Projectile Motion Apik

1.0 OBJECTIVES: 1. To determine the range horizontal displacement as a function of the projectile angle. 2. To determine the maximum height of projection (vertical distance) as a function of the

angle of inclination. 3. To determine the maximum range horizontal displacement as a function of the initial

velocity. 2.0 THEORY: A projectile is an object that has only one force acting known as gravity. There are several examples of projectiles such as: •

An object dropped from rest is a projectile (provided that the influence of air resistance is negligible).

•

An object which is thrown vertically upward is also a projectile (provided that the influence of air resistance is negligible).

•

An object is which thrown upward at an angle to the horizontal is also a projectile (provided that the influence of air resistance is negligible).

A projectile is any object which once projected or dropped continues in motion by its own inertia and is influenced only by the downward force of gravity.

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Figure 1: Schematic diagram of projectile motion apparatus In motion of projectile as shown in the figure 1 above, the components of the acceleration are: (1) (2) If the resistance of the air is neglected, denoting by gun, and by

and

and

the coordinates of a

the components of the initial velocity

of the projectile of a

bullet), we integrate twice in t and obtain (3) (4) (5) (6) If the projectile is fired in the xy plane from the origin O, we have

=

= 0 and,

the equation of motion reduce to: (7) (8) (9) (10)

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3.0 APPARATUS:

Figure 2: Set of Apparatus 1. 1 ballistic pendulum 2. 1 recording paper 3. 1 steel ball, diameter 19mm 4. 1 two-tier platform support 5. 1 meter scale, length = 1000mm 6. 1 speed measuring attachment 4.0 PROCEDURES: 1. The ballistic unit was setup and the height of the ballistic unit platform was adjusted properly. 2. The projection angle was set to read 100 by turning the adjusting screw. 3. The ball was set in ballistic units, the spring was pull inside the unit using the first slot

and the ball was fire upwards until reached recording carbon paper (point of impact). 4. The reading for initial velocity of the ball was recorded from the meter (resolution in 0.1m/s) 3

5. The horizontal distance was measured from the starting point until the point of impact

and the readings was recorded. Roughly the ball height (vertical distance) of the projection was measure using ball view (ball projectile) and the readings was recorded. 6. Step no 4 until step no 5 was repeated three times for each angle and the readings for

initial velocity, maximum height and horizontal displacement for the different angles was recorded in the experimental data table then the average value was calculated. 7. The experiment (step no 2- no 6) was repeated for angle 200, 300, 400 and 500.

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5.0 EXPERIMENTAL DATA:

Angle of inclination (º) 10º

Average 20º

Average 30º

Average 40º

Average 50º

Average

Initial velocity (m/s)

Experiment maximum height (m)

Experiment horizontal displacement (m)

2.23

0.015

0.022

2.22

0.013

0.022

2.19

0.016

0.021

2.21

0.015

0.022

2.19

0.050

0.039

2.19

0.048

0.038

2.19

0.047

0.038

2.19

0.048

0.038

2.11

0.072

0.050

2.10

0.070

0.049

2.13

0.075

0.050

2.11

0.072

0.050

2.08

0.115

0.054

2.07

0.116

0.055

2.09

0.118

0.056

2.08

0.116

0.055

2.06

0.140

0.053

2.08

0.145

0.055

2.06

0.142

0.054

2.07

0.142

0.054

Table 1: Experimental Data

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Angle of inclination (º)

Initial

Experimental

Theoretical

Experimental

Theoretical

Time, T

velocity

maximum

maximum

horizontal

horizontal

(s)

(m/s)

height

height

displacement

displacement

(m)

(m)

(m)

(m)

10º

2.21

0.015

0.008

0.022

0.081

0.039

20º

2.19

0.048

0.029

0.038

0.157

0.076

30º

2.11

0.072

0.057

0.050

0.196

0.108

40º

2.08

0.116

0.091

0.055

0.217

0.136

50º

2.07

0.142

0.128

0.054

0.215

0.162

Table 2: Theoretical Data

6.0 DATA ANALYSIS: 6

(8) When the steel ball hit the platform the final velocity = 0 m/s, Therefore:

(11) (10)

Substituted equation (11) into equation (10)

(12)

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Sample Calculation: For theoretical maximum height and theoretical displacement for the steel ball travel: ,

Maximum Height, h

Time, t

Horizontal Distance, x

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7.0 DISCUSSION: 1. The schematic diagram of projectile motion apparatus shown in figure 1. 2. The theoretical maximum height of projection, h as a function of the angle of

projection, φ was shown in data analysis. 3. The theoretical maximum range of projection, s as a function of the angle of

projection, φ was shown in data analysis. 4. In the graph (S- θ) for experimental and theoretical values. I have plotted the graph

with upward curve. The maximum horizontal distance (displacement) of the steel ball happened when the angle of projection is 40º. 5. In the graph (h- θ) for experimental and theoretical values for both graph, we can see

that when angle of projection was increased the value of maximum height also increased. The line for experimental is higher than line for theoretical. 6. In this experiment, there are lots of errors. Some of the errors are human error. First,

when we took the reading of horizontal displacement, maybe the platform was move and would affect the reading. Then, we had a difficult situation to take the point for maximum height because we take a reading when the ball still moves. This problem also can affect the accuracy of value for maximum height. Besides that, the initial velocity in this experiment is not constant. It will change when we repeat the step of experiment. From my suggestion, I think that we must fully concentrate when doing this experiment and we must reduced the sources of errors such as make sure that the platform does not move and use another technique take the maximum height of the ball move. For an example, we can use handy cam to take video and capture the ball movement when the ball is projectile. From there we can analyst this video to take maximum height that more accurate. We can also reduced the errors by conducted the experimental in vacuum space because there was air resistance disturb our experiment in this laboratory.

8.0 CONCLUSIONS: From this experiment, I can say that our group had achieved the objectives to determine the range horizontal displacement as a function of the projectile angle. We also can determine the maximum height of projection (vertical distance) as a function of the angle of inclination using each formula. Besides that, we also can determine the maximum range horizontal displacement as a function of the initial velocity.

9.0 REFERENCES: P.B Ferdinand, E.R Johnston, W.E Clausen. (2004). Vector mechanics for engineers: Mc Graw Hill R.C Hibbeler. (2004). Engineering mechanics statics: Pearson Prentice Hall