From classical mechanics, we know that the force is the rate of change of momentum, one of it's simplest forms is F=ma, so if a body moves with constant velocity, then its acceleration is zero, and by the previous definition has no force, although for example if a car of constant speed strikes some person, he may be injured. Is there any explanation?
The obstacle changes the velocity of the car by v2-v2=dv, say -10 m/s. Since the car has some mass, the crash will take some time dt, say 0.2 seconds. Now calculate the acceleration a=dv/dt and you have what you need to calculate the average force during the crash.
@ Khaled
In colliding systems, its the momentum and energy which is conserved, and not the force. If you go to a railway station and a Coolie (luggage carriers) comes to you to carry your luggage on his head. In that case, force due to gravity which the coolie has to oppose acts upwards in a vertical plane, while he walks in the horizontal plane (the displacement). The angle theta made between direction of force and displacement is 90 degrees. Then, as per Physics, work done, W = F.d = F d cos theta = 0. Do not give this argument to the collie when he asks for the money! :)
In the above example, I have assumed zero friction, and the only work done is against the gravity!
@ Herbert,
Your argument is not rational! What if the obstacle is an ant? Change in speed will be nearly zero. So, then the ant isn't crushed?
@ Vikash, the speed of the car (vc) is nearly constant, it carries the center of gravity. But before the crash, we had v(ant)=0 and after the crash, we have in the inelastic case v(ant)=vc. If the ant is very(!) elasic, it is accelerated to 2*vc. In both cases, this acceleration takes place in a very short period of time, resulting in a very high force, smashing the ant. Look at the windshield of the car.
@ Herbert,
What an irony! In the first post, you talk about force and in your second post, you are using results which are obtained after imposing conservation of energy and momentum which I had already said.
Going back to your first post; assuming m_car >> m_ant
Lets handle the simple elastic collision.
v after collision = v before collision for car. So, acceleration of the car, a=dv/dt = 0 again! So again the ant does not get impacted by any force!
So, my point is that instead of explaining it terms of forces involved better use principles of momentum and energy conservation.
Give a suitable reason for down-voting?
You can't use the acceleration of the car to calculate the force on the ant!
My post clearly implies.. force delivered on the ant! I do not want to take this argument any further for very obvious reasons!
Vikash
There is a distinction to be made between force and energy. Force induces energy in a body, causing it to increase its velocity.
Once the energy has been induced in a body, the velocity will be maintained on account of the amount of energy induced. The velocity will remain constant unless losses occur due to friction of other causes.
When the car hits a person as in you example, it is the energy expended during the collison that will injure the person and dammage the car due to the inertia of mass of the person resisting the longitudinal inertia of the moving car
Vikash
My apologies. I see that I read only the posts answering your initial question.
You are absolutely right.
Introducing a second object breaks translation invariance-it's translation invariance, that expresses the fact that momentum, thus velocity of one of the objects is constant. Specifying the position of a new object means that there will appear a force, when the two objects try to occupy the same position.
The speed of the car does not remain constant during the actual collision. Its momentum changes, and so does the momentum of the victim.
In the case of car moving with constant speed there are 2 forces. 1 is coming from the engine and, 2 is coming from friction. This is absolutely NOT the same thing as , say, to consider the frame of reference moving with constant velocity with respect to observer. In the case of car the balance of forces is very fragile/unstable. I would also strongly recommend to read about D'Alambert 's priciple. It reduces dynamics to statics in the sense that if one adds to all forces applied to a body also a force of inertia, then the total sum of forces is exactly zero. More details you can find by reading Cornelius Lanczos "The Variational principles of mechanics", chapter 4.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Mechanics
- Classical Mechanics