A bullet ricochets off a steel plate problem

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SUMMARY

The forum discussion centers on calculating the average force exerted by a bullet ricocheting off a steel plate. The user initially calculated the average force as approximately 20000N using the formula F_avg = ΔP/Δt, but the expected solution is 9.5*10^7N. The user expressed confusion regarding the change in momentum, particularly when considering direction changes. A key insight provided by another user emphasizes that momentum is a vector quantity, and the change in momentum must account for both magnitude and direction, not just speed and energy.

PREREQUISITES
  • Understanding of basic mechanics principles, including kinetic energy and momentum.
  • Familiarity with vector mathematics, particularly in the context of physics.
  • Knowledge of the equations of motion, specifically v^2 = v_0^2 + 2aΔx.
  • Experience with calculating average force using F_avg = ΔP/Δt.
NEXT STEPS
  • Study vector representation of momentum and how to calculate changes in momentum directionally.
  • Learn about the implications of friction on motion and how to model it in calculations.
  • Explore the concept of elastic and inelastic collisions to understand momentum conservation.
  • Review examples of force calculations in mechanics, focusing on scenarios involving direction changes.
USEFUL FOR

This discussion is beneficial for physics students, particularly those studying mechanics, as well as educators looking for insights into common misconceptions about momentum and force calculations.

Deckname
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Homework Statement
What's the median resisitive force the plate offers against the bullet given the following info? (in the picture attached)
Relevant Equations
none have been given, most likely ##F_{avg}=\frac{\Delta p}{\Delta t}##
I have calculated KE_i and KE_f, took the difference between the initial and final kinetic energy of the bullet to be equal to the work spent to overcome the friction, and divided it by the distance traveled, but arrive at around 20000N. The solution should be 9.5*10^7.

Not sure what else to try at this point. Suggestions or hints please? Also this is a part of my second year mechanics seminar, and I wouldn't be asking for the solution or anything here unless passing the subject literally depended on it, as missing even 1 solution out of the 29 exercises I've already solved, it's still counted a fail. So please lend a hand!
 

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your handwritten stuff is (1) not really acceptable for this forum and (2) not readable even if it were.
 
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Alright, thanks for pointing that out, I won't post handwritten stuff again. But then again I've explained what I've done in the OP (forgot to add I divided the work by distance, since F=W/d) and I've also attached a picture of the problem itself that I made in paint to be clearly readable.
 
What is the change in the bullet’s momentum?
 
Nugatory said:
What is the change in the bullet’s momentum?
Alright, I now realize I'm supposed to calculate the solution through F_avg=ΔP/Δt, but how do you calculate the change in momentum when not only the momentum changed, but also it's direction? I'm confused now.
 
I've used the ##F_{avg}=\frac{\Delta P}{\Delta t}## and have arrived at the same result of ~##20000N##. I have calculated ##\Delta t## by using ##v^2={v_0}^2+2a \Delta x## to calculate the acceleration and plugged it in ##t=\frac{\Delta v}{a}## to get time. I calculated ##\Delta p## by taking into consideration the velocity vectors parallel to the trajectory of the bullet, since this is the change in momentum we want to consider, and I then plugged all of that into the first equation I mentioned, ##F_{avg}##, and got ##20000N## again.

I'm actually confused now, am I constantly making a mistake in all the different ways this can be solved, since I keep arriving at the almost identical result (different but a few hundreds of N), or is the result my professor has provided wrong?
 
Deckname said:
I've used the ##F_{avg}=\frac{\Delta P}{\Delta t}## and have arrived at the same result of ~##20000N##. I have calculated ##\Delta t## by using ##v^2={v_0}^2+2a \Delta x## to calculate the acceleration and plugged it in ##t=\frac{\Delta v}{a}## to get time. I calculated ##\Delta p## by taking into consideration the velocity vectors parallel to the trajectory of the bullet, since this is the change in momentum we want to consider, and I then plugged all of that into the first equation I mentioned, ##F_{avg}##, and got ##20000N## again.

I'm actually confused now, am I constantly making a mistake in all the different ways this can be solved, since I keep arriving at the almost identical result (different but a few hundreds of N), or is the result my professor has provided wrong?
You are still misunderstanding change in momentum. Momentum is a vector, obtained by multiplying mass by the velocity vector. The change in momentum is the change in the vector. You are only looking at change in speed and energy, which are scalars.
E.g. in an elastic bounce there is no change in speed or energy but maybe a substantial change in velocity and momentum.

To get the duration of the change (Δt), assume the frictional force is constant and find the time for the given drop in tangential velocity.