Because my other lab was a little too inconclusive (cricket chirping when the crickets never chirped), I decided to do another project. I love my dog and in order to spend time with him and do physics, I decided there had to be things about him I could study in physics. One thought that came to mind was the Human Power Output lab I did last year. If my power output could be measured, the dog’s could too. In order to do more than one calculation, I decided to weigh him down with something and measure his output under various loads. I expected his output and work to be higher when carrying more, which, according to my calculations, was incorrect. I think I now know why and will explain later, though I may have had a lot of error.

In order to measure the output of Dog carrying different weights, I needed to have a way to keep the weights on him. This was extremely difficult. Someone suggested I tie a bag of weights around his neck, but I didn’t really see this as a realistic setup for the dog. My brother and I tried to build a cart he could pull things in. We took a milk crate and tied roller blades and aluminum baseball bats onto it (for balance). We then took Dog outside. Unfortunately, I think dogs are like horses; they have to be broken in and need to get used to the idea that something is behind them. His ‘reins’, two leashes, were getting tangled up, so we got cardboard wrapping paper tubes to lace them through, much like the wooden poles used on horses to keep them straight. It was all right until it began to rain; the cardboard fell apart and the dog wasn’t even running in a straight line because he was scared and trying to get rid of the cart behind him.

My brother and I then toyed with idea of having Dog pull different people of various weights while on bicycle or roller blades, but when I considered the different error that could come in that – different skates/bicycles, different efficiency of the wheels, the force of friction – I decided tot try to find a way for the dog to carry the weight. I thought a saddle bag might be nice, but I didn’t know where to get one. I tried to make one out of an old towel, but after an extremely long time, I had only completed less than 5% of it (we took apart our sewing machine a long time ago and never put it back together – no one can remember where the parts are). My brother suggested I use an old pair of pants, stuffing them full of weight and using them much in the same way saddle bags are used on horses.

That is exactly what I ended up doing, with a few changes I had not envisioned. First, I had to find an old pair of jeans and a large belt. I looped the belt through the back of the pants and tightened it snugly under Dog’s tummy. I then put a leash around his front/chest, much like a horse, and tied a bandana over his back to hold the whole thing in place. I left the jeans unzipped so I could stuff the weight inside the pants, and sealed the pant legs by tying them underneath the dog. As weights, I used common things found around the house. Books, salt, canned food, and weights. I couldn’t go much higher because nothing bigger would fit into my pants.

In order to find the work of the dog and the power output, I had to find a lot of other stuff. These are the equations I used to get what I wanted:

As you can see, I needed the velocity to find the acceleration, which I needed to find the force. I the used the force to find work which I needed in order to calculate power.

I set up my experiment by going to Cook Park (the Principal at Deer Creek forbade me to use their field). I measured off three full measures of my tape measure, not in metric units, of course. It seemed a lot farther at the time than it actually was (60 ft.). I put my weights in his pants of mine that he was wearing and had my mother hold him and let him go, while I timed him at the end of the run. The mass I calculated by having Josh Marles stand on a scale holding the dog and subtracted their weights, which left 75 pounds. I didn’t think he weighed that much. I then added the masses of the objects to this weight, including the mass of the saddle. I then averaged all of the times ( I timed him five times with each weight – I thought more than that might make him tired or mad) so I had one average time for each trial. In this way I was able to solve the first two of my five equations for T. For the rest of the formulas, I just plugged in my previous answer or the mass which I had already calculated.

Alone Books Books & Cans Water Weights
 

5.13 4.68 4.85 4.51 5.03	6.66 5.85 5.09 5.69 6.13	6.15 5.52 6.60 5.93 6.20	5.96 6.30 7.12 6.92 7.53	7.96 8.85 10.82 9.53 10.15
4.84 secs.	5.884 secs	6.08 secs	6.766 secs	9.462 secs
Mass =34 kgs	35.8 kgs	36.3 kgs	39 kgs	39.9 kgs
18.288 m	18.288 m	18.288 m	18.288 m	18.288 m

This data table shows the dog’s five different times in seconds; below that the avg. of those five times, the masses carried by the dog, and the distance in meters.
 

	Alone	Books	Books & Cans	Water	Weights
Velocity	3.7785 m/s	3.10809 m/s	3.00789 m/s	2.70292 m/s	1.93278 m/s
Acceleration	.7807 m/s.	.52822 m/s	.4947 m/s	.39948 m/s	.204269 m/s
Force	26.5432 N	18.91054 N	17.958 N	15.58355 N	8.15029 N
Work	485.423 J	345.836 J	328.423 J	284.99 J	149.0526 J
Power	100.3 W	58.78 W	54.02 W	42.12 W	15.75 W

The results I found are all bases on the assumption that the dog was at constant acceleration. There is a lot of uncertainty. The dog could have become tired after a while, the timing could be off, the scales that I got my masses from could be bad, the dog didn’t always run in a straight line, and the reaction time was slow. I’m sure there are more, but these are the major ones. I can’t really mathematically compensate for the problems the dog had – not running straight, being tired, or not knowing hen or to whom to run. Weaver suggests that time is the most important factor n problems dealing with velocity and acceleration and that it is often not controlled well. Because he is probably right, having written a book and all, I’ve wiggled my time by a whole .5 of a second, which actually ends up making a difference quite a bit in my uncertainty. I could possibly compensate for the scale by guessing how much it could have been off. But as for the dog, he sometimes had problems, sometimes didn’t, probably jumped the gun sometimes, so I think that by the time that I’d adjusted and wiggled the numbers, I’d be right back where I started, although I’ll still wiggle them for human error. There is a lot of room for error as can be seen by the charts.
 

X=18.14 X=18.44	Alone	Books	Books & Cams	Water	Weights
Time 1	4.34 s	5.384 s	5.58 s	6.266 s	8.962 s
Time 2	5.34 s	6.384 s	6.58 s	7.266 s	9.462
Mass 1	31.5 kgs	33.3 kgs	33.8 kgs	36.5 kgs	37.4 kgs
Mass 2	36.5 kgs	38.3 kgs	38.8 kgs	41.5 kgs	42.4 kgs

Above is a table which contains the adjustments I have made for uncertainty; .5 of a second for time, 2.5 kg for mass, and .15 m for distance. Below are the velocities, accelerations, forces, work, and power for the uncertainty.
 

Velocity	4.17926 m/s 3.45281 m/s	3.36888 m/s 2.88816 m/s	3.2505 m/s 2.0802 m/s	2.89466 m/s 2.53757 m/s	2.02388 m/s 1.94864 m/s
Acceleration	.962964 m/s .646596 m/s	.625718 m/s .452416 m/s	.582533 m/s .435855 m/s	.461964 m/s .349239 m/s	.225828 m/s .205943 m/s
Force	30.33 F 23.6 F	20.836 F 17.327 F	19.6896 F 16.52318 F	16.8617 F 14.4934 F	8.446 F 8.732 F
Work	550.186 J 435 J	377.93 J 319.477 J	357.1306 J 304.6545 J	305.8376 J 267.2298 J	153.1937 J 161 J
Power	126.77 W 81.49 W	70.195 W 50.044 W	64 W 46.3 W	48.809 W 36.77 W	17.094 W 17.015 W

I was certain that the dog would put out more power when he had to carry more weight, but my calculations told me I was wrong. I considered that I did the whole thing wrong and that there was a lot of error, but then I got to thinking and it makes sense. The reason the dog’s power output and work are so much lower is because the longer the time, the less the acceleration, which causes all subsequent answers out to be lower. Why? Well, it is because of this. If the dog were to put out more work, or more power, then there is no reason why the time should decrease. In fact, the time would stay the same because the extra power and work would compensate and there would be no loss of time. When I think about it long enough it makes sense in a sort of twisted way. That worries me though, because it makes me wonder if I have gone off the deep end, but there is the possibility I’m right or on the right track, at least.

Now I think I have a much better understanding of all of the concepts I used, especially time. If I were to do this again, I would do several things differently. One, I’d get a better kind of bag to put the weight in. Secondly, I would time the dog more than five times, by taking oh, six weeks let’s say, and doing it over and over once a week for a longer period of time. I might also make some kind of race track or some kind of attraction for the dog like food so he would stay on course. All in all, I am very pleased with my results. Even though they were not at all like my hypothesis, I’m gal to have learned something new, or at least I think I have, and think it was a better way, though more time consuming to understand concepts of physics.