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Home Q & A Board Science-Related Homework Help Physics
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nuxeh nuxeh
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11 years ago
Suppose a car is traveling in a straight line at a constant velocity of 100 km/h, isn't the acceleration of an object traveling at a constant velocity 0?

Lets just say that the car weighs 1,000 kg, F=ma, suppose that the car hits a person, wouldn't the force of the impact be 0 if the acceleration of this constant velocity is 0? After all 1,000 x 0 = 0

I don't understand this concept, please explain why the person would experience a greater impact than 0 Frowning Face Thank you.
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#1
11 years ago
The car is not accelerating when traveling at a constant speed, yes, that is true.
But when the car hits something, it is no longer traveling at constant speed.
During the collision the car changes speed and hence accelerates (negatively).
It is THIS neg. acceleration that causes a force F = ma to act on the person.

Add'l comment: Your logic and physics proves it impossible for an object traveling at constant speed, to strike an object at rest, and not experience some change in speed during collision.
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IlluminatusIlluminatus
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#2
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11 years ago
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#3
11 years ago
The force of impact on the person depends on the mass and acceleration of the PERSON, not the mass and acceleration of the CAR.  There are two "F=ma" equations here:

(net force on car) = (car's mass)×(car's acceleration)
(net force on person) = (person's mass)×(person's acceleration)

This is further complicated by the fact that the impact force between car and person (let's call that "F_cp") might be only ONE part of the "net" force acting on one or the other object.  That is:
net force on car = F_cp + (other forces on car)
net force on person = F_cp + (other forces on person)

So the general equations (during the time of impact) would be:

F_cp + (other forces on car) = (car's mass)×(car's acceleration)
F_cp + (other forces on person) = (person's mass)×(person's acceleration)

And you can certainly set that up so that (car's acceleration)=0 while F_cp is nonzero.  For example, if F_cp is 55N and (other forces on car) = -55N, then (car's acceleration) will be zero (car will travel at constant velocity), but the impact force will still be nonzero.
wrote...
#4
11 years ago
In this example you must not consider what has happened to the car, but what is happening to the person. If you take an extreme case where the car, travelling at 100km/h = 27.7m/s were to hit a person with mass 70kg. In this scenario the car does not change its velocity at all, but the person is attached to the front of the car and is carried along with the car. Now calculate the force on the person:
 The person will be accelerated from zero velocity to 27.7m/s in a very short time - say 0.10sec. Calculate as follws:
Acceleration of person :
 v = u +at
27.7 = 0+ a*0.1
a = 277m/s²

What is the force required to do this:
 Force = mass * acceleration
 Force = 70*277
 Force = 19,390N

It is the force accelerating the person that causes the damage.  Of course in a real situation, the person would be thrown aside, or knocked out of the way, but the fact still remains that the person is violently accelerated from zero velocity to quite a high velocity in an extremely short time. This is high acceleration, resulting in a large force acting on the person, that causes the damage or even death.
wrote...
#5
11 years ago
Ok, think of it this way. What is acceleration ? Is the velocity of a stationary body by definition 0? The Velocity of a moving object is not ), correct? Well if a moving object hits a staionary object, isn't there a change in velocity? I mean if a car is going 100 kph and slams into an immovable object it decelerates fairly quickly from 100kph to 0 in a fraction of second.

This is a very simplistic version and in real life both objects the moving and the stationary will accelerate (+,-).
wrote...
#6
11 years ago
Hi Ican, well it is VERY difficult to even consider this concept when you are using such unmatched masses. A person is so light (70kg or so) compared with a car, which could weigh 1,000kg or more! Try applying the concept to two ice pucks on an ice table (or even two marbles rolling on the floor) and you will readily see the effect on each object, even if the masses of the ice pucks (or marbles) are different from each other. The other thing that most people seem to have missed is that such a scenario invokes conservation of momentum rather than conservation of energy, since the impact between a car and a person will cause plastic deformation of the car (and the person), so it is simpler to consider conservation of momentum, since the deceleration of the car and acceleration of the person is instantaneous (i.e. doesn't occur over time).

Cheers
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