# Terminal Velocity Lab

 Materials: Computer and School Network Time Allotment: 3 Class Days

### Purpose:

This activity simulates a sky diver making her first jump from a plane at 1000 meters. Before the fall, she decides to use Physics Explorer to find out what is in store for her. Thus, the purpose of this activity is to model the motion of a falling skydiver using Physics Explorer and to relate such a motion to Newton's first and second laws of motion.

1. Log on to the school server in the usual manner.
2. Open the Physics Explorer application (One Body model) by double-clicking on its icon; it is found in the directory Science-Math/Science Apps/Physics.
3. Choose Open... from the File menu and navigate to the Unit 2 folder.
4. Open the file titled Skydiver.

Check that the readings in the Diving Data window are as follows:

### Part 1: Free Fall

The first thing our diver wants to know is what will happen if she falls with no friction and no parachute. With what speed would she strike the ground? And would she survive such a jump?

1. Click on "Jump" to observe the motion.
1. What is the average speed of the motion? PSYW

2. Is the speed just before impact greater or less than the average speed?

3. Can you use the graph to figure out the speed of the motion just before impact? Explain how you could.

2. To examine the time just before impact more closely, click on the "Show Close-Up Graphs" button. Click on the "Jump" button. Calculate the average speed for the portion of the motion shown on each close-up graph. Note: you may wish to decrease the time increment (delta-t) for a more accurate simulation. Use the "single Step" button as necessary.
1. Calculate the average speed over the last 200 m. PSYW

2. Calculate the average speed over the last 50 m. PSYW

3. Which should give the closest approximation to the instantaneous speed of the skydiver at impact? Explain your answer.

Click on the "Show Velocity Window" button and run the simulation again to check your results.

3. Since hitting the ground at more than about 10 m/s is likely to result in injury, the above results are daunting.Therefore our diver is interested in knowing exactly how much she can count on air resistance to slow her down. The air resistance (drag) on a person while falling through the atmosphere is equivalent ot about 10 N*s/m (out of a range of 0 to 100).

In the Diving Data window, set the air resistance (air friction) to this value and repeat the simulated skydive. Note the time at which the diver hits the ground.

1. In what ways are these graphs of height vs. time and velocity vs. time different than the case of no air resistance (free fall)?

2. Explain the reason for the shapes of each of the two graphs. In other words, what do the features of each of the graphs tell you about the motion of the object? Be clear, specific and complete.

3. What was the speed of the skydiver at impact? __________

4. Based on your answers for the speeds of impact for cases with no air resistance and with an air resistance of 10 N*s/m, state if you think the diver can survive impact. Explain.

### Part 2: Highly Damped Fall

Clearly our diver needs a parachute, but what will its effect be on her fall? And when should she open the parachute?

1. Return to the Diving Data window. Try some simulated jumps, clicking on the "Open Chute" button at various heights, with different initial values of air resistance (air friction). Make a note of all observations/measurements.

2. Switch to the Velocity window. Make sure that the initial air resistance (air friction) is set back to 10 N*s/m before each of the following simulations.
1. How is her velocity upon impact related to the height at which she opens her parachute?

2. Explain what happens to the velocity-time graphs (and why it happens) at the moment that the parachute is opened.

3. Turn on the Acceleration Vector display in the Diving Data window; depress your mouse on the "Vectors to Show" pop-up menu, and select "Acceleration" from the po-up menu. Describe what happens to the acceleration vector at the various stages of the motion (before, immediately after, and some time after chute opening).
• Before opening:

• Immediately after opening:

• Several seconds after opening:

4. Explain what the various features of the velocity-time graph indicate about the features of the actual motion (direction of motion, speeding up , slowing down or constant speed) of the skydiver. Explain thoroughly.

• Before opening:

• Immediately after opening:

• Several seconds after opening:

5. Use a free-body diagram (labeling each force according to type) to show the direction and type of forces acting upon the skydiver before opening the parachute, immediately after opening, and several seconds after opening. The length of each vector arrow should be indicative of the relative magnitude of the force.

 Before opening Immediately after opening Several seconds after opening

6. Use <, >, and = signs to compare the relative magnitude of the force of air resistance to the force of gravity for each of these three distinct moments in the trajectory of the skydiver.

 Before opening Immediately after opening Several seconds after opening Fgrav ______ Fair Fgrav ______ Fair Fgrav ______ Fair

7. Open the chute at about 800 m, and from the velocity-time graph estimate the acceleration just immediately after opening the parachute. (Try this same procedure with the initial air resistance set to zero.)

Acceleration = ________________ (show the calculation you used)

What physical effect(s) on the diver do you think the behavior of the acceleration vector (including the numerical value you have just found) indicates?

### Conclusion:

Exhaustively describe the motion of a falling skydiver from the time she exits the plane at a high elevation to the time that her chute is opening to the time that she reaches a terminal velocity, to the time that she reaches the ground. Relate the description of the skydiver's motion to the relative magnitudes of the force of gravity and the force of air resistance. Do a bang-up job!