Finding the mean net force during a collision

In summary: Anyway, as you can see, the vector sum of u and v is in the same direction as the arrow. If you want to emphasize that the velocity has changed, you could put a dot over the vector sum.
  • #1
youmei0426
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Homework Statement


upload_2018-12-31_13-43-56.png


Homework Equations


F=ma=mv/t[/B]

The Attempt at a Solution


I used the equation F=mv/t, in which I find the change in velocity and change in time before and after the collision. The change in time is t2-t1, but the problem comes when I am calculating the change in velocity. Shouldn't the change be (v-u)? The answer is D, in which the velocity becomes the sum of u and v, and I don't understand why. Thanks in advance!
 

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  • #2
velocity is a vector, and as such , it has both magnitude and direction.
 
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  • #3
This is what it looks like visually:

wall.jpg

As PhantomJay has stated, you need to actually understand what the equation you are using really means and what each of the variables are. The FULL equation here is:

[tex]\vec{F} = m \frac{\Delta \vec{v}}{\Delta t}[/tex]

Since velocity is a vector, the CHANGE in velocity will require that you know the directions of the initial and final velocity. If we designate +x direction as the same direction as "u" (as in the fig), then the final velocity is "-v".

This, Δv = -vi - ui = - (v+u)i;

and
Δt = t2 - t1

This means that the force exerted by the wall is

[tex]\vec{F} = -m \frac{v+u}{t_2 - t_1} \hat{i}[/tex]

The negative sign means that the force exerted BY the wall ONTO the mass is in the -x direction, i.e. to the left in the figure. The answer options in the question only care about the magnitude. But even so, as you can see, you can't ignore that these are vectors till the very end.

Moral of the story here is that you need to do this very carefully and to follow the "rules" meticulously. Otherwise, you'll get trapped with the signs issue.

Zz.
 

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  • #4
ZapperZ said:
This is what it looks like visually:

View attachment 236639
Hmmm... i would show it as v with an arrow to the left, or, equivalently if puzzlingly, -v with an arrow to the right.
 

FAQ: Finding the mean net force during a collision

What is the definition of mean net force during a collision?

The mean net force during a collision is the average of all the forces acting on an object during a collision. It takes into account both the magnitude and direction of the forces.

How is the mean net force calculated during a collision?

The mean net force can be calculated by dividing the total force acting on the object by the duration of the collision. This can be represented mathematically as Fnet = ∑F / Δt, where Fnet is the mean net force, ∑F is the sum of all the forces, and Δt is the duration of the collision.

Why is it important to find the mean net force during a collision?

Finding the mean net force during a collision is important because it allows us to understand the overall effect of the forces on the object. This information can be used to analyze the impact of the collision and make predictions about the resulting motion of the object.

What factors can affect the mean net force during a collision?

The mean net force during a collision can be affected by the mass and velocity of the objects involved, as well as the nature and direction of the forces acting on the objects. Other factors such as friction and air resistance may also play a role.

How can the mean net force during a collision be applied in real-world situations?

The mean net force during a collision can be applied in various real-world situations, such as car accidents, sports collisions, and industrial accidents. It can also be used in engineering and design to ensure the safety and efficiency of products and structures.

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