How Does a Pellet Gun's Force Affect a Wall?

[WarpDrive]

I am having trouble understanding another of my homework problems.

A Pellet gun fires ten 2.14 grams pellets per second with a speed of 483 m/s. The pellets are stopped by a rigid wall. a) find the momentum of each pellet. b) Calculate the average force exerted by the stream of pellets on the wall. c) if each pellet is in contact with the wall for 1.25ms, what is the average force exerted on th ewall by each pellet while in contact? Why is this so different from b?

I got the answers to a and c, but I don't understand b. My teacher mentioned something about integrating something, but I don't understand what. I know that J = Favg*deltaT and J = integral(F dt), but how do I use that to find Favg? He said you get an answer of something per second, because of the integral, but I'm just getting more and more confused about it.

Thanks!

 

[Doc Al]

You realize that $$J = F_{ave} \Delta t$$, but what else does impulse equal? Answer/hint: The change in momentum.

 

[quicknote]

As a fellow scientist, I can understand your confusion with this problem. Let me break it down for you and hopefully provide some clarification.

Firstly, let's define some terms. Momentum is the product of an object's mass and velocity, and it is a measure of its motion. In this problem, each pellet has a mass of 2.14 grams and a velocity of 483 m/s. Therefore, the momentum of each pellet can be calculated using the formula p = mv, where p is momentum, m is mass, and v is velocity.

a) To find the momentum of each pellet, simply plug in the given values into the formula p = (0.00214 kg)(483 m/s) = 1.034 m/s.

b) Now, let's consider the average force exerted by the stream of pellets on the wall. To do this, we need to understand the concept of impulse. Impulse is the change in an object's momentum, and it is equal to the average force exerted on the object multiplied by the time it is in contact with the object. Mathematically, it can be represented as J = Favg * deltaT, where J is impulse, Favg is average force, and deltaT is the time interval.

In this problem, the stream of pellets is in contact with the wall for a very short period of time (1.25 ms or 0.00125 s). Therefore, we can assume that the change in momentum is equal to the final momentum, which is zero, since the pellets are stopped by the wall. Hence, we can write the equation as J = (0 - 1.034) = Favg * 0.00125. This simplifies to Favg = -827.2 N, which is the average force exerted by the stream of pellets on the wall.

c) Now, let's compare this result to the average force exerted on the wall by each pellet while in contact. This can be calculated by dividing the average force (Favg) by the number of pellets (10) and the time interval (0.00125 s). Therefore, Favg per pellet = -827.2 N / (10 * 0.00125 s) = -66.176 N.

So why is this different from the value we obtained in part b? This is because in part b, we were calculating the average force exert