Lab 3- Non-Constant acceleration problem

Purpose

Solve non-constant acceleration problem by both numerical approach and analytical approach. Here is the question.

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 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 – 20t. Find how far the elephant goes before coming to rest.

Numerical Approach

1. Put appropriate values in for Vo and Xo.

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

3. 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.

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

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

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

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

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

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

10. In the H9 calculate the position of the elephant.

11. Change the time interval from 1 second to 0.1s and see if it makes a difference.

12. Change the time interval to 0.05s instead of 0.1s and see if it makes a difference.

So we can derive the conclusion that if we change the interval from 1s to 0.1s, it makes a huge difference. But if we change the interval from 0.1s to 0.05s, it makes a quite small difference.

Questions

1. When the interval equals to 0.05s, the result of numerical approach approximately equals to the result of analytical approach.

2. Choose smaller time interval until the result stops changing. That time interval is small enough.

3. Using the numerical approach with a 0.05s interval, the result is 164.0363m.

Comments

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