Newton's Second Law — Net Force problem

[adams_695]

Homework Statement

A group of budding engineers made a cannon 1.0 m in length that shoots potatoes. They recorded the speed at which a potato could be launched. They measured it to be a constant 63 m/s over a horizontal distance of 1.0 m. The potato had a mass of 174 g. Assuming the potato accelerated from rest in the cannon, what was the magnitude of the force that the cannon exerted of the potato? (assume the potato hits a wall after 1.0 m and stops moving) (Answer to one decimal place)

Relevant Equations

Newton's Second Law/Third Law

 

[phinds]

Posting your work sideways is bad form

 

[adams_695]

Posting your work sideways is bad form

edited.

 

[adams_695]

Posting your work sideways is bad form

is the working correct from what you can see?

 

[Andrew Mason]

is the working correct from what you can see?

From what you have written you are relating the work done on the potato to its kinetic energy. That is correct if you are assuming that the friction in the cannon barrel is negligible. Since that is not stated you should mention it (you can get bonus marks for noticing things like that!). Your calculations appear to be correct. Good job.

AM

 

[haruspex]

is the working correct from what you can see?

The question is flawed. It ought to tell you to assume the force applied is constant. If it is not then you do not have enough information to find the average force.

 

[gingerjake]

I'm just a biologist, but it doesn't look right to me. Close but no cigar. This is a time:distance problem and the correct SI units is kg not g. Thus:
average velocity: (63 m/s - 0 m/s)/2 = 31.5 m/s
time to terminal velocity: 1 m/31.5 m/s=.032s
acceleration to go 1 meter: 1 m= a/2 m/s^2 * t^2: rearranged a= 2*1/.032^2=1953.1 m/s^2
F=ma: F=0.174 kg * 1953.1 m/s^2 = 339.8 kgm^2 = 339.8 N

 

[haruspex]

I'm just a biologist, but it doesn't look right to me. Close but no cigar. This is a time:distance problem and the correct SI units is kg not g. Thus:
average velocity: (63 m/s - 0 m/s)/2 = 31.5 m/s
time to terminal velocity: 1 m/31.5 m/s=.032s
acceleration to go 1 meter: 1 m= a/2 m/s^2 * t^2: rearranged a= 2*1/.032^2=1953.1 m/s^2
F=ma: F=0.174 kg * 1953.1 m/s^2 = 339.8 kgm^2 = 339.8 N

Your method ought to have given exactly the same answer, 345.3N. Since it did not, your more circuitous route must have introduced some rounding or arithmetic error. Try keeping more decimal places.

 

[PeroK]

The question is flawed. It ought to tell you to assume the force applied is constant. If it is not then you do not have enough information to find the average force.

As an object accelerates it takes more power to generate a constant acceleration. These questions are doubly flawed, therefore, as the assumption of constant acceleration is unlikely to be valid.

 

[gingerjake]

I'm lucky I even got an answer. U R right, I truncated the 1/31.5 quotient before I squared it. Should have kept all 11 digits. {:-)

 

[Dr. Courtney]

https://arxiv.org/ftp/arxiv/papers/1305/1305.0966.pdf
See Fig 3 for real potato cannon pressure curves.

The force curves would just be the pressure times the cross sectional area.

Real physicists measure this stuff rather than calculate based on flawed assumptions.

 

[Andrew Mason]

As an object accelerates it takes more power to generate a constant acceleration. These questions are doubly flawed, therefore, as the assumption of constant acceleration is unlikely to be valid.

It would just require a source of constant pressure gas applied to the chamber. A large compressor could do that quite easily.

AM

 

[Dr. Courtney]

It would just require a source of constant pressure gas applied to the chamber. A large compressor could do that quite easily.

In practice, no projectile launchers, including potato cannons work this way, because it's not really easy. A large compressor is not enough, one needs to design a system with adequate flow from the compressor to the chamber and also work out the details so that the flow is just right to maintain constant pressure. Most projectile launchers that use a compressed gas allow a fixed reservoir of gas to simply expand as the projectile is pushed in the barrel. The designs that are closest to having a constant pressure (thus a constant force) achieve this simply by having the reservoir volume large enough so that the final volume (reservoir plus barrel volume) is only a smidge larger than the initial volume (reservoir volume). But such a large reservoir volume introduces other issues of cost and size.

The other main approach is using combustion designs. Most of these reach a peak pressure before the projectile is half way down the tube and then the pressure drops.

 

[Andrew Mason]

The question is flawed. It ought to tell you to assume the force applied is constant. If it is not then you do not have enough information to find the average force.

It is an odd question. It omits necessary assumptions and it adds an unnecessary assumption about what happens to the potato after launch.

AM

 

[sojsail]

is the working correct from what you can see?

I think your solution is equivalent to one of a list of perhaps 2 or 3 methods that would get full credit.

One quibble about your worksheet: in one line you gave g as the unit where I think you knew, from how you converted the numerical part, is kg. That could cost you.

There were several comments about finer details, that were true, but I expect they were intended to be neglected. For example, in projectile motion problems, they often do not tell you to ignore air drag, but then give you no info regarding how to consider air drag.