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Name: Leo M.
Status: educator
Age: 40s
Location: N/A
Country: N/A
Date: 9/12/2004

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?

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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