18-Sept-2016: Non-Constant acceleration problem/Activity

Purpose: To figure out the motion of the an object with a non-constant acceleration and the way to calculate the non-acceleration problem.

Model: P(x)=∫ V(x) dx, V(x)=∫ a(x) dx, and a(x)=Fnet / m

    P(x) is displacement of the object, V(x) is the velocity of the object, a(x) is the acceleration of the object, Fnet is the net force of the object, and m is the mass of the object.

The problem: 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 1500-kg rocket mounted on the elephant's back generates a constant 8000 N 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 kg - 20 kg/s*t.

Process: 

    Put appropriate values in for Vo adn Xo.

    Set Δt to be 1 second. Put in the other appropriate values in cell B1 through B4. (Recell that teh force is negative here, since it points in the negative x-direction.)

    Input a formula into cell A9 that will calculate the appropriate time, and that you can fill down. Use $B$5 in our formula, so the cell doesn't change as I fill down.

    Input a formula into cell B8 that will let me calculate the acceleration at any time. Fill down

    In cell C9 calculate the average acceleration for that first Δt interval.

    In cell D9 calculate the change in velocity for that first time interval.

    In cell E9 calculate the speed at the end of that time interval.

    In cell F9 calculate the average speed at the end of  that time interval.

    In cell G9 calculate the change in position of the elephant during that time internal.

    In the H9 calculate the position of the elephant.

    Then when the velocith between zero, we get the time is between 19s and 20s, and the displacement of the elephant is between 222.309 m and 223.454 m.

    However, because the Δt is not small enough, the displacement is not accurate enough.

    Therefore, we change the time interval from 1s to 0.1s. Then we get:

    Then when the velocith between zero, we get the time is between 19.6s and 19.7s, and the displacement of the elephant is between 246.119 m and 246.127 m.

    However, because the Δt is not small enough, the displacement is not accurate enough.

    Therefore, we change the time interval from 0.1s to 0.05s. Then we get:

    Then when the velocith between zero, we get the time is between 19.65s and 19.7s, and the displacement of the elephant is between 247.409 m and 244.411 m.

    By the calculation of mathemstic, the x(t)=248.7m. If our x is close enough to it, it means Δt is small enough.