momentum


 * __Question__: What momentum is required for a horse to clear a jump at 4 feet?**


 * __Materials__:**
 * LoggerPro**
 * Horse**
 * Video Camera**
 * Rider**
 * A GREAT ATTITUDE! :D**


 * __Procedure__:**
 * 1. Take the video of a horse jumping.**
 * 2. Upload video to the computer.**
 * 3. Find the mass of the horse using the equation**
 * [Girth (cm) × Girth (cm) × Length (cm)] / 11,900 = Weight(kg)**
 * 4. Save video to desktop.**
 * 5. Open LoggerPro.**
 * 6. Go to insert, then click movie, and choose movie from saved desktop.**
 * 7. Open the movie and click the button with the three dots, then click the button with one red dot on the menu that pops up**
 * 8. Stop the video when you want to start tracking the velocity, and click the same spot on the horse for each frame**
 * 9. Using the graph that appears, find the horizontal velocity (x-velocity) which is the velocity of the horse**
 * 10. Find Momentum using the equation P=M*V, with the mass in kg (shown below), and the velocity of the graph found**
 * - where P=momentum in kg x m/s, M= mass in kg, and V= velocity in m/s**


 * __Data/Calculations__:**
 * Length: 62.5 in.**
 * Girth: 75.75 in.**


 * 1 inch = 2.54 cm.**


 * 63.5 x 2.54 = 166.37 cm.**
 * 75.75 x 2.54 = 192.41 cm.**


 * (192.41 x 192.41 x 166.37)/ 11,900 = __517.587 kg__**



[[image:[graph.PNG]]
 * This is a graph of the position of the horse before it jumps, when it is in the air, and when it lands. The black line represents the slope of this graph prior to the jump.**


 * the slope of the horizontal position graph is 10.623, meaning that the velocity is 10.623 ft/second because the slope of a position graph is equal to the velocity of the moving object.**
 * We now need to convert the velocity into meters/second:**
 * 1 foot = .3048 meters**
 * 10.623 x .3048 = __3.238 meters/second__**


 * Now we can solve for momentum:**
 * P = M x V**
 * P = 517.587 x 3.238**
 * __P = 1675.890 kg x m/s__**, **the momentum before the jump**


 * The black line on the graph below represents the velocity while the horse is in the air**


 * The slope of the horizontal position graph at 1.933 seconds is 2.430, meaning that the horse has slowed down since the jump and is now going 2.430 ft/s.**
 * We now need to convert the velocity into meters/second:**
 * 2.430 x .3048 = __.828 m/s__**


 * The momentum of the horse at this point can now be modeled by:**
 * P = .828 x 517.587**
 * __P = 428.637 kg x m/s__, the momentum while the horse is in the air**


 * __Conclusion__:**
 * The momentum that a horse needs to clear a 4 foot jump is 428.637. By analyzing the video and dotting the same spot on each frame, we found that the velocity of the horse before the jump was . By previously making the measurements and using the equation provided for mass, we found the mass to be 517.587 kg. Since momentum is mass times velocity, the momentum is .828 x 517.587=428.637__,__ for the momentum needed to clear a 4 foot jump. The momentum makes sense because a greater velocity is needed to clear a 4 foot jump. The momentum we found makes sense for the horse because of his mass. However, momentum depends upoon mass and velocity. If we found the mass of a smaller horse, or a pony, then a greater velocity would be needed to clear the jump at the same momentum. The same goes for a horse with a larger mass; the horse would need a smaller velocity to clear the jump with the same momentum. When looking at the graph of the velocity of the horse, there is a pattern; the graph makes a wave shape tracking downward as the time continues. This is because right before the jump, the horse accelerates to maintain the highest velocity to clear the jump. However, once the horse takes off over the jump the velocity immediately decreases due to the horse having a large amount of air resistance. The velocity contiunes to decrease because once the horse leaves the ground there is no possible way to increase the velocity, so it decreases over time.** **We did not consider the breed or the conformation, the build and bone structure, of the horse as well because that would affect the horse's ability to jump. Also, a source of error could be that we rounded when measurimg not only the girth and the length of the horse, but finding the velocity as well. The height of the jump could also be a source of error because it could be slightly above or below the said measurement. The camera was moving with the horse while filming the jump, which altered the actual velocity when calculating using LoggerPro. The weight of the rider was unknown, which could also affect the momentum because it would increase the total mass.**