Virtual Lab: Projectile



Virtual Lab 1: Projectile Motion

Purpose

This virtual experiment investigates the principles of projectile motion. Using these principles, you will calculate elements of projectile motion and compare your results to the results of a computer program.

Theory

The motions of a projectile in the horizontal and vertical directions can be considered separately.

The motion in the vertical direction is subject to the force of gravity and a = g. In the horizontal direction, there is no force or acceleration and the distance traveled is given by formula (1) with a = 0.

|Table One |

|Kinematic Formulas for Projectile Motion |

|(These formulas apply in each direction separately.) |

|vf = v0 + a t |a = acceleration |

|d = d0 + v0t + ½ a t2 |d0 =initial position |

|vf2 = v02 + 2a (d – d0) |d = total distance traveled |

|d = d0 + ½ (v0 + v) t |v0 = initial velocity |

| |vf = final velocity |

| |t = time of travel |

Applying these formulas to this experiment we have:

|Table Two |

|Kinematic Formulas for Projectile Motion |

|Applied to this Virtual Experiment |

|Horizontal Direction |Vertical Direction |

|component of vo in x direction |component of vo in y direction |

|v0X = v0 cosθ |v0Y = v0 sinθ |

|x = v0Xt |vfy = v0y + a t |

| |y = v0y t + ½ a t2 |

| |vfy2 = v0y2 + 2ay |

| |y = ½ (v0y + vfy) t |

Preliminary Procedure

We will practice using the program and try to understand the basic concepts of projectile motion. Start with these steps:

1) Choose a projectile (down arrow next to “Cannonball”), an angle (by rotating the canon) and an initial speed (slider below the cannon).

2) Fire the projectile (RED icon).

3) Place the “crosshair circle” that is attached to the “Time, Range, Height” box over the various dots on the projectile path. The time, range, and height at that particular point will be shown.

Procedure Part I – Basic Concepts

4) Prepare a data sheet.

5) By using the simulator, answer the following questions on your data sheet:

a) Will changing the mass of the projectile affect the range?

b) Will changing the diameter of the projectile affect the range?

c) How does changing the initial speed of the projectile affect the range?

d) How does changing the angle affect the range?

e) What angle will give the projectile the maximum range?

Procedure Part II – Calculate & Verify

6) Choose an angle (not 450) and an initial speed (no more than 15 m/s). Record both on your data sheet.

7) First calculate on your data sheet the maximum vertical height and horizontal range from the origin. Show all calculations including the equations, numbers and units.

You may use these steps to do the calculation: (Find the appropriate formulas in Table Two.)

a) Calculate the maximum vertical height. (Hint: what is vy at this height?)

b) Calculate the time it will take to go up and then go down to the ground. (Hint: the y speed at the bottom is equal and opposite to the initial y speed.)

c) Calculate the horizontal distance it will travel during this time.

8) Input your angle and the initial speed into the simulator and FIRE!

9) Use the crosshair circle from the program and measure the horizontal range from the cannon to the end of the red or blue projectile path. Record the “Range” number from the box onto your data sheet. This is the horizontal range of the projectile.

10) Calculate the percent discrepancy of the horizontal range between your calculated value and the measured value, using the measured value as base.

11) Use the crosshair circle and measure the maximum vertical height at the peak of the projectile’s path. Record the “Height” number from the box onto your data sheet. That is the maximum height of the projectile.

12) Calculate the percent discrepancy of the maximum height between your calculated value and the measured value, using the measured value as base.

Question #1: There is another angle that can achieve the same horizontal range without changing the initial speed. What is that other angle? Verify your answer using the simulator.

Procedure Part III – Firing a projectile horizontally from a cliff

13) Raise the cannon to a height of your choice and record that height onto your data sheet.

14) Set the angle to be 00 and choose an initial speed (no more than 15 m/s). Record both on your data sheet.

15) Input the angle and the initial speed into the simulator and FIRE!

16) Place the crosshair at the end of the path and copy the “Range” number from the box onto your data sheet. The “Range” number is the horizontal distance from the base of the column to where the projectile has landed.

Procedure Part IV – Target Practice

17) Lower the cannon back to ground level.

18) Place the red target somewhere from the canon and record its distance on the data sheet. Use trial and error and find TWO sets of initial speed and angle combinations that will hit the center of the target (three stars). Record both sets of data on your data sheet.

Lab Report

Part II

Question #2: Following Question # 1 under Procedure Part II: If there is air resistance, will the two angles you get from Procedure Part II produce the same horizontal range? If not, at which angle will the projectile travel further? (Try it on the simulator with the cannonball at maximum diameter.)

Part III

1) Using the angle and the initial speed from part III, along with the initial height of the projectile, calculate the horizontal range of the projectile from the base of the column.

2) Find the percent discrepancy of the horizontal range between your calculated value and the simulation value from 16 using the simulation value as the base.

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