# B Is there impulse during a collision only?

1. Dec 11, 2016

### Ali Hamaiz

I know there are many websites on Internet but I can not understand any. My teacher says impulse is only during a collision of one body with other (when a car collide with other car etc.). My question is will there be impulse when a body is accelerating , when it collides with the air molecules , and with the ground (as it moves when it collides with the ground). I am confused in this topic and what does it means that impulse is the integral of net force. J=∫F dt

Last edited: Dec 11, 2016
2. Dec 11, 2016

### Staff: Mentor

Since force is mass times acceleration according to Newton's second law, and velocity is the integral of acceleration, i.e. the amount of change summed over a period of time, to yield a final velocity, it follows, that mass times velocity - the impulse - is the integral of force.
$$F = m \cdot a(t) \Longrightarrow \int F = \int m \cdot a(t) dt = m\cdot \int a(t)dt = m \cdot v(t) = Imp$$
So far to the mathematical part of your question. On Wikipedia we find:
Mathematically there is no difference between momentum and impulse, as there isn't a difference between velocity and speed. So it is basically about how we use the two terms. The equation above shows us, that only the (not changing) mass of an object and its velocity plays a role for its impulse, resp. momentum. Since both have nothing to do with a collision, the momentum is a property of a moving object. O.k., zero velocity leads to zero momentum, so we don't even need movement. A collision can be viewed as a kind of measurement: all of a sudden the velocity changes in a short period of time and the impulse is transferred to another object, in your example above to another car (Newton's third law). This "measures" the amount of impulse. So I guess (I'm no native English speaker), that impulse is reserved to the transfer of momentum and therefore a sort of collision is needed, whereas momentum is reserved to the object's property independent of any measurement. If you consider collisions with air molecules (or with the road the car is driving on), then you get the concept of air resistance (or friction). They also result in a change of velocity and therefore a change of momentum. However, they are harder to measure than the collision measurement with another car would be.

3. Dec 11, 2016

### Ali Hamaiz

@fresh_42 So this means that there will be no impulse acting on a body during collision with the ground and to define these terms we use friction not the impulse .But can we say there is impulse as the momentum of a body is transfered to the air molecules (if we get to measure the rate of collision).

4. Dec 11, 2016

### Staff: Mentor

Why that? Any collision with a massive object transfers impulse, even to the ground. But in this case we have
$$\text{ mass}_{\text{ object }} \cdot \text{ change of velocity}_{\text{ object}} = \text{ mass}_{\text{ earth}}\cdot \text{ change of velocity}_{\text{ earth}}$$
so you won't see much of a change in velocity of the ground (=earth).
No. Forget the friction in this case. It was only an example of a source for change in velocity.
Well, yes. Driving a car causes airflow as a result of the collision of the car with air molecules.

For short:
momentum = mass $\cdot$ velocity
impulse = momentum transfer during a collision

5. Dec 11, 2016

### Ali Hamaiz

I know get it , the conclusion is that yes there is impulse when the collision is with the air molecules but we do not consider it because there magnitudes are small .