PHY 1951 Projectile Motion Online Lab PDF

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Projectile Motion Lab Online Purpose The purpose of this activity is to examine some of the basic behaviors and properties of simple projectile motion. Among those properties and behaviors that will be examined are, how does the initial angle at launch affect the range of the projectile?

Theory Projectile motion is a form of motion in which an object (called the projectile) is launched at an initial angle θ, with an initial velocity 𝑣𝑖 . While the projectile is in flight, only the force of gravity (we are ignoring any air resistance) is acting on the projectile. Since, near the Earth’s surface, the force of gravity causes masses to be accelerated downwards at a constant rate of 𝑔 = 9.81 𝑚⁄ 2 , we can use the 𝑠 simple Kinematic equations to describe projectile motion. Using the standard coordinate system where the x-direction is purely horizontal and the y-direction is purely vertical, we obtain the following equations of projectile motion for the y-direction: 1 𝑦 = 𝑦𝑖 + 𝑣𝑖𝑦 𝑡 − 𝑔𝑡2 2

1 𝑦 = (𝑣𝑦 − 𝑣𝑖𝑦 )𝑡 2

𝑣𝑦 = 𝑣𝑖𝑦 − 𝑔𝑡

2 − 2𝑔∆𝑦 𝑣𝑦2 = 𝑣𝑖𝑦

Since gravity acts purely in the vertical direction, and we have no other forces acting on the projectile during flight, the acceleration in the x-direction is zero: 𝑎𝑥 = 0. This results in our kinematic equations in the x-direction reducing to the following; 𝛥𝑥 = 𝑣𝑥 𝑡

𝑣𝑥 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

Assuming that the initial angle θ is measured from the horizontal, then the projectile’s velocity components are given by; 𝑣𝑥 = 𝑣𝑖 cos(𝜗)

𝑣𝑦 = 𝑣𝑖 sin(𝜗 )

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From the above diagram we can see the behaviors of the velocity vector, and its components, of a projectile while it is in flight. The x-component is constant through the entire flight while the ycomponent is constantly changing. The y-component is equal to zero when the projectile is at its maximum height, and therefore the velocity vector is at its minimum value when the projectile is at its maximum height. The x-displacement, 𝛥𝑥 = 𝑥 − 𝑥𝑖 , the projectile goes through during its flight is called ‘the range’ of the projectile. One of the things we will look at in this activity is how changing the initial launch angles affects the range of the projectile.

Set Up 1. Go the following website https://phet.colorado.edu/en/simulation/projectile-motion a. Now you should see the following screen.

2. Click on ‘DOWNLOAD’ to download the simulator program, and then open the software once it has downloaded.

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3. Once it opens you should see the following.

4. Click the option furthest to the right called ‘Lab” 5. Now you should see the following.

6. On the right set the mass to 1.00 kg, the diameter to 0.10 m, make sure gravity is set to 9.81 m/s2, and finally make sure Air Resistance is NOT checked. 7. In the white box at the bottom left of the screen set the initial speed to 15 m/s.

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8. In the white box at the top of the screen and off center to the right you will find a ‘device’ you can drag around the screen to measure the Time of Flight, Range, and Height. We will be using this mostly to measure the range during the lab, and occasionally the time of flight.

Procedure for part 1 1. Make sure the height of the cannon is set to 0 m. You can read the current height of the cannon directly to its left. If it is not set to 0 m, ‘click and hold down’ on the cannon to set the height to 0 m. 2. Set the ‘cannon’ to an angle of 250. 3. Click on the red button near the bottom left of the screen to ‘fire’ the cannon. 4. Use the ‘device’ to measure the range of the projectile, and record the range in table 1. 5. Repeat this process for all the angles listed in table 1. 6. For 450 also measure and record the time of flight.

Procedure for part 2 1. 2. 3. 4. 5. 6. 7.

Now ‘click and hold down’ on the cannon to raise the height of the cannon to 10 m. Set the initial velocity of 12 m/s. Set the launch angle to 00. Click on the red button near the bottom left of the screen to ‘fire’ the cannon. Use the ‘device’ to measure the Range of the projectile, and record the range in table 2. Repeat process for all the angles listed in table 2. For 450 also measure and record the time of flight.

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Analysis of Projectile Motion Lab

Name Stefany Pascua Course/Section PHY-1951-005 Physics for Scientist and Engineers 1 Laboratory Instructor Stephen Flowers Table 1: Even Plane Height (𝑦 = 0) (20 points) 𝜟𝒙

25o 17.57

30o 19.86

35o 21.55

40o 22.59

45o 22.94

50o 22.59

55o 21.55

60o 19.86

65o 17.57

70o 14.74

75o 11.47

80o 7.81

Time of flight for 450: 2.16 s 1. Using Excel or some other graphing software, Graph Range vs. Initial Launch Angle. Do you notice a symmetry in the graph? If so, what is that symmetry? Turn this graph in with your lab worksheet. (10 points)

Yes, I notice a vertical symmetry in the graph with an axis of symmetry of x = 45o. 1

2. Using the equation 𝑦 = 𝑦𝑖 + 𝑣𝑖𝑦 𝑡 − 𝑔𝑡2 calculate the time of flight for the initial launch angle 2 of 45o. (5 points) Vy = Vsin(θ) = 15sin (45 o ) = 10.61 y = yi + viyt – ½gt2 = 0

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85o 3.98

0 = 0 + 10.61t - ½ (9.81) t2 t = 2.16 3. Using equation 𝛥𝑥 = 𝑣𝑖𝑥 𝑡 calculate the theoretical range for your projectile with the initial launch angle of 45o. (5 points) Vix = Vcos(θ) = 15cos (45 o) = 10.61 Δx = vixt Δx = 10.61(2.16) Δx = 22.92 4. Calculate the % difference between your measured range, and your theoretical range for the initial launch angle of 45o. (5 points) Percent error = |Theoretical Value – Experimental Value/Theoretical Value|*100 Percent error = |22.92 - 22.94/22.92|*100 = 0.08726% 5. Do the results of our experiment confirm theoretical predictions? Defend your answer. (10 points) Yes, the results of our experiment confirm theoretical predictions. The calculated percent error of less that 1% indicates that the experimental value is very close to the theoretical value.

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Table 2: Uneven surface (20 points) ∆𝑥 ∆𝑥

00 17.13 450 21.5

50 18.39 500 20.4

100 19.57 550 18.9

150 20.62 600 17.02

Initial Height: 200 21.5 650 14.79

250 22.14 700 12.24

300 22.5 750 9.43

350 22.54 800 6.4

𝒚𝒊 = 𝟏𝟎𝒎 400 22.21 850 3.24

Time of flight for 450: 2.53 s 6. Using Excel or some other graphing software, Graph Range vs. Initial Launch Angle. Do you notice a symmetry in the graph? If so, what is that symmetry? Turn this graph in with your lab worksheet. (10 points)

No, I don’t notice a symmetry in the graph. 1

7. Using the equation 𝑦 = 𝑦𝑖 + 𝑣𝑖𝑦 𝑡 − 𝑔𝑡 2 calculate the time of flight for the initial launch angle of 45o. (5 points)

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Vy = Vsin(θ) = 12sin (45 o ) = 8.49 y = yi + viyt – ½gt2 = 0 0 = 10 + 8.49t - ½ (9.81) t2 t = 2.54 8. Using equation 𝛥𝑥 = 𝑣𝑖𝑥 𝑡 calculate the theoretical range for your projectile with the initial launch angle of 45o. (5 points) Vix = Vcos(θ) = 12cos (45 o) = 8.49 Δx = vixt Δx = 8.49(2.53)

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Δx = 21.48 9. Calculate the % difference between your measured range, and your theoretical range for the initial launch angle of 45o. (5 points) Percent error = |Theoretical Value – Experimental Value/Theoretical Value|*100 Percent error = |21.48 - 21.5/21.48|*100 = 0.0931099%

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