Understand Momentum, Force and Impulse

[Aman Trivedi]

Hi everyone! I've been getting confused with Momentum, Force and Impulse. From my understanding force when applied on object helps it gain momentum, the higher the force applied the higher the acceleration therefore more the momentum. And according to Sir Isaac Newton's first law of motion, the object that the force was applied on will keep moving, therefore won't change its momentum until another force slows it down. Once it does slow the object down the change in momentum would equal to the impulse applied on the object. Therefore the impulse would determine the objects momentum post the collision? Am I right? If not could you please give me a very simplified explanation on why impulse and momentum differ?

 

[vanhees71]

Momentum is (non-relativistic physics)
$$\vec{p}=m \vec{v}.$$
Force is
$$\dot{\vec{p}}=\vec{F},$$
and impulse is the change of momentum between two times
$$\vec{p}(t_2)-\vec{p}(t_1)=\int_{t_1}^{t_2} \mathrm{d} t \dot{\vec{p}}(t)=\int_{t_1}^{t_2} \mathrm{d} t \vec{F}.$$

 

[Aman Trivedi]

Momentum is (non-relativistic physics)
$$\vec{p}=m \vec{v}.$$
Force is
$$\dot{\vec{p}}=\vec{F},$$
and impulse is the change of momentum between two times
$$\vec{p}(t_2)-\vec{p}(t_1)=\int_{t_1}^{t_2} \mathrm{d} t \dot{\vec{p}}(t)=\int_{t_1}^{t_2} \mathrm{d} t \vec{F}.$$

I understand the relationship, but it would help if you could give me a example in terms of a real world
Situation where momentum and impulse come into play... Thanks (:

 

[jtbell]

Therefore the impulse would determine the objects momentum post the collision?

Yes, the change in an object's momentum equals the impulse (force x time-interval) delivered to it by the force.

Analogously, the change in an object's kinetic energy equals the work (force x distance) delivered to it by the force. (assuming potential energy doesn't come into play)

(and in either case, "force x whatever" must be understood to mean an integral if the force is not constant.)

 

[Drakkith]

From my understanding force when applied on object helps it gain momentum, the higher the force applied the higher the acceleration therefore more the momentum.

Momentum is the product of mass and velocity. Acceleration is the result of applying a force to a mass. What happens when an object is moving in the opposite direction that the applied force points? Well, it would lose momentum instead, not gain it. So a net applied force doesn't lead to momentum, it leads to a change in momentum.

Once it does slow the object down the change in momentum would equal to the impulse applied on the object. Therefore the impulse would determine the objects momentum post the collision? Am I right? If not could you please give me a very simplified explanation on why impulse and momentum differ?

Stick to the basic definitions and you can't go wrong. Momentum is a quantity that is the product of an objects mass times its velocity. Impulse is a change in the momentum and is equal to the integral of the applied force over time.

I understand the relationship, but it would help if you could give me a example in terms of a real world
Situation where momentum and impulse come into play... Thanks (:

An obvious example would be rockets, but you could also imagine being in a car that is accelerating. A sports car with 500 horsepower can apply a larger force to the ground than a sedan with 100 horsepower. So if both cars floor their gas pedals and accelerate for the same amount of time, the impulse of the sports car is larger than the impulse of the sedan. The sports car gains more velocity and momentum over that time than the sedan.