Question

The forces that A and B exert on each other are very large but last for a very short time. If we choose a time interval from just before to just after the collision, what is the approximate value of the impulse applied to the two-object system due to forces exerted on the system by objects outside the system?

Answer 1

The impulse applied to the two object outside the system can be find out using the formula,

$I=\dfrac{\Delta p}{\Delta t}$

What is impulse of force?

Impulse of force is the product of force applied on the object to the time for which the force is excreted on it.

Given information-

The forces excreted by A and B is in large amount but for small interval of time.

As A and B interacts each other then their total momentum remain constant. Thus,

$p_{1i}+p_{2i}=p_{1f}+p_{2f}$

Here $p_i,p_f$ is the initial and final momentum respectively.

As the mass and velocity is not given in the problem. Consider $m$ as mass and $v$ as velocity.

Let the collision is elastic. Now when the body A comes with contact of body B, the A exert the force $F_A$ on B and B exert $F_B$ on A.

$I=\dfrac{\Delta p}{\Delta t}$

As the value of both forces are equal by the third law of motion. Use the net force to calculate the impulse with the given equations.

Hence, the impulse applied to the two object outside the system can be find out using the formula,

$I=\dfrac{\Delta p}{\Delta t}$

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