replies:
Leo -
Weight in the metric system is measured in Newtons. It is a force. The
number of Newtons is equal to the mass in kg times the change in speed in
m/sec2 (acceleration or deceleration).... F = ma. A Newton is equal to a kg
m/sec2.
To answer your question you would have to make an assumption of the time
required to stop the box. If it is assumed that it takes one second...
force = 1kg X 60,000m/sec2 = 60,000 Newtons.
You might find the subjects of energy, impulse and pressure to be useful in
your line of thinking. These might help to explore the injury caused by
your object.
Larry Krengel
The weight of the tissue box will not change, of course, but its effect
on the driver's head will depend on the rate at which its speed is
reduced by the collision. If it happens quickly, there will be a large
force for a short period of time; if it happens slowly, there will be
a small force for a relatively long period of time.
Tim Mooney
Leo M.,
You would need to use momentum and energy. The tissue box keeps moving at
the original speed. The driver has come to a halt. Work done by the head
on the box equals the change of kinetic energy. Average force times the
distance the box travels while in contact equals the work. Average force
multiplied by the time of contact equals the change of momentum. The box
probably comes to a rest during the collision with the head.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
I "weight" of the tissue box, or the force which it hits the drivers
head would be determined by the time it takes to stop the car.
The car is moving at 60Km/hour or 60km/(3600sec)=1km/60sec or 16.67
m/sec.
If the car stops (decelerates) in 1 second then the force is 16.67
Newtons, commensurately for 0.5 seconds the force on the tissue box would
be 2(16.07) Newtons, etc. This would really hurt, it would be like
dropping a 1kilo weight onto your toe.
The acceleration due to gravity is 9.8 m./s/s and the force of the
falling kilo would be 9.8 newtons. I put that in, so that you have a
frame of reference.
Calculate other forces? Scale to the mass of the tissue box.
Dr. Harold Myron
Dear Leo,
Since, as Newton told us in his 2nd law, F = ma, the total net force exerted
on (or by) an object of total mass m is given by the product of the mass of
the object and the acceleration of its center of mass.
You could exert the force on the object with your hand and then, by Newton's
3rd law (for every action there is an equal and opposite reaction), the
object will exert a force on your hand equal in magnitude but opposite in
direction to the force your hand is exerting on the object.
So the velocity does not directly give you the force; you must know the
acceleration. If the tissue box were to stop instantaneously, the force
would be infinite. This is clearly not the case. If the box is travelling
at 60 mph (about 27 m/s) and stops with constant acceleration in
10 cm = 0.1 m (about 4 inches), its acceleration is 3645 m/s^2 (using
v^2=2ax).
So the force exerted by this 1 kg box of tissues would be
F = ma = 1 kg * 3645 m/s^2 = 3645 N, which is about 820 lb.
Pretty lethal! However, if he is not wearing seat belts or protected by an
air bag, the driver is probably out through the windshield and smashing into
the brick wall and wouldn't notice the tissue box. If the driver has a mass
of 90 kg and, hits the brick wall at 60 mph and stops in 1 cm, the force on
him would be about 3.2 E6 N = 740,000 lb. That would destroy any human,
especially as the force is probably concentrated on a small part of the
head.
If the air bag opens and the front of the car has a crumple zone, the driver
might have as much as 1.5 m = 5 ft to stop. The force on him would then be
about 20,000 lb. This is a force the human body can stand if it is spread
out over a large part of the body.
Other items and speeds can be calculated in the same way.
Best, Dick Plano...
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