How Do Momentum, Impulse, and Impact Relate to Newton's Second Law?

[thingsfallapart]

Hi- I have a quiz tomorrow on Newton's 1st and 2nd Laws. I'm kind of iffy with the second law, especially when it comes to impulse and impact. What is impact, and how can you measure impulse? For example, what if an object is dropped onto a soft couch, etc, etc.. basic theories... i haven't yet studied conservation of momentum so leave that out.. someone please explain the 2nd law and all that momentum/impact/impulse PLEASE!

 

[arildno]

Now, I assume you have learned about integration:
Newton's 2.law for a single object (I'll use a point particle with constant mass as my object) states:
F=ma,
where F is the sum of all forces acting on the object, m is the mass of the object, and a the acceleration of the object.
Let's integrate Newton's law from time t=0 to a time t=T.
Then we have:
$$\int_{0}^{T}Fdt=mv(T)-mv(0)$$
where v(T) is the velocity of the object at time t=T and v(0) is the velocity of the object at time t=0.
Hence, the right-hand side of the equation is simply the change in the object's momentum between times 0 and T.

What is the left-hand side?
That is the impulse I acting upon the object in the time interval 0 to T, or:
$$I=\int_{0}^{T}Fdt$$

The integrated version of Newton's 2.law states therefore:
The impulse acting upon an object during a time interval is equal to the object's momentum change during the same interval.

Is it okay so far?

 

[M98Ranger]

Hi there,

No problem, I'm happy to help explain the concepts of momentum, impulse, and impact. These are all related to Newton's second law, which states that the net force acting on an object is equal to its mass times its acceleration (F=ma).

Momentum is a measure of an object's motion and is defined as the product of its mass and velocity (p=mv). In other words, an object with a larger mass or a higher velocity will have a greater momentum. This can also be thought of as the amount of "motion" an object has.

Impulse is the change in momentum of an object and is equal to the force applied to the object multiplied by the time it is applied (J=FΔt). This means that if a force is applied to an object for a longer period of time, the change in momentum will be greater.

Impact is the force that is applied to an object when it collides with another object. This force is related to both the mass and velocity of the objects involved, as well as the duration of the impact. The longer the objects are in contact, the greater the impact force will be.

To measure impulse, you can use a force sensor and a timer. You would measure the force applied to the object and the time it is applied, and then calculate the impulse using the equation J=FΔt.

In the example of an object being dropped onto a soft couch, the couch would exert a force on the object to slow it down and bring it to a stop. This would result in a change in momentum, and therefore an impulse. The impact force would also depend on the mass of the object and the velocity at which it is dropped.

I hope this helps clarify the concepts of momentum, impulse, and impact. Good luck on your quiz!