4-Sept-2014: Non-Constant Acceleration Problem (Activity)

Purpose:
The purpose of this activity was to experience non-constant acceleration from a kinematics problem. This activity will use different equations that will help solve for acceleration, velocity, and position when the object accelerates for a short amount of time. Also, to use excel to check our answer.
Apparatus:
The situation is "A 5000-kg elephant on frictionless roller skates is going 25 m/s when it gets to the bottom of a hill and arrives on level ground. At that point a rocket mounted on the elephant's back generates a constant 8000N thrust opposite the elephant's direction of motion. The mass of the rocket changes with time (due to burning the fuel at a rate of 20 kg/s) so that the m(t) = 1500-20 kg/s*t. The question is asking to find how far the elephant goes before coming to rest.
Explanation:
First we need to find the equation for acceleration with every mass totaled together, so it would be Fnet/m(t).

With the acceleration as a function with respect to time, we can then find velocity as another function with respect to time.

With the velocity as a function with respect to time, we can find position as a function with respect to time.

To find how far the elephant goes before stopping completely, we need to find when final velocity reaches zero. When we set the velocity function to zero, we find that time is 19.7 seconds. Then we plug in time into the position function, which gets us around 250 meters. 

After finding the distance, we used excel to check our answers. The first column input is time, where the time interval is 1/20th of a second. The second column is acceleration function and the third column is the average of the acceleration of the previous 1/20th of a second. The fourth column is change in velocity and the fifth column is the instant velocity at that specific time. The last two columns consists of change in distance and the total distance travel by the elephant with the rocket. According to excel, the time the elephant took to come to a complete stop was around 19.7 seconds, and the distanced traveled was 248.7 meters. The percent difference was 0.53%.

Conclusion:

The activity required the use of formulas of non-constant acceleration and excel inputs. The calculations weren't that different from excels answers. With this being said, we can further use excel in future lab and lecture activities, instead of calculating everything by hand.