Virtual Lab 1
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 OneKinematic Formulas for Projectile Motion
(These formulas apply in each direction separately.)
(1) vf = v0 + a t
(2) d = d0 + v0t + ½ a t2
(3) vf2 = v02 + 2a (d – d0)
(4) d = d0 + ½ (v0 + v) t / a = acceleration
d0 =initial position
d = total distance traveled
v0 = initial velocity
vf = final velocity
t = time of travel
Applying these formulas to this experiment we have:
Table TwoKinematic Formulas for Projectile Motion
Applied to this Virtual Experiment
Horizontal Direction / Vertical Direction
component of vo in x direction
v0X = v0 cosθ / component of vo in y direction
v0Y = v0 sinθ
(1) x = v0Xt / (1) vfy = v0y + a t
(2) y = v0y t + ½ a t2
(3) vfy2 = v0y2 + 2ay
(4) y = ½ (v0y + vfy) t
Basic 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, then an angle and an initial speed.
2) Enter this information in the box on the upper right.
3) Fire the projectile.
4) The horizontal and vertical ranges are shown.
You will also measure these distances by using the tape measure from the program. You can measure distances by lining up the “+” next to the yellow dot on the beginning and drag the other “+” to the other end of the distance you wish to measure.
Procedure Part I – Basic Concepts
5) By using the simulator, answer the following questions on your data sheet:
a) How does changing the mass of the projectile affect the range?
b) How does 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 tape measure from the program and measure the horizontal range from the cannon to the red or blue projectile path. Record the number from the tape measure onto your data sheet. This is the horizontal range of the projectile. [Do not use the number in the “range” box on your screen.]
10) Calculate the percent discrepancy of the horizontal range between your calculated value (from 5) and the measured value (from 7), using the measured value as base.
11) Use the tape measure to measure the maximum vertical height. You need to place the tape measure on the white horizontal line directly underneath the peak projectile path so the yellow line of the tape measure will be vertical. Record the number from the tape measure onto your data sheet. That is the maximum height of the projectile. Do not use the number in the “height” box on your screen.
12) Calculate the percent discrepancy of the maximum height between your calculated value (from 5) and the measured value (from 9), 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.
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) Copy the “range” and “height” numbers from the simulation screen onto your data sheet.
17) The “range” number is the horizontal distance from the base of the column to where the projectile has landed. The absolute value of the “height” number is the initial height of the projectile before being fired.
Procedure Part IV – Target Practice
18) Lower the cannon back to ground level.
19) Place the red target somewhere in mid air. Use trial and error and find TWO sets of initial speed and angle combinations that will hit the center of the target. One set when the projectile is on its way up, and the other set on its way down. 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 a lot of 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? Explain your answer.
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 14 using the simulation value as the base.
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