Momentum & Impulse: Rank Greatest to Least

[Justinmcg67]

Homework Statement

Straight from book: Marshall pushes crates starting from rest across the floor of his classroom for 3 seconds with a net force as shown. For each crate, rank the following from greatest to least... (a) Impulse delivered (b) Change in momentum (c) Final speed (d) Momentum in 3 seconds.

All crates are pushed to the right...

Crate A) F=100N, M=30kg
Crate B) F=75N, M=20kg
Crate C) F=50N, M=10kg

Homework Equations

I'm using the following to try and make some sense of this...

Impulse = Δp = Force * Time = Δmv
Momentum = mv

The Attempt at a Solution

Here is where a bit of confusion is setting in for me. I use the Force * Time equation to get an impulse, for crate A I got 300N, for crate B I got 225N, and for crate C I got 150N. Now, isn't 10N equal to 1 kg? However, in a YouTube explantion, which I didn't fully understand, nor does my book make a correlation between force (Newtons) and kilograms, which I find to be quite odd; in any case, 10 N = 1 kg, however it noted that 1N = 1 kg m/s. I don't understand how you go from 10N = 1 kg to 1N = 1kg m/s?

I'm really struggling with this problem not because of equation but because I simply do not understand how I am to begin calculating this problem and what units to use. Also, I'm sure I could find speed/velocity but at this point before I start throwing numbers around and getting it wrong, a nice description of how I should approach this is what I am after. Please don't solve the problem for me, but rather if this 1N = 1kg m/s thing could be explained and how they are related I would great;y appreciate it. As it was taught that Newtons are a force and Kilograms are a unit of mass, two very different things.

 

[cepheid]

The Attempt at a Solution

Here is where a bit of confusion is setting in for me. I use the Force * Time equation to get an impulse, for crate A I got 300N, for crate B I got 225N, and for crate C I got 150N.

There is a problem here. You have expressed your answers in Newtons. But the Newton is a unit of force. Your results here are not forces, they are impulses. Impulse = force*time. Therefore, your answers should be in dimensions of force*time, which would have units of Newton-seconds. Always include units in your calculations, and carry them all the way through to the final step, in order to avoid these types of errors. For example, if you had written:

impulse = (100 N)*(3 s) = 300 Ns

you would have immediately seen that the units of the final answer were Ns.

Now, isn't 10N equal to 1 kg?

Let me stop you right there. NO, 10 N is NOT equal to 1 kg. Not only that, but this is a completely nonsensical statement. The 10 N is a force, and the 1 kg is a mass. Force and mass are two totally different physical quantities. You cannot equate two physical quantities that are not of the same type. Saying that force = mass makes about as much sense as saying time = temperature. It's meaningless. You can only equate one quantity that is a force to another quantity that is a force, or one quantity that is temperature to another quantity that is a temperature, etc. To make sure that you don't mistakenly equate two different types of physical quantities, check to make sure that your equations are dimensionally consistent i.e. the units of the stuff on the left hand side are the same as the units of the stuff on the right-hand side.

Now, it is true that an object whose mass is 1 kg will have a weight of 10 N (9.81 N, actually) if it is on the surface of the Earth. The object's weight is a measure of the amount of force with which the Earth's gravity pulls on it. So, weight is a force. If you took that 1 kg mass and put it somewhere else, e.g. on the surface of the moon, then its weight (in Newtons) would be lower, because the moon has less gravity and therefore does not pull down on the object as hard. However, its mass would never change: it would always be 1 kg no matter where it was.

However, in a YouTube explantion, which I didn't fully understand, nor does my book make a correlation between force (Newtons) and kilograms, which I find to be quite odd; in any case, 10 N = 1 kg, however it noted that 1N = 1 kg m/s. I don't understand how you go from [STRIKE]10N = 1 kg [/STRIKE]to 1N = 1kg m/s?

I crossed out the thing that you wrote that was wrong. I've already explained above why it was wrong. Now, remember from Newton's 2nd Law that force = mass*acceleration. Remember that any quantity in physics can be derived from some combination of the base quantities, mass, length, and time. So, the equation above (Newton's 2nd) tells us that the dimensions of force, in terms of fundamental quantities, are mass*length/time². By definition, 1 Newton is the amount of force required to accelerate a mass of 1 kg at an acceleration of 1 m/s². Therefore:

1 N = 1 kg * 1 m/s² (definition of the Newton)

 

[Justinmcg67]

I ended up going to tutoring first thing in the morning and I got great explanation as how to solve the problem. Thank you very much for helping me though. :-)